Submission #73752413

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Source Code Expand

#include <bits/stdc++.h>
using namespace std;

static constexpr int NMAX = 20;
static constexpr int DIRS = 4;  // 0:U 1:R 2:D 3:L
static constexpr int M = 5;

struct Grid {
    int N = NMAX;
    vector<string> v;
    vector<string> h;

    bool wall_ahead(int i, int j, int dir) const {
        if (dir == 0) {
            if (i == 0) return true;
            return h[i - 1][j] == '1';
        }
        if (dir == 2) {
            if (i == N - 1) return true;
            return h[i][j] == '1';
        }
        if (dir == 1) {
            if (j == N - 1) return true;
            return v[i][j] == '1';
        }
        if (j == 0) return true;
        return v[i][j - 1] == '1';
    }

    void step_forward(int& i, int& j, int dir) const {
        if (dir == 0) {
            --i;
        } else if (dir == 2) {
            ++i;
        } else if (dir == 1) {
            ++j;
        } else {
            --j;
        }
    }
};

struct Precomp {
    // cell = i*N + j
    uint8_t wall[400][4];        // 0/1
    uint16_t next_cell[400][4];  // when no wall
};

static Precomp build_precomp(const Grid& g) {
    Precomp p{};
    for (int i = 0; i < g.N; i++) {
        for (int j = 0; j < g.N; j++) {
            int cell = i * g.N + j;
            for (int d = 0; d < 4; d++) {
                p.wall[cell][d] = g.wall_ahead(i, j, d) ? 1 : 0;
                int ni = i, nj = j;
                if (!p.wall[cell][d]) g.step_forward(ni, nj, d);
                p.next_cell[cell][d] = (uint16_t)(ni * g.N + nj);
            }
        }
    }
    return p;
}

struct Automaton {
    array<array<int, 2>, M> act{};
    array<array<int, 2>, M> nxt{};
};

struct Automaton6 {
    static constexpr int M6 = 6;
    array<array<int, 2>, M6> act{};
    array<array<int, 2>, M6> nxt{};
};

struct EvalResult {
    int best_cov = 0;
    int best_start_node = -1;
};

struct EvalM6Workspace {
    int V = 0;
    vector<int> nxt_node;
    vector<int> cycle_id;
    vector<int> vis;
    vector<int> instep;
    vector<int> path;
    vector<int> node_cell;
    vector<int> cycle_cov;
    array<int, 400> cell_stamp{};
    int stamp = 1;
};

struct Automaton4 {
    int a0[4]{}, b0[4]{};
    int a1[4]{}, b1[4]{};
};

struct OutputSolution {
    int m = 1;
    int start_i = 0;
    int start_j = 0;
    int start_dir = 0;
    vector<array<int, 4>> trans;  // [a0,b0,a1,b1]
};

static int node_id(int s, int i, int j, int dir) {
    return (((s * NMAX + i) * NMAX + j) * DIRS + dir);
}

static void decode_node(int id, int& s, int& i, int& j, int& dir) {
    dir = id % DIRS;
    id /= DIRS;
    j = id % NMAX;
    id /= NMAX;
    i = id % NMAX;
    id /= NMAX;
    s = id;
}

static void build_next(const Precomp& p,
                       const Automaton& a,
                       vector<int>& nxt_node) {
    const int V = M * NMAX * NMAX * DIRS;
    nxt_node.assign(V, -1);

    for (int s = 0; s < M; ++s) {
        for (int i = 0; i < NMAX; ++i)
            for (int j = 0; j < NMAX; ++j)
                for (int dir = 0; dir < DIRS; ++dir) {
                    const int cell = i * NMAX + j;
                    const int widx = p.wall[cell][dir] ? 1 : 0;
                    const int act = a.act[s][widx];
                    const int ns = a.nxt[s][widx];

                    int ncell = cell;
                    int ndir = dir;
                    if (act == 0) {
                        if (widx) {
                            ndir = (dir + 1) & 3;
                        } else {
                            ncell = p.next_cell[cell][dir];
                        }
                    } else if (act == 1) {
                        ndir = (dir + 1) & 3;
                    } else {
                        ndir = (dir + 3) & 3;
                    }

                    const int ni = ncell / NMAX;
                    const int nj = ncell % NMAX;
                    const int u = node_id(s, i, j, dir);
                    const int v = node_id(ns, ni, nj, ndir);
                    nxt_node[u] = v;
                }
    }
}

static void compute_cycle_id(int V, const vector<int>& nxt_node, vector<int>& cycle_id, vector<bitset<400>>& cycle_cells) {
    cycle_id.assign(V, -1);
    vector<int> vis(V, 0);
    vector<int> instep(V, -1);
    vector<int> path;
    path.reserve(1024);
    cycle_cells.clear();

    for (int st = 0; st < V; ++st) {
        if (vis[st] != 0) continue;

        path.clear();
        int cur = st;
        while (vis[cur] == 0 && instep[cur] == -1) {
            instep[cur] = static_cast<int>(path.size());
            path.push_back(cur);
            cur = nxt_node[cur];
        }

        if (vis[cur] == 0 && instep[cur] != -1) {
            const int start = instep[cur];
            const int cid = static_cast<int>(cycle_cells.size());
            cycle_cells.push_back(bitset<400>());
            for (int idx = start; idx < static_cast<int>(path.size()); ++idx) {
                const int u = path[idx];
                cycle_id[u] = cid;
                vis[u] = 1;

                int tmp = u;
                tmp /= DIRS;
                const int j = tmp % NMAX;
                tmp /= NMAX;
                const int i = tmp % NMAX;
                cycle_cells[cid].set(i * NMAX + j, true);
            }
        }

        for (int idx = static_cast<int>(path.size()) - 1; idx >= 0; --idx) {
            const int u = path[idx];
            if (vis[u] != 0) continue;
            const int v = nxt_node[u];
            cycle_id[u] = cycle_id[v];
            vis[u] = 1;
        }

        for (int u : path) instep[u] = -1;
    }
}

static EvalResult evaluate(const Precomp& p, const Automaton& a) {
    const int V = M * NMAX * NMAX * DIRS;

    vector<int> nxt_node;
    build_next(p, a, nxt_node);

    vector<int> cycle_id;
    vector<bitset<400>> cycle_cells;
    compute_cycle_id(V, nxt_node, cycle_id, cycle_cells);

    vector<char> reachable(cycle_cells.size(), 0);
    for (int i = 0; i < NMAX; ++i) {
        for (int j = 0; j < NMAX; ++j) {
            for (int dir = 0; dir < DIRS; ++dir) {
                const int u = node_id(0, i, j, dir);
                const int cid = cycle_id[u];
                if (cid >= 0) reachable[cid] = 1;
            }
        }
    }

    EvalResult res;
    int best_cycle = -1;
    for (int cid = 0; cid < static_cast<int>(cycle_cells.size()); ++cid) {
        if (reachable[cid] == 0) continue;
        const int cov = static_cast<int>(cycle_cells[cid].count());
        if (cov > res.best_cov) {
            res.best_cov = cov;
            best_cycle = cid;
        }
    }

    if (best_cycle != -1) {
        for (int i = 0; i < NMAX && res.best_start_node == -1; ++i) {
            for (int j = 0; j < NMAX && res.best_start_node == -1; ++j) {
                for (int dir = 0; dir < DIRS; ++dir) {
                    const int u = node_id(0, i, j, dir);
                    if (cycle_id[u] == best_cycle) {
                        res.best_start_node = u;
                        break;
                    }
                }
            }
        }
    }

    return res;
}

static int node_id6(int s, int i, int j, int dir) {
    return (((s * NMAX + i) * NMAX + j) * DIRS + dir);
}

static void decode_node6(int id, int& s, int& i, int& j, int& dir) {
    dir = id % DIRS;
    id /= DIRS;
    j = id % NMAX;
    id /= NMAX;
    i = id % NMAX;
    id /= NMAX;
    s = id;
}

static EvalM6Workspace init_m6_workspace() {
    EvalM6Workspace ws;
    ws.V = Automaton6::M6 * NMAX * NMAX * DIRS;
    ws.nxt_node.assign(ws.V, -1);
    ws.cycle_id.assign(ws.V, -1);
    ws.vis.assign(ws.V, 0);
    ws.instep.assign(ws.V, -1);
    ws.path.reserve(1024);
    ws.node_cell.assign(ws.V, 0);
    ws.cycle_cov.reserve(2048);
    ws.cell_stamp.fill(0);
    for (int u = 0; u < ws.V; u++) {
        int tmp = u / DIRS;
        int j = tmp % NMAX;
        tmp /= NMAX;
        int i = tmp % NMAX;
        ws.node_cell[u] = i * NMAX + j;
    }
    return ws;
}

static EvalResult evaluate_m6_fast(const Precomp& p,
                                   const Automaton6& a,
                                   EvalM6Workspace& ws) {
    const int V = ws.V;
    auto& nxt_node = ws.nxt_node;
    auto& cycle_id = ws.cycle_id;
    auto& vis = ws.vis;
    auto& instep = ws.instep;
    auto& path = ws.path;
    auto& cycle_cov = ws.cycle_cov;

    for (int s = 0; s < Automaton6::M6; ++s) {
        for (int i = 0; i < NMAX; ++i)
            for (int j = 0; j < NMAX; ++j)
                for (int dir = 0; dir < DIRS; ++dir) {
                    const int cell = i * NMAX + j;
                    const int widx = p.wall[cell][dir] ? 1 : 0;
                    const int act = a.act[s][widx];
                    const int ns = a.nxt[s][widx];

                    int ncell = cell, nd = dir;
                    if (act == 0) {
                        if (widx) {
                            nd = (dir + 1) & 3;
                        } else {
                            ncell = p.next_cell[cell][dir];
                        }
                    } else if (act == 1) {
                        nd = (dir + 1) & 3;
                    } else {
                        nd = (dir + 3) & 3;
                    }

                    const int ni = ncell / NMAX;
                    const int nj = ncell % NMAX;
                    const int u = node_id6(s, i, j, dir);
                    const int v = node_id6(ns, ni, nj, nd);
                    nxt_node[u] = v;
                }
    }

    std::fill(cycle_id.begin(), cycle_id.end(), -1);
    std::fill(vis.begin(), vis.end(), 0);
    std::fill(instep.begin(), instep.end(), -1);
    cycle_cov.clear();

    for (int st = 0; st < V; st++) {
        if (vis[st] != 0) continue;
        path.clear();
        int cur = st;
        while (vis[cur] == 0 && instep[cur] == -1) {
            instep[cur] = (int)path.size();
            path.push_back(cur);
            cur = nxt_node[cur];
        }

        if (vis[cur] == 0 && instep[cur] != -1) {
            const int begin = instep[cur];
            const int cid = (int)cycle_cov.size();
            cycle_cov.push_back(0);

            ws.stamp++;
            if (ws.stamp == INT_MAX) {
                ws.stamp = 1;
                ws.cell_stamp.fill(0);
            }

            int cov = 0;
            for (int idx = begin; idx < (int)path.size(); idx++) {
                const int u = path[idx];
                cycle_id[u] = cid;
                vis[u] = 1;
                const int cell = ws.node_cell[u];
                if (ws.cell_stamp[cell] != ws.stamp) {
                    ws.cell_stamp[cell] = ws.stamp;
                    cov++;
                }
            }
            cycle_cov[cid] = cov;
        }

        for (int idx = (int)path.size() - 1; idx >= 0; idx--) {
            const int u = path[idx];
            if (vis[u] != 0) continue;
            cycle_id[u] = cycle_id[nxt_node[u]];
            vis[u] = 1;
        }
        for (int u : path) instep[u] = -1;
    }

    vector<char> reachable(cycle_cov.size(), 0);
    for (int i = 0; i < NMAX; ++i) {
        for (int j = 0; j < NMAX; ++j) {
            for (int dir = 0; dir < DIRS; ++dir) {
                const int u = node_id6(0, i, j, dir);
                const int cid = cycle_id[u];
                if (cid >= 0) reachable[cid] = 1;
            }
        }
    }

    EvalResult res;
    int best_cycle = -1;
    for (int cid = 0; cid < (int)cycle_cov.size(); cid++) {
        if (reachable[cid] == 0) continue;
        if (cycle_cov[cid] > res.best_cov) {
            res.best_cov = cycle_cov[cid];
            best_cycle = cid;
        }
    }

    if (best_cycle != -1) {
        for (int i = 0; i < NMAX && res.best_start_node == -1; ++i) {
            for (int j = 0; j < NMAX && res.best_start_node == -1; ++j) {
                for (int dir = 0; dir < DIRS; ++dir) {
                    const int u = node_id6(0, i, j, dir);
                    if (cycle_id[u] == best_cycle) {
                        res.best_start_node = u;
                        break;
                    }
                }
            }
        }
    }
    return res;
}

static char action_char(int action) {
    if (action == 0) return 'F';
    if (action == 1) return 'R';
    return 'L';
}

static char dir_char(int dir) {
    if (dir == 0) return 'U';
    if (dir == 1) return 'R';
    if (dir == 2) return 'D';
    return 'L';
}

static void make_diagonal_automaton(Automaton4& aut, int wall_config) {
    aut.a0[0] = 0;
    aut.b0[0] = 1;
    aut.a0[1] = 1;
    aut.b0[1] = 2;
    aut.a0[2] = 0;
    aut.b0[2] = 3;
    aut.a0[3] = 2;
    aut.b0[3] = 0;

    for (int s = 0; s < 4; s++) {
        const int cfg = (wall_config >> (3 * s)) & 7;
        const int action_bit = cfg & 1;
        const int next_state = (cfg >> 1) & 3;
        aut.a1[s] = action_bit != 0 ? 2 : 1;  // L or R
        aut.b1[s] = next_state;
    }
}

static int evaluate_m4_diagonal(const Grid& g,
                                const Precomp& p,
                                const Automaton4& aut,
                                int& out_start_i,
                                int& out_start_j,
                                int& out_start_dir,
                                int& out_start_state) {
    constexpr int M4 = 4;
    const int total_cells = g.N * g.N;
    const int total_nodes = total_cells * DIRS * M4;

    vector<int> nxt(total_nodes, -1);
    for (int i = 0; i < g.N; i++)
        for (int j = 0; j < g.N; j++) {
            const int cell = i * NMAX + j;
            for (int d = 0; d < DIRS; d++) {
                for (int s = 0; s < M4; s++) {
                    const int node = (cell * DIRS + d) * M4 + s;
                    const bool wall = p.wall[cell][d];
                    const int act = wall ? aut.a1[s] : aut.a0[s];
                    const int ns = wall ? aut.b1[s] : aut.b0[s];

                    int ncell = cell, nd = d;
                    if (act == 0) {
                        if (wall) {
                            nd = (d + 1) & 3;
                        } else {
                            ncell = p.next_cell[cell][d];
                        }
                    } else if (act == 1) {
                        nd = (d + 1) & 3;
                    } else {
                        nd = (d + 3) & 3;
                    }

                    nxt[node] = (ncell * DIRS + nd) * M4 + ns;
                }
            }
        }

    vector<int> state(total_nodes, 0);  // 0=unvisited, 1=in path, 2=done
    vector<int> path;
    path.reserve(total_nodes);

    int best_cov = -1;
    int best_start = 0;

    for (int start = 0; start < total_nodes; start++) {
        if (state[start] != 0) continue;

        path.clear();
        int cur = start;
        while (state[cur] == 0) {
            state[cur] = 1;
            path.push_back(cur);
            cur = nxt[cur];
        }

        if (state[cur] == 1) {
            int cycle_start_idx = 0;
            for (int idx = 0; idx < (int)path.size(); idx++) {
                if (path[idx] == cur) {
                    cycle_start_idx = idx;
                    break;
                }
            }

            vector<char> in_cycle(total_cells, 0);
            for (int idx = cycle_start_idx; idx < (int)path.size(); idx++) {
                const int node = path[idx];
                const int cell = node / (DIRS * M4);
                in_cycle[cell] = 1;
            }

            int cov = 0;
            for (int cell = 0; cell < total_cells; cell++) {
                cov += in_cycle[cell] != 0 ? 1 : 0;
            }

            if (cov > best_cov) {
                best_cov = cov;
                best_start = path[cycle_start_idx];
            }
        }

        for (int node : path) state[node] = 2;
    }

    const int cell = best_start / (DIRS * M4);
    out_start_i = cell / g.N;
    out_start_j = cell % g.N;
    out_start_dir = (best_start / M4) % DIRS;
    out_start_state = best_start % M4;
    return best_cov;
}

static void print_zero_added_walls(const Grid& g) {
    for (int i = 0; i < g.N; ++i) {
        cout << string(g.N - 1, '0') << '\n';
    }
    for (int i = 0; i < g.N - 1; ++i) {
        cout << string(g.N, '0') << '\n';
    }
}

static OutputSolution make_m4_solution(const Automaton4& aut,
                                       int start_i,
                                       int start_j,
                                       int start_dir,
                                       int start_state) {
    constexpr int M4 = 4;
    OutputSolution sol;
    sol.m = M4;
    sol.start_i = start_i;
    sol.start_j = start_j;
    sol.start_dir = start_dir;
    sol.trans.reserve(M4);
    for (int new_s = 0; new_s < M4; new_s++) {
        const int old_s = (new_s + start_state) % M4;
        const int b0 = (aut.b0[old_s] - start_state + M4) % M4;
        const int b1 = (aut.b1[old_s] - start_state + M4) % M4;
        sol.trans.push_back({aut.a0[old_s], b0, aut.a1[old_s], b1});
    }
    return sol;
}

// BEGIN AUTO M5 AUTOMATA
static const vector<array<int, 20>> kSeedAutomataRawM5 = {
    {0, 0, 1, 1, 0, 2, 1, 4, 1, 3, 1, 3, 0, 3, 2, 4, 2, 0, 2, 0},
    {0, 0, 1, 1, 0, 2, 2, 1, 1, 3, 1, 2, 0, 3, 2, 4, 2, 0, 2, 0},
    {0, 0, 1, 1, 0, 3, 1, 0, 1, 1, 1, 2, 2, 2, 1, 4, 1, 0, 2, 2},
    {0, 0, 1, 1, 0, 3, 1, 1, 2, 1, 2, 4, 1, 4, 1, 4, 0, 2, 2, 0},
    {0, 0, 1, 1, 0, 4, 1, 0, 1, 0, 2, 0, 0, 3, 1, 2, 1, 3, 1, 2},
    {0, 0, 1, 1, 0, 4, 1, 4, 2, 0, 2, 0, 0, 3, 2, 2, 1, 3, 2, 0},
    {0, 0, 1, 1, 1, 3, 2, 2, 2, 0, 2, 0, 0, 4, 2, 3, 2, 1, 1, 3},
    {0, 0, 1, 1, 1, 4, 1, 1, 0, 3, 1, 2, 1, 0, 1, 3, 0, 4, 1, 2},
    {0, 0, 1, 1, 1, 4, 1, 2, 1, 0, 1, 1, 0, 2, 1, 1, 0, 4, 1, 3},
    {0, 0, 1, 1, 1, 4, 2, 3, 2, 1, 2, 1, 2, 0, 2, 0, 0, 2, 1, 4},
    {0, 0, 1, 2, 0, 1, 1, 4, 1, 1, 1, 3, 1, 0, 1, 1, 0, 3, 1, 2},
    {0, 0, 1, 2, 0, 1, 2, 3, 1, 1, 1, 1, 0, 4, 2, 4, 2, 0, 2, 0},
    {0, 0, 1, 2, 0, 3, 1, 0, 1, 4, 1, 3, 1, 0, 1, 4, 0, 4, 1, 1},
    {0, 0, 1, 2, 1, 0, 1, 1, 1, 3, 1, 1, 0, 4, 2, 3, 2, 2, 1, 3},
    {0, 0, 1, 2, 2, 0, 2, 0, 0, 3, 2, 1, 1, 4, 1, 3, 0, 4, 2, 1},
    {0, 0, 1, 2, 2, 2, 1, 3, 1, 3, 1, 4, 0, 1, 1, 3, 1, 0, 2, 1},
    {0, 0, 1, 2, 2, 2, 1, 3, 1, 3, 1, 4, 0, 1, 1, 4, 1, 0, 1, 3},
    {0, 0, 1, 3, 0, 1, 1, 4, 1, 1, 2, 1, 0, 2, 2, 3, 1, 0, 1, 0},
    {0, 0, 1, 3, 0, 1, 2, 2, 0, 4, 1, 2, 1, 1, 1, 1, 2, 0, 2, 4},
    {0, 0, 1, 3, 0, 1, 2, 2, 0, 4, 2, 4, 1, 1, 1, 4, 2, 0, 1, 3},
    {0, 0, 1, 3, 0, 2, 2, 1, 1, 0, 1, 3, 1, 4, 2, 3, 0, 4, 1, 1},
    {0, 0, 1, 3, 0, 4, 2, 1, 1, 0, 1, 0, 1, 1, 1, 2, 2, 3, 1, 1},
    {0, 0, 1, 3, 1, 0, 2, 0, 0, 2, 1, 1, 0, 4, 1, 0, 1, 2, 1, 1},
    {0, 0, 1, 3, 1, 0, 2, 0, 1, 4, 2, 1, 0, 2, 1, 0, 0, 4, 1, 1},
    {0, 0, 1, 3, 2, 2, 2, 2, 1, 3, 1, 2, 0, 1, 2, 4, 2, 0, 2, 0},
    {0, 0, 1, 3, 2, 3, 1, 2, 0, 1, 1, 4, 1, 2, 2, 3, 1, 0, 1, 0},
    {0, 0, 1, 3, 2, 3, 1, 2, 0, 1, 2, 4, 1, 2, 2, 3, 2, 0, 2, 0},
    {0, 0, 1, 4, 0, 1, 1, 3, 1, 0, 1, 1, 0, 2, 2, 0, 1, 1, 1, 2},
    {0, 0, 1, 4, 0, 3, 1, 2, 0, 2, 1, 1, 1, 0, 1, 3, 1, 2, 1, 2},
    {0, 0, 1, 4, 2, 0, 2, 1, 0, 1, 1, 0, 0, 3, 2, 2, 1, 3, 1, 3},
    {0, 0, 1, 4, 2, 0, 2, 4, 2, 3, 2, 1, 1, 4, 1, 3, 0, 2, 2, 2},
    {0, 0, 2, 1, 0, 2, 1, 1, 2, 3, 2, 2, 0, 3, 1, 4, 1, 0, 1, 0},
    {0, 0, 2, 1, 0, 2, 2, 4, 2, 3, 2, 3, 0, 3, 1, 4, 1, 0, 1, 0},
    {0, 0, 2, 1, 0, 3, 2, 0, 2, 1, 2, 2, 1, 2, 2, 4, 2, 0, 1, 2},
    {0, 0, 2, 1, 0, 3, 2, 1, 1, 1, 1, 4, 2, 4, 2, 4, 0, 2, 1, 0},
    {0, 0, 2, 1, 0, 4, 2, 0, 2, 0, 1, 0, 0, 3, 2, 2, 2, 3, 2, 2},
    {0, 0, 2, 1, 0, 4, 2, 4, 1, 0, 1, 0, 0, 3, 1, 2, 2, 3, 1, 0},
    {0, 0, 2, 1, 2, 3, 1, 2, 1, 0, 1, 0, 0, 4, 1, 3, 1, 1, 2, 3},
    {0, 0, 2, 1, 2, 4, 1, 3, 1, 1, 1, 1, 1, 0, 1, 0, 0, 2, 2, 4},
    {0, 0, 2, 1, 2, 4, 2, 1, 0, 3, 2, 2, 2, 0, 2, 3, 0, 4, 2, 2},
    {0, 0, 2, 1, 2, 4, 2, 2, 2, 0, 2, 1, 0, 2, 2, 1, 0, 4, 2, 3},
    {0, 0, 2, 2, 0, 1, 1, 3, 2, 1, 2, 1, 0, 4, 1, 4, 1, 0, 1, 0},
    {0, 0, 2, 2, 0, 1, 2, 4, 2, 1, 2, 2, 2, 0, 2, 3, 0, 3, 2, 4},
    {0, 0, 2, 2, 0, 1, 2, 4, 2, 1, 2, 3, 2, 0, 2, 1, 0, 3, 2, 2},
    {0, 0, 2, 2, 0, 3, 2, 0, 2, 4, 2, 3, 2, 0, 2, 4, 0, 4, 2, 1},
    {0, 0, 2, 2, 1, 0, 1, 0, 0, 3, 1, 1, 2, 4, 2, 3, 0, 4, 1, 1},
    {0, 0, 2, 2, 1, 2, 2, 3, 2, 3, 2, 4, 0, 1, 2, 3, 2, 0, 1, 1},
    {0, 0, 2, 2, 1, 2, 2, 3, 2, 3, 2, 4, 0, 1, 2, 4, 2, 0, 2, 3},
    {0, 0, 2, 2, 2, 0, 2, 1, 2, 3, 2, 1, 0, 4, 1, 3, 1, 2, 2, 3},
    {0, 0, 2, 3, 0, 1, 1, 2, 0, 4, 1, 4, 2, 1, 2, 4, 1, 0, 2, 3},
    {0, 0, 2, 3, 0, 1, 1, 2, 0, 4, 2, 2, 2, 1, 2, 1, 1, 0, 1, 4},
    {0, 0, 2, 3, 0, 2, 1, 1, 2, 0, 2, 3, 2, 4, 1, 3, 0, 4, 2, 1},
    {0, 0, 2, 3, 0, 4, 1, 1, 2, 0, 2, 0, 2, 1, 2, 2, 1, 3, 2, 1},
    {0, 0, 2, 3, 1, 2, 1, 2, 2, 3, 2, 2, 0, 1, 1, 4, 1, 0, 1, 0},
    {0, 0, 2, 3, 1, 3, 2, 2, 0, 1, 1, 4, 2, 2, 1, 3, 1, 0, 1, 0},
    {0, 0, 2, 3, 1, 3, 2, 2, 0, 1, 2, 4, 2, 2, 1, 3, 2, 0, 2, 0},
    {0, 0, 2, 3, 2, 0, 1, 0, 0, 2, 2, 1, 0, 4, 2, 0, 2, 2, 2, 1},
    {0, 0, 2, 3, 2, 0, 1, 0, 2, 4, 1, 1, 0, 2, 2, 0, 0, 4, 2, 1},
    {0, 0, 2, 4, 0, 1, 2, 3, 2, 0, 2, 1, 0, 2, 1, 0, 2, 1, 2, 2},
    {0, 0, 2, 4, 0, 3, 2, 2, 0, 2, 2, 1, 2, 0, 2, 3, 2, 2, 2, 2},
    {0, 0, 2, 4, 1, 0, 1, 1, 0, 1, 2, 0, 0, 3, 1, 2, 2, 3, 2, 3},
    {0, 0, 2, 4, 1, 0, 1, 4, 1, 3, 1, 1, 2, 4, 2, 3, 0, 2, 1, 2},
    {0, 1, 1, 0, 0, 3, 1, 4, 1, 1, 1, 1, 2, 4, 2, 4, 1, 0, 1, 2},
    {0, 1, 1, 0, 1, 0, 2, 3, 1, 4, 2, 0, 0, 2, 1, 3, 2, 3, 2, 4},
    {0, 1, 1, 0, 1, 2, 1, 2, 0, 4, 2, 0, 0, 1, 1, 0, 2, 3, 2, 2},
    {0, 1, 1, 0, 1, 2, 1, 2, 0, 4, 2, 0, 0, 4, 2, 0, 2, 0, 2, 3},
    {0, 1, 1, 0, 1, 2, 1, 2, 0, 4, 2, 0, 2, 3, 2, 2, 2, 0, 2, 3},
    {0, 1, 1, 0, 1, 2, 1, 2, 0, 4, 2, 3, 0, 1, 1, 0, 2, 3, 2, 2},
    {0, 1, 1, 0, 1, 2, 1, 3, 0, 4, 2, 0, 0, 4, 2, 0, 2, 0, 2, 2},
    {0, 1, 1, 0, 1, 2, 2, 0, 2, 0, 2, 3, 2, 4, 2, 2, 0, 4, 2, 2},
    {0, 1, 1, 0, 1, 2, 2, 2, 0, 4, 2, 0, 2, 3, 1, 2, 2, 0, 2, 3},
    {0, 1, 1, 0, 1, 3, 1, 2, 0, 4, 1, 4, 0, 4, 2, 0, 2, 0, 2, 3},
    {0, 1, 1, 0, 1, 3, 1, 3, 0, 1, 1, 2, 0, 4, 2, 3, 2, 2, 2, 0},
    {0, 1, 1, 0, 1, 3, 1, 3, 2, 0, 2, 0, 0, 2, 2, 4, 0, 2, 2, 1},
    {0, 1, 1, 0, 1, 3, 2, 0, 2, 0, 2, 3, 0, 2, 1, 4, 1, 4, 1, 3},
    {0, 1, 1, 0, 1, 4, 1, 4, 1, 1, 1, 1, 2, 0, 1, 2, 0, 3, 2, 0},
    {0, 1, 1, 0, 1, 4, 2, 0, 0, 1, 1, 4, 2, 2, 2, 4, 0, 3, 1, 2},
    {0, 1, 1, 0, 1, 4, 2, 0, 0, 3, 2, 4, 2, 0, 1, 2, 0, 3, 2, 4},
    {0, 1, 1, 0, 1, 4, 2, 0, 2, 3, 2, 4, 0, 1, 1, 4, 0, 2, 1, 3},
    {0, 1, 1, 0, 2, 2, 1, 0, 1, 0, 1, 4, 0, 3, 1, 2, 1, 3, 1, 4},
    {0, 1, 1, 0, 2, 2, 2, 0, 0, 3, 1, 2, 1, 0, 1, 4, 0, 2, 2, 1},
    {0, 1, 1, 0, 2, 2, 2, 0, 0, 3, 1, 4, 1, 0, 2, 4, 0, 3, 2, 1},
    {0, 1, 1, 0, 2, 2, 2, 0, 0, 4, 1, 2, 2, 3, 2, 2, 1, 0, 2, 3},
    {0, 1, 1, 0, 2, 3, 2, 2, 2, 4, 1, 0, 0, 4, 2, 3, 1, 0, 1, 3},
    {0, 1, 1, 0, 2, 3, 2, 3, 0, 2, 1, 3, 1, 0, 2, 4, 2, 2, 2, 2},
    {0, 1, 1, 0, 2, 4, 2, 0, 0, 1, 1, 4, 1, 2, 2, 4, 0, 3, 1, 2},
    {0, 1, 1, 0, 2, 4, 2, 0, 0, 3, 1, 4, 1, 0, 2, 2, 0, 3, 1, 4},
    {0, 1, 1, 0, 2, 4, 2, 0, 1, 0, 1, 3, 0, 4, 2, 0, 0, 2, 1, 4},
    {0, 1, 1, 0, 2, 4, 2, 0, 1, 0, 2, 3, 0, 2, 1, 4, 0, 2, 1, 4},
    {0, 1, 1, 0, 2, 4, 2, 2, 0, 1, 1, 0, 1, 0, 2, 4, 0, 3, 1, 4},
    {0, 1, 1, 0, 2, 4, 2, 3, 1, 0, 1, 4, 0, 0, 2, 2, 0, 2, 2, 0},
    {0, 1, 1, 0, 2, 4, 2, 3, 2, 3, 2, 4, 0, 2, 1, 4, 1, 0, 1, 3},
    {0, 1, 1, 1, 1, 2, 1, 2, 0, 2, 1, 3, 1, 4, 1, 4, 0, 4, 1, 0},
    {0, 1, 1, 2, 1, 2, 1, 0, 0, 3, 1, 4, 2, 0, 2, 0, 1, 1, 1, 1},
    {0, 1, 1, 2, 1, 2, 1, 0, 0, 3, 2, 2, 2, 4, 2, 0, 0, 1, 1, 2},
    {0, 1, 1, 2, 1, 2, 1, 0, 0, 3, 2, 4, 2, 0, 2, 0, 2, 1, 2, 4},
    {0, 1, 1, 2, 1, 2, 1, 0, 0, 3, 2, 4, 2, 0, 2, 2, 0, 1, 1, 4},
    {0, 1, 1, 2, 1, 2, 1, 0, 0, 3, 2, 4, 2, 0, 2, 2, 2, 1, 2, 1},
    {0, 1, 1, 2, 1, 2, 1, 0, 0, 4, 2, 2, 0, 1, 2, 1, 2, 0, 2, 3},
    {0, 1, 1, 2, 1, 2, 1, 0, 0, 4, 2, 3, 0, 1, 2, 0, 2, 0, 2, 2},
    {0, 1, 1, 2, 1, 2, 1, 0, 0, 4, 2, 3, 2, 1, 2, 2, 2, 0, 2, 0},
    {0, 1, 1, 2, 1, 2, 1, 0, 0, 4, 2, 3, 2, 1, 2, 3, 2, 0, 2, 0},
    {0, 1, 1, 2, 1, 2, 2, 0, 0, 3, 1, 4, 2, 0, 2, 2, 1, 2, 1, 2},
    {0, 1, 1, 2, 1, 2, 2, 0, 0, 3, 2, 4, 2, 0, 2, 2, 2, 4, 1, 0},
    {0, 1, 1, 2, 1, 2, 2, 0, 0, 4, 1, 0, 2, 1, 2, 1, 2, 0, 2, 3},
    {0, 1, 1, 2, 1, 2, 2, 0, 0, 4, 2, 3, 2, 3, 1, 0, 2, 0, 2, 2},
    {0, 1, 1, 2, 1, 2, 2, 3, 0, 4, 2, 0, 2, 3, 1, 0, 2, 0, 2, 2},
    {0, 1, 1, 2, 1, 3, 1, 3, 0, 1, 1, 0, 0, 4, 2, 0, 2, 0, 2, 3},
    {0, 1, 1, 2, 1, 3, 1, 3, 0, 1, 1, 0, 0, 4, 2, 2, 2, 2, 2, 3},
    {0, 1, 1, 2, 1, 3, 1, 3, 0, 1, 1, 2, 0, 4, 2, 3, 2, 0, 2, 2},
    {0, 1, 1, 2, 1, 3, 1, 3, 1, 4, 1, 4, 0, 4, 2, 0, 2, 0, 2, 3},
    {0, 1, 1, 2, 1, 3, 1, 3, 2, 2, 1, 0, 0, 4, 2, 3, 2, 0, 2, 0},
    {0, 1, 1, 2, 1, 4, 1, 0, 0, 3, 2, 4, 2, 0, 2, 0, 0, 3, 2, 2},
    {0, 1, 1, 2, 1, 4, 1, 0, 1, 1, 1, 1, 2, 0, 1, 4, 0, 3, 2, 0},
    {0, 1, 1, 2, 1, 4, 1, 4, 0, 4, 1, 3, 1, 2, 1, 1, 0, 2, 1, 0},
    {0, 1, 1, 2, 1, 4, 1, 4, 1, 3, 1, 3, 2, 0, 2, 4, 0, 3, 2, 0},
    {0, 1, 1, 2, 1, 4, 2, 3, 2, 3, 1, 4, 0, 1, 2, 4, 0, 2, 1, 0},
    {0, 1, 1, 2, 2, 0, 1, 4, 1, 3, 1, 3, 0, 3, 2, 0, 0, 1, 1, 2},
    {0, 1, 1, 2, 2, 2, 1, 4, 0, 3, 1, 0, 1, 0, 2, 2, 1, 3, 1, 3},
    {0, 1, 1, 2, 2, 2, 2, 3, 0, 2, 2, 3, 2, 4, 2, 4, 0, 4, 2, 0},
    {0, 1, 1, 2, 2, 2, 2, 4, 0, 3, 1, 0, 1, 0, 2, 2, 2, 4, 2, 0},
    {0, 1, 1, 2, 2, 2, 2, 4, 0, 3, 1, 4, 1, 0, 2, 2, 0, 1, 1, 0},
    {0, 1, 1, 2, 2, 3, 2, 0, 1, 2, 1, 3, 0, 4, 1, 0, 1, 0, 2, 3},
    {0, 1, 1, 2, 2, 3, 2, 4, 1, 4, 1, 3, 0, 2, 1, 0, 0, 1, 2, 3},
    {0, 1, 1, 2, 2, 4, 1, 3, 1, 0, 2, 2, 0, 0, 1, 0, 1, 3, 1, 4},
    {0, 1, 1, 2, 2, 4, 2, 0, 0, 4, 2, 1, 1, 0, 1, 2, 0, 3, 2, 3},
    {0, 1, 1, 2, 2, 4, 2, 0, 1, 2, 1, 4, 1, 0, 2, 4, 0, 3, 1, 0},
    {0, 1, 1, 3, 0, 2, 2, 3, 2, 3, 1, 0, 1, 0, 2, 4, 2, 1, 2, 1},
    {0, 1, 1, 3, 1, 2, 1, 0, 0, 4, 2, 3, 0, 4, 2, 3, 2, 0, 2, 0},
    {0, 1, 1, 3, 1, 2, 2, 0, 0, 4, 1, 2, 0, 1, 1, 4, 2, 0, 2, 2},
    {0, 1, 1, 3, 1, 3, 1, 0, 0, 1, 2, 1, 0, 4, 2, 2, 2, 0, 2, 3},
    {0, 1, 1, 3, 1, 3, 1, 0, 1, 1, 1, 1, 0, 4, 1, 2, 2, 0, 2, 0},
    {0, 1, 1, 3, 1, 3, 1, 0, 2, 0, 2, 0, 0, 2, 1, 4, 1, 1, 1, 1},
    {0, 1, 1, 3, 1, 3, 1, 0, 2, 0, 2, 4, 0, 2, 2, 3, 0, 0, 2, 0},
    {0, 1, 1, 3, 1, 3, 1, 0, 2, 0, 2, 4, 0, 2, 2, 3, 0, 1, 2, 1},
    {0, 1, 1, 3, 1, 3, 1, 0, 2, 1, 2, 3, 0, 4, 2, 2, 2, 0, 2, 0},
    {0, 1, 1, 3, 1, 3, 1, 2, 0, 1, 1, 3, 0, 4, 2, 3, 2, 0, 2, 2},
    {0, 1, 1, 3, 1, 3, 2, 0, 2, 0, 2, 4, 0, 2, 1, 0, 0, 2, 1, 4},
    {0, 1, 1, 3, 1, 3, 2, 0, 2, 1, 2, 1, 0, 4, 1, 0, 2, 0, 2, 2},
    {0, 1, 1, 3, 1, 3, 2, 2, 0, 1, 1, 2, 0, 4, 1, 0, 2, 0, 2, 3},
    {0, 1, 1, 3, 1, 4, 1, 0, 2, 0, 1, 4, 1, 3, 2, 0, 0, 2, 2, 4},
    {0, 1, 1, 3, 1, 4, 1, 3, 2, 3, 2, 4, 0, 1, 1, 4, 0, 2, 2, 0},
    {0, 1, 1, 3, 1, 4, 1, 4, 2, 0, 2, 0, 1, 2, 1, 2, 0, 2, 2, 4},
    {0, 1, 1, 3, 1, 4, 2, 0, 2, 0, 2, 3, 0, 2, 1, 0, 0, 2, 1, 0},
    {0, 1, 1, 3, 1, 4, 2, 0, 2, 3, 2, 4, 0, 1, 1, 4, 0, 2, 1, 0},
    {0, 1, 1, 3, 2, 0, 1, 0, 2, 4, 2, 4, 0, 2, 2, 0, 1, 3, 1, 4},
    {0, 1, 1, 3, 2, 3, 2, 0, 1, 0, 2, 4, 0, 2, 1, 0, 0, 2, 2, 1},
    {0, 1, 1, 3, 2, 3, 2, 4, 1, 0, 2, 3, 0, 2, 1, 0, 0, 1, 1, 3},
    {0, 1, 1, 3, 2, 4, 1, 0, 1, 3, 1, 0, 0, 3, 1, 4, 1, 0, 1, 2},
    {0, 1, 1, 3, 2, 4, 2, 0, 1, 0, 2, 4, 0, 2, 1, 0, 0, 2, 1, 0},
    {0, 1, 1, 3, 2, 4, 2, 0, 1, 0, 2, 4, 1, 3, 1, 4, 0, 2, 1, 0},
    {0, 1, 1, 3, 2, 4, 2, 4, 0, 1, 2, 2, 1, 2, 1, 4, 0, 3, 1, 0},
    {0, 1, 1, 4, 1, 2, 1, 2, 0, 3, 2, 0, 2, 0, 2, 2, 1, 3, 1, 0},
    {0, 1, 1, 4, 1, 2, 1, 2, 0, 3, 2, 0, 2, 0, 2, 2, 1, 3, 1, 3},
    {0, 1, 1, 4, 1, 2, 1, 2, 2, 0, 2, 2, 0, 3, 2, 0, 1, 3, 1, 3},
    {0, 1, 1, 4, 1, 3, 1, 3, 2, 0, 2, 3, 0, 2, 2, 0, 1, 2, 1, 4},
    {0, 1, 1, 4, 1, 3, 2, 0, 2, 0, 2, 4, 0, 2, 1, 0, 0, 2, 1, 3},
    {0, 1, 1, 4, 1, 3, 2, 0, 2, 4, 2, 3, 0, 2, 1, 3, 0, 1, 1, 0},
    {0, 1, 1, 4, 1, 4, 1, 0, 0, 1, 2, 2, 2, 0, 2, 4, 0, 3, 2, 2},
    {0, 1, 1, 4, 1, 4, 1, 0, 1, 2, 2, 0, 2, 0, 1, 2, 0, 3, 2, 4},
    {0, 1, 1, 4, 1, 4, 1, 0, 2, 0, 2, 0, 2, 1, 2, 1, 0, 2, 2, 3},
    {0, 1, 1, 4, 1, 4, 1, 0, 2, 0, 2, 0, 2, 1, 2, 3, 0, 2, 2, 3},
    {0, 1, 1, 4, 1, 4, 1, 0, 2, 0, 2, 3, 2, 1, 2, 1, 0, 2, 2, 0},
    {0, 1, 1, 4, 1, 4, 1, 0, 2, 1, 2, 1, 2, 0, 2, 0, 0, 3, 2, 2},
    {0, 1, 1, 4, 1, 4, 1, 0, 2, 1, 2, 2, 2, 0, 2, 0, 0, 3, 2, 2},
    {0, 1, 1, 4, 1, 4, 1, 2, 2, 3, 2, 4, 0, 1, 1, 0, 0, 2, 2, 3},
    {0, 1, 1, 4, 1, 4, 2, 0, 0, 1, 1, 4, 2, 2, 2, 4, 0, 3, 1, 0},
    {0, 1, 1, 4, 1, 4, 2, 0, 2, 0, 2, 4, 2, 3, 1, 0, 0, 2, 2, 3},
    {0, 1, 1, 4, 1, 4, 2, 0, 2, 2, 1, 0, 2, 0, 2, 4, 0, 3, 2, 2},
    {0, 1, 1, 4, 1, 4, 2, 2, 0, 1, 1, 4, 2, 0, 2, 4, 0, 3, 1, 2},
    {0, 1, 1, 4, 2, 2, 2, 0, 0, 3, 1, 0, 1, 0, 2, 2, 1, 4, 1, 2},
    {0, 1, 1, 4, 2, 2, 2, 0, 0, 3, 1, 2, 1, 0, 1, 0, 1, 4, 2, 2},
    {0, 1, 1, 4, 2, 3, 2, 0, 1, 4, 1, 3, 0, 2, 2, 2, 0, 1, 1, 0},
    {0, 1, 1, 4, 2, 4, 2, 2, 0, 1, 1, 0, 1, 0, 2, 4, 0, 3, 1, 2},
    {0, 1, 1, 4, 2, 4, 2, 2, 2, 3, 1, 4, 1, 0, 2, 4, 0, 3, 1, 0},
    {0, 1, 1, 4, 2, 4, 2, 3, 1, 3, 1, 0, 0, 1, 2, 4, 0, 2, 1, 4},
    {0, 1, 1, 4, 2, 4, 2, 4, 1, 0, 1, 3, 1, 3, 2, 0, 0, 2, 1, 0},
    {0, 1, 2, 0, 0, 3, 2, 4, 2, 1, 2, 1, 1, 4, 1, 4, 2, 0, 2, 2},
    {0, 1, 2, 0, 1, 2, 1, 0, 0, 3, 2, 2, 2, 0, 2, 4, 0, 2, 1, 1},
    {0, 1, 2, 0, 1, 2, 1, 0, 0, 3, 2, 4, 2, 0, 1, 4, 0, 3, 1, 1},
    {0, 1, 2, 0, 1, 2, 1, 0, 0, 4, 2, 2, 1, 3, 1, 2, 2, 0, 1, 3},
    {0, 1, 2, 0, 1, 2, 2, 0, 2, 0, 2, 4, 0, 3, 2, 2, 2, 3, 2, 4},
    {0, 1, 2, 0, 1, 3, 1, 2, 1, 4, 2, 0, 0, 4, 1, 3, 2, 0, 2, 3},
    {0, 1, 2, 0, 1, 4, 1, 0, 0, 1, 2, 4, 2, 2, 1, 4, 0, 3, 2, 2},
    {0, 1, 2, 0, 1, 4, 1, 0, 0, 3, 2, 4, 2, 0, 1, 2, 0, 3, 2, 4},
    {0, 1, 2, 0, 1, 4, 1, 0, 2, 0, 1, 3, 0, 2, 2, 4, 0, 2, 2, 4},
    {0, 1, 2, 0, 1, 4, 1, 0, 2, 0, 2, 3, 0, 4, 1, 0, 0, 2, 2, 4},
    {0, 1, 2, 0, 1, 4, 1, 2, 0, 1, 2, 0, 2, 0, 1, 4, 0, 3, 2, 4},
    {0, 1, 2, 0, 1, 4, 1, 3, 1, 3, 1, 4, 0, 2, 2, 4, 2, 0, 2, 3},
    {0, 1, 2, 0, 1, 4, 1, 3, 2, 0, 2, 4, 0, 0, 1, 2, 0, 2, 1, 0},
    {0, 1, 2, 0, 2, 0, 1, 3, 2, 4, 1, 0, 0, 2, 2, 3, 1, 3, 1, 4},
    {0, 1, 2, 0, 2, 2, 1, 0, 1, 0, 1, 3, 1, 4, 1, 2, 0, 4, 1, 2},
    {0, 1, 2, 0, 2, 2, 1, 2, 0, 4, 1, 0, 1, 3, 2, 2, 1, 0, 1, 3},
    {0, 1, 2, 0, 2, 2, 2, 2, 0, 3, 1, 4, 1, 0, 1, 0, 1, 1, 1, 4},
    {0, 1, 2, 0, 2, 2, 2, 2, 0, 4, 1, 0, 0, 1, 2, 0, 1, 3, 1, 2},
    {0, 1, 2, 0, 2, 2, 2, 2, 0, 4, 1, 0, 0, 4, 1, 0, 1, 0, 1, 3},
    {0, 1, 2, 0, 2, 2, 2, 2, 0, 4, 1, 0, 1, 3, 1, 2, 1, 0, 1, 3},
    {0, 1, 2, 0, 2, 2, 2, 2, 0, 4, 1, 3, 0, 1, 2, 0, 1, 3, 1, 2},
    {0, 1, 2, 0, 2, 2, 2, 3, 0, 4, 1, 0, 0, 4, 1, 0, 1, 0, 1, 2},
    {0, 1, 2, 0, 2, 3, 1, 0, 1, 0, 1, 3, 0, 2, 1, 4, 1, 4, 2, 3},
    {0, 1, 2, 0, 2, 3, 1, 0, 1, 0, 1, 3, 0, 2, 2, 4, 2, 4, 2, 3},
    {0, 1, 2, 0, 2, 3, 2, 2, 0, 4, 2, 4, 0, 4, 1, 0, 1, 0, 1, 3},
    {0, 1, 2, 0, 2, 3, 2, 3, 0, 1, 2, 2, 0, 4, 1, 3, 1, 2, 1, 0},
    {0, 1, 2, 0, 2, 3, 2, 3, 1, 0, 1, 0, 0, 2, 1, 4, 0, 2, 1, 1},
    {0, 1, 2, 0, 2, 4, 1, 0, 0, 1, 2, 4, 1, 2, 1, 4, 0, 3, 2, 2},
    {0, 1, 2, 0, 2, 4, 1, 0, 0, 3, 1, 4, 1, 0, 2, 2, 0, 3, 1, 4},
    {0, 1, 2, 0, 2, 4, 1, 0, 1, 3, 1, 4, 0, 1, 2, 4, 0, 2, 2, 3},
    {0, 1, 2, 0, 2, 4, 2, 4, 2, 1, 2, 1, 1, 0, 2, 2, 0, 3, 1, 0},
    {0, 1, 2, 1, 2, 2, 2, 2, 0, 2, 2, 3, 2, 4, 2, 4, 0, 4, 2, 0},
    {0, 1, 2, 2, 1, 0, 2, 3, 0, 4, 1, 3, 2, 2, 1, 0, 1, 3, 2, 0},
    {0, 1, 2, 2, 1, 0, 2, 4, 2, 3, 2, 3, 0, 3, 1, 0, 0, 1, 2, 2},
    {0, 1, 2, 2, 1, 2, 1, 0, 0, 4, 2, 3, 0, 1, 2, 2, 2, 0, 1, 2},
    {0, 1, 2, 2, 1, 2, 1, 3, 0, 2, 1, 3, 1, 4, 1, 4, 0, 4, 1, 0},
    {0, 1, 2, 2, 1, 2, 1, 3, 0, 4, 2, 0, 1, 4, 2, 2, 2, 0, 1, 2},
    {0, 1, 2, 2, 1, 2, 1, 4, 0, 3, 2, 0, 2, 0, 1, 2, 1, 4, 1, 0},
    {0, 1, 2, 2, 1, 2, 1, 4, 0, 3, 2, 4, 2, 0, 1, 2, 0, 1, 2, 0},
    {0, 1, 2, 2, 1, 2, 2, 4, 0, 3, 2, 0, 2, 0, 1, 2, 2, 3, 2, 3},
    {0, 1, 2, 2, 1, 3, 1, 0, 2, 2, 2, 3, 0, 4, 2, 0, 2, 0, 1, 3},
    {0, 1, 2, 2, 1, 3, 1, 4, 2, 4, 2, 3, 0, 2, 2, 0, 0, 1, 1, 3},
    {0, 1, 2, 2, 1, 4, 1, 0, 0, 4, 1, 1, 2, 0, 2, 2, 0, 3, 1, 3},
    {0, 1, 2, 2, 1, 4, 1, 0, 2, 2, 2, 4, 2, 0, 1, 4, 0, 3, 2, 0},
    {0, 1, 2, 2, 1, 4, 2, 3, 2, 0, 1, 2, 0, 0, 2, 0, 2, 3, 2, 4},
    {0, 1, 2, 2, 2, 2, 1, 0, 0, 3, 1, 4, 1, 0, 1, 2, 1, 4, 2, 0},
    {0, 1, 2, 2, 2, 2, 1, 0, 0, 3, 2, 4, 1, 0, 1, 2, 2, 2, 2, 2},
    {0, 1, 2, 2, 2, 2, 1, 0, 0, 4, 1, 3, 1, 3, 2, 0, 1, 0, 1, 2},
    {0, 1, 2, 2, 2, 2, 1, 0, 0, 4, 2, 0, 1, 1, 1, 1, 1, 0, 1, 3},
    {0, 1, 2, 2, 2, 2, 1, 3, 0, 4, 1, 0, 1, 3, 2, 0, 1, 0, 1, 2},
    {0, 1, 2, 2, 2, 2, 2, 0, 0, 3, 1, 2, 1, 4, 1, 0, 0, 1, 2, 2},
    {0, 1, 2, 2, 2, 2, 2, 0, 0, 3, 1, 4, 1, 0, 1, 0, 1, 1, 1, 4},
    {0, 1, 2, 2, 2, 2, 2, 0, 0, 3, 1, 4, 1, 0, 1, 2, 0, 1, 2, 4},
    {0, 1, 2, 2, 2, 2, 2, 0, 0, 3, 1, 4, 1, 0, 1, 2, 1, 1, 1, 1},
    {0, 1, 2, 2, 2, 2, 2, 0, 0, 3, 2, 4, 1, 0, 1, 0, 2, 1, 2, 1},
    {0, 1, 2, 2, 2, 2, 2, 0, 0, 4, 1, 2, 0, 1, 1, 1, 1, 0, 1, 3},
    {0, 1, 2, 2, 2, 2, 2, 0, 0, 4, 1, 3, 0, 1, 1, 0, 1, 0, 1, 2},
    {0, 1, 2, 2, 2, 2, 2, 0, 0, 4, 1, 3, 1, 1, 1, 2, 1, 0, 1, 0},
    {0, 1, 2, 2, 2, 2, 2, 0, 0, 4, 1, 3, 1, 1, 1, 3, 1, 0, 1, 0},
    {0, 1, 2, 2, 2, 3, 2, 3, 0, 1, 2, 0, 0, 4, 1, 0, 1, 0, 1, 3},
    {0, 1, 2, 2, 2, 3, 2, 3, 0, 1, 2, 0, 0, 4, 1, 2, 1, 2, 1, 3},
    {0, 1, 2, 2, 2, 3, 2, 3, 0, 1, 2, 2, 0, 4, 1, 3, 1, 0, 1, 2},
    {0, 1, 2, 2, 2, 3, 2, 3, 1, 2, 2, 0, 0, 4, 1, 3, 1, 0, 1, 0},
    {0, 1, 2, 2, 2, 3, 2, 3, 2, 4, 2, 4, 0, 4, 1, 0, 1, 0, 1, 3},
    {0, 1, 2, 2, 2, 4, 1, 3, 1, 3, 2, 4, 0, 1, 1, 4, 0, 2, 2, 0},
    {0, 1, 2, 2, 2, 4, 2, 0, 0, 3, 1, 4, 1, 0, 1, 0, 0, 3, 1, 2},
    {0, 1, 2, 2, 2, 4, 2, 0, 2, 1, 2, 1, 1, 0, 2, 4, 0, 3, 1, 0},
    {0, 1, 2, 2, 2, 4, 2, 4, 0, 4, 2, 3, 2, 2, 2, 1, 0, 2, 2, 0},
    {0, 1, 2, 2, 2, 4, 2, 4, 2, 3, 2, 3, 1, 0, 1, 4, 0, 3, 1, 0},
    {0, 1, 2, 3, 0, 2, 1, 3, 1, 3, 2, 0, 2, 0, 1, 4, 1, 1, 1, 1},
    {0, 1, 2, 3, 1, 0, 2, 0, 1, 4, 1, 4, 0, 2, 1, 0, 2, 3, 2, 4},
    {0, 1, 2, 3, 1, 3, 1, 0, 2, 0, 1, 4, 0, 2, 2, 0, 0, 2, 1, 1},
    {0, 1, 2, 3, 1, 3, 1, 4, 2, 0, 1, 3, 0, 2, 2, 0, 0, 1, 2, 3},
    {0, 1, 2, 3, 1, 4, 1, 0, 2, 0, 1, 4, 0, 2, 2, 0, 0, 2, 2, 0},
    {0, 1, 2, 3, 1, 4, 1, 0, 2, 0, 1, 4, 2, 3, 2, 4, 0, 2, 2, 0},
    {0, 1, 2, 3, 1, 4, 1, 4, 0, 1, 1, 2, 2, 2, 2, 4, 0, 3, 2, 0},
    {0, 1, 2, 3, 1, 4, 2, 0, 2, 3, 2, 0, 0, 3, 2, 4, 2, 0, 2, 2},
    {0, 1, 2, 3, 2, 2, 1, 0, 0, 4, 2, 2, 0, 1, 2, 4, 1, 0, 1, 2},
    {0, 1, 2, 3, 2, 2, 2, 0, 0, 4, 1, 3, 0, 4, 1, 3, 1, 0, 1, 0},
    {0, 1, 2, 3, 2, 3, 1, 0, 1, 0, 1, 3, 0, 2, 1, 4, 1, 4, 2, 0},
    {0, 1, 2, 3, 2, 3, 1, 0, 1, 0, 1, 4, 0, 2, 2, 0, 0, 2, 2, 4},
    {0, 1, 2, 3, 2, 3, 1, 0, 1, 1, 1, 1, 0, 4, 2, 0, 1, 0, 1, 2},
    {0, 1, 2, 3, 2, 3, 1, 2, 0, 1, 2, 2, 0, 4, 2, 0, 1, 0, 1, 3},
    {0, 1, 2, 3, 2, 3, 2, 0, 0, 1, 1, 1, 0, 4, 1, 2, 1, 0, 1, 3},
    {0, 1, 2, 3, 2, 3, 2, 0, 1, 0, 1, 0, 0, 2, 2, 4, 2, 1, 2, 1},
    {0, 1, 2, 3, 2, 3, 2, 0, 1, 0, 1, 4, 0, 2, 1, 3, 0, 0, 1, 0},
    {0, 1, 2, 3, 2, 3, 2, 0, 1, 0, 1, 4, 0, 2, 1, 3, 0, 1, 1, 1},
    {0, 1, 2, 3, 2, 3, 2, 0, 1, 1, 1, 3, 0, 4, 1, 2, 1, 0, 1, 0},
    {0, 1, 2, 3, 2, 3, 2, 0, 2, 1, 2, 1, 0, 4, 2, 2, 1, 0, 1, 0},
    {0, 1, 2, 3, 2, 3, 2, 2, 0, 1, 2, 3, 0, 4, 1, 3, 1, 0, 1, 2},
    {0, 1, 2, 3, 2, 4, 1, 0, 1, 0, 1, 3, 0, 2, 2, 0, 0, 2, 2, 0},
    {0, 1, 2, 3, 2, 4, 1, 0, 1, 3, 1, 4, 0, 1, 2, 4, 0, 2, 2, 0},
    {0, 1, 2, 3, 2, 4, 2, 0, 1, 0, 2, 4, 2, 3, 1, 0, 0, 2, 1, 4},
    {0, 1, 2, 3, 2, 4, 2, 3, 1, 3, 1, 4, 0, 1, 2, 4, 0, 2, 1, 0},
    {0, 1, 2, 3, 2, 4, 2, 4, 1, 0, 1, 0, 2, 2, 2, 2, 0, 2, 1, 4},
    {0, 1, 2, 4, 1, 2, 1, 0, 0, 3, 2, 0, 2, 0, 1, 2, 2, 4, 2, 2},
    {0, 1, 2, 4, 1, 3, 1, 0, 2, 4, 2, 3, 0, 2, 1, 2, 0, 1, 2, 0},
    {0, 1, 2, 4, 1, 4, 1, 2, 0, 1, 2, 0, 2, 0, 1, 4, 0, 3, 2, 2},
    {0, 1, 2, 4, 1, 4, 1, 2, 1, 3, 2, 4, 2, 0, 1, 4, 0, 3, 2, 0},
    {0, 1, 2, 4, 1, 4, 1, 4, 2, 0, 2, 3, 2, 3, 1, 0, 0, 2, 2, 0},
    {0, 1, 2, 4, 2, 2, 2, 2, 0, 3, 1, 0, 1, 0, 1, 2, 2, 3, 2, 0},
    {0, 1, 2, 4, 2, 2, 2, 2, 0, 3, 1, 0, 1, 0, 1, 2, 2, 3, 2, 3},
    {0, 1, 2, 4, 2, 2, 2, 2, 1, 0, 1, 2, 0, 3, 1, 0, 2, 3, 2, 3},
    {0, 1, 2, 4, 2, 3, 1, 0, 1, 0, 1, 3, 0, 2, 2, 3, 0, 1, 2, 4},
    {0, 1, 2, 4, 2, 3, 1, 0, 1, 0, 1, 4, 0, 2, 2, 0, 0, 2, 2, 3},
    {0, 1, 2, 4, 2, 3, 1, 0, 1, 4, 1, 3, 0, 2, 2, 3, 0, 1, 2, 0},
    {0, 1, 2, 4, 2, 3, 2, 3, 1, 0, 1, 3, 0, 2, 1, 0, 2, 2, 2, 4},
    {0, 1, 2, 4, 2, 4, 1, 0, 0, 1, 2, 4, 1, 2, 1, 4, 0, 3, 2, 0},
    {0, 1, 2, 4, 2, 4, 1, 0, 1, 0, 1, 4, 1, 3, 2, 0, 0, 2, 1, 3},
    {0, 1, 2, 4, 2, 4, 1, 0, 1, 2, 2, 0, 1, 0, 1, 4, 0, 3, 1, 2},
    {0, 1, 2, 4, 2, 4, 1, 2, 0, 1, 2, 4, 1, 0, 1, 4, 0, 3, 2, 2},
    {0, 1, 2, 4, 2, 4, 2, 0, 0, 1, 1, 2, 1, 0, 1, 4, 0, 3, 1, 2},
    {0, 1, 2, 4, 2, 4, 2, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 2, 1, 3},
    {0, 1, 2, 4, 2, 4, 2, 0, 1, 0, 1, 0, 1, 1, 1, 3, 0, 2, 1, 3},
    {0, 1, 2, 4, 2, 4, 2, 0, 1, 0, 1, 3, 1, 1, 1, 1, 0, 2, 1, 0},
    {0, 1, 2, 4, 2, 4, 2, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 3, 1, 2},
    {0, 1, 2, 4, 2, 4, 2, 0, 1, 1, 1, 2, 1, 0, 1, 0, 0, 3, 1, 2},
    {0, 1, 2, 4, 2, 4, 2, 0, 2, 2, 1, 0, 1, 0, 2, 2, 0, 3, 1, 4},
    {0, 1, 2, 4, 2, 4, 2, 2, 1, 3, 1, 4, 0, 1, 2, 0, 0, 2, 1, 3},
    {0, 2, 1, 0, 0, 0, 2, 2, 1, 3, 1, 3, 0, 4, 2, 1, 2, 0, 2, 3},
    {0, 2, 1, 0, 0, 0, 2, 3, 1, 3, 1, 1, 0, 4, 1, 3, 2, 0, 2, 3},
    {0, 2, 1, 0, 0, 2, 1, 1, 1, 3, 1, 3, 0, 4, 2, 0, 2, 1, 2, 3},
    {0, 2, 1, 0, 0, 3, 1, 4, 2, 1, 2, 0, 1, 0, 2, 1, 1, 4, 1, 1},
    {0, 2, 1, 0, 0, 3, 2, 0, 1, 1, 1, 1, 2, 0, 1, 4, 1, 4, 2, 1},
    {0, 2, 1, 0, 0, 3, 2, 0, 1, 1, 1, 4, 2, 0, 2, 1, 0, 3, 1, 0},
    {0, 2, 1, 0, 0, 3, 2, 0, 1, 1, 2, 4, 2, 0, 2, 1, 1, 4, 1, 1},
    {0, 2, 1, 0, 0, 3, 2, 1, 1, 1, 1, 4, 2, 0, 2, 0, 0, 0, 2, 3},
    {0, 2, 1, 0, 0, 4, 2, 0, 1, 1, 1, 3, 0, 4, 1, 4, 2, 0, 2, 1},
    {0, 2, 1, 0, 0, 4, 2, 3, 1, 1, 2, 0, 2, 3, 1, 1, 2, 0, 2, 1},
    {0, 2, 1, 0, 1, 0, 2, 3, 2, 1, 2, 1, 2, 4, 2, 4, 0, 4, 1, 1},
    {0, 2, 1, 0, 1, 4, 2, 0, 2, 3, 1, 0, 1, 0, 1, 1, 0, 4, 1, 3},
    {0, 2, 1, 0, 2, 0, 2, 3, 1, 3, 1, 4, 0, 1, 2, 0, 0, 0, 2, 3},
    {0, 2, 1, 0, 2, 0, 2, 3, 1, 4, 1, 4, 2, 3, 2, 4, 0, 1, 2, 0},
    {0, 2, 1, 0, 2, 0, 2, 4, 1, 3, 1, 4, 0, 1, 2, 0, 0, 1, 2, 0},
    {0, 2, 1, 0, 2, 0, 2, 4, 1, 4, 1, 3, 0, 1, 1, 3, 0, 1, 2, 0},
    {0, 2, 1, 0, 2, 1, 1, 3, 1, 3, 2, 0, 0, 4, 2, 1, 2, 0, 2, 3},
    {0, 2, 1, 0, 2, 1, 1, 3, 1, 3, 2, 1, 0, 4, 2, 3, 2, 0, 2, 0},
    {0, 2, 1, 0, 2, 3, 2, 3, 1, 4, 2, 0, 0, 3, 2, 4, 2, 0, 2, 1},
    {0, 2, 1, 0, 2, 4, 2, 4, 0, 1, 1, 4, 1, 2, 1, 2, 1, 0, 1, 3},
    {0, 2, 1, 1, 0, 2, 1, 0, 1, 3, 1, 3, 0, 4, 2, 1, 2, 1, 2, 3},
    {0, 2, 1, 1, 0, 2, 1, 3, 2, 3, 2, 0, 0, 4, 1, 0, 1, 1, 2, 3},
    {0, 2, 1, 1, 0, 2, 1, 4, 1, 4, 2, 0, 2, 1, 2, 4, 0, 3, 1, 0},
    {0, 2, 1, 1, 0, 3, 1, 0, 2, 4, 2, 0, 1, 0, 2, 4, 0, 3, 1, 0},
    {0, 2, 1, 1, 0, 3, 1, 2, 2, 3, 2, 0, 0, 4, 1, 0, 1, 0, 1, 3},
    {0, 2, 1, 1, 0, 3, 1, 4, 1, 1, 2, 0, 2, 0, 2, 1, 0, 2, 1, 3},
    {0, 2, 1, 1, 0, 3, 1, 4, 1, 1, 2, 4, 2, 0, 2, 1, 0, 2, 1, 0},
    {0, 2, 1, 1, 0, 3, 2, 0, 1, 1, 1, 0, 2, 0, 2, 4, 2, 4, 2, 1},
    {0, 2, 1, 1, 0, 3, 2, 1, 1, 1, 1, 4, 2, 4, 2, 0, 0, 2, 1, 1},
    {0, 2, 1, 1, 0, 3, 2, 1, 1, 1, 2, 4, 2, 0, 2, 0, 2, 3, 2, 3},
    {0, 2, 1, 1, 0, 3, 2, 1, 2, 4, 2, 4, 2, 1, 1, 0, 1, 0, 1, 4},
    {0, 2, 1, 1, 0, 3, 2, 4, 1, 1, 1, 0, 2, 4, 2, 1, 0, 2, 1, 1},
    {0, 2, 1, 1, 0, 3, 2, 4, 1, 1, 2, 0, 2, 0, 2, 1, 2, 4, 1, 0},
    {0, 2, 1, 1, 0, 4, 1, 0, 2, 1, 2, 3, 2, 4, 1, 1, 1, 0, 2, 1},
    {0, 2, 1, 1, 0, 4, 2, 1, 1, 1, 1, 0, 0, 2, 1, 1, 2, 3, 2, 0},
    {0, 2, 1, 1, 0, 4, 2, 1, 1, 1, 1, 3, 0, 2, 1, 4, 2, 0, 2, 0},
    {0, 2, 1, 1, 0, 4, 2, 1, 1, 1, 1, 3, 1, 4, 1, 4, 2, 0, 2, 0},
    {0, 2, 1, 1, 0, 4, 2, 3, 1, 1, 1, 3, 0, 2, 1, 4, 2, 0, 2, 1},
    {0, 2, 1, 1, 1, 1, 2, 0, 2, 3, 2, 3, 0, 4, 1, 0, 1, 0, 1, 3},
    {0, 2, 1, 1, 1, 1, 2, 3, 1, 3, 1, 3, 0, 4, 2, 0, 2, 0, 1, 0},
    {0, 2, 1, 1, 1, 2, 1, 0, 2, 3, 2, 0, 0, 4, 1, 0, 1, 0, 2, 3},
    {0, 2, 1, 1, 1, 3, 1, 3, 2, 4, 2, 4, 1, 0, 1, 4, 0, 3, 1, 0},
    {0, 2, 1, 2, 1, 4, 1, 0, 0, 1, 1, 2, 2, 2, 2, 4, 0, 3, 1, 2},
    {0, 2, 1, 3, 0, 2, 1, 0, 2, 3, 2, 1, 0, 4, 1, 1, 1, 0, 2, 3},
    {0, 2, 1, 3, 0, 2, 1, 3, 1, 3, 2, 1, 0, 4, 1, 0, 2, 0, 2, 3},
    {0, 2, 1, 3, 0, 2, 1, 3, 2, 3, 2, 0, 0, 4, 1, 1, 1, 0, 2, 3},
    {0, 2, 1, 3, 0, 2, 2, 3, 1, 3, 1, 0, 0, 4, 2, 1, 2, 0, 2, 3},
    {0, 2, 1, 3, 0, 2, 2, 3, 2, 3, 2, 1, 0, 4, 1, 0, 1, 1, 1, 3},
    {0, 2, 1, 3, 0, 3, 2, 4, 1, 1, 1, 1, 2, 4, 2, 1, 0, 2, 1, 0},
    {0, 2, 1, 3, 0, 4, 1, 0, 2, 1, 2, 0, 1, 2, 1, 0, 1, 0, 2, 1},
    {0, 2, 1, 3, 0, 4, 1, 0, 2, 1, 2, 0, 1, 3, 1, 1, 1, 0, 2, 1},
    {0, 2, 1, 3, 0, 4, 1, 0, 2, 1, 2, 1, 1, 4, 1, 4, 1, 0, 1, 1},
    {0, 2, 1, 3, 0, 4, 2, 0, 1, 1, 1, 1, 0, 2, 1, 3, 2, 3, 2, 1},
    {0, 2, 1, 3, 0, 4, 2, 0, 1, 1, 1, 1, 1, 4, 1, 3, 2, 0, 2, 1},
    {0, 2, 1, 3, 0, 4, 2, 0, 1, 1, 2, 1, 2, 3, 1, 0, 2, 0, 1, 1},
    {0, 2, 1, 3, 0, 4, 2, 1, 1, 1, 1, 0, 0, 4, 2, 3, 2, 0, 2, 0},
    {0, 2, 1, 3, 0, 4, 2, 1, 2, 1, 1, 0, 1, 4, 1, 4, 1, 0, 1, 1},
    {0, 2, 1, 3, 0, 4, 2, 3, 1, 1, 2, 1, 0, 0, 2, 2, 2, 0, 1, 1},
    {0, 2, 1, 3, 0, 4, 2, 3, 2, 1, 2, 1, 0, 2, 2, 0, 1, 0, 1, 1},
    {0, 2, 1, 3, 1, 0, 2, 3, 2, 3, 1, 4, 0, 1, 1, 0, 1, 4, 2, 0},
    {0, 2, 1, 3, 1, 0, 2, 4, 2, 4, 2, 0, 0, 2, 1, 3, 0, 1, 1, 4},
    {0, 2, 1, 3, 1, 2, 1, 3, 0, 4, 2, 2, 0, 1, 2, 3, 2, 3, 2, 0},
    {0, 2, 1, 3, 1, 3, 1, 4, 1, 4, 2, 3, 0, 1, 2, 0, 2, 0, 2, 4},
    {0, 2, 1, 3, 1, 3, 2, 2, 0, 1, 2, 3, 0, 3, 1, 4, 0, 0, 1, 2},
    {0, 2, 1, 3, 1, 4, 2, 2, 2, 3, 1, 0, 1, 0, 1, 1, 0, 4, 1, 3},
    {0, 2, 1, 3, 1, 4, 2, 3, 2, 3, 2, 4, 0, 1, 1, 0, 0, 2, 1, 3},
    {0, 2, 1, 3, 2, 0, 1, 4, 1, 4, 1, 0, 1, 3, 2, 0, 0, 1, 2, 4},
    {0, 2, 1, 3, 2, 0, 1, 4, 1, 4, 1, 0, 1, 3, 2, 4, 0, 1, 2, 0},
    {0, 2, 1, 3, 2, 0, 2, 0, 1, 3, 1, 0, 0, 1, 1, 4, 1, 2, 1, 2},
    {0, 2, 1, 3, 2, 0, 2, 0, 1, 3, 1, 4, 0, 1, 2, 3, 1, 1, 1, 1},
    {0, 2, 1, 3, 2, 0, 2, 0, 1, 4, 1, 0, 0, 1, 2, 4, 0, 1, 2, 3},
    {0, 2, 1, 3, 2, 0, 2, 0, 2, 4, 1, 4, 0, 0, 2, 1, 1, 3, 2, 4},
    {0, 2, 1, 3, 2, 0, 2, 3, 1, 3, 1, 0, 0, 1, 2, 4, 0, 2, 1, 1},
    {0, 2, 1, 3, 2, 0, 2, 3, 1, 3, 1, 4, 0, 1, 2, 0, 1, 4, 1, 0},
    {0, 2, 1, 3, 2, 0, 2, 3, 1, 4, 2, 0, 0, 1, 1, 0, 0, 1, 1, 0},
    {0, 2, 1, 3, 2, 0, 2, 4, 1, 4, 1, 4, 0, 2, 2, 1, 0, 1, 2, 3},
    {0, 2, 1, 3, 2, 0, 2, 4, 1, 4, 1, 4, 1, 1, 1, 1, 0, 1, 2, 0},
    {0, 2, 1, 3, 2, 0, 2, 4, 1, 4, 1, 4, 1, 1, 1, 3, 0, 1, 2, 0},
    {0, 2, 1, 3, 2, 1, 1, 0, 1, 3, 2, 0, 0, 4, 2, 1, 2, 0, 2, 3},
    {0, 2, 1, 3, 2, 3, 2, 4, 1, 4, 2, 0, 0, 2, 1, 4, 0, 1, 1, 0},
    {0, 2, 1, 3, 2, 4, 2, 0, 2, 0, 1, 0, 0, 1, 2, 3, 1, 3, 1, 4},
    {0, 2, 1, 4, 0, 0, 1, 3, 1, 4, 1, 0, 2, 0, 2, 4, 0, 3, 1, 1},
    {0, 2, 1, 4, 0, 2, 1, 0, 1, 4, 2, 1, 2, 0, 2, 4, 0, 3, 1, 1},
    {0, 2, 1, 4, 0, 2, 2, 1, 1, 4, 1, 1, 2, 0, 2, 4, 0, 3, 2, 1},
    {0, 2, 1, 4, 0, 3, 2, 0, 1, 1, 1, 0, 2, 0, 2, 4, 0, 3, 2, 2},
    {0, 2, 1, 4, 0, 3, 2, 1, 1, 1, 1, 1, 2, 0, 2, 0, 0, 2, 1, 1},
    {0, 2, 1, 4, 0, 3, 2, 1, 2, 1, 2, 4, 1, 0, 1, 1, 0, 2, 2, 0},
    {0, 2, 1, 4, 0, 3, 2, 4, 1, 1, 1, 0, 2, 0, 2, 0, 0, 3, 1, 2},
    {0, 2, 1, 4, 0, 4, 1, 0, 1, 1, 2, 3, 0, 2, 1, 1, 2, 3, 2, 1},
    {0, 2, 1, 4, 0, 4, 1, 0, 2, 1, 2, 1, 0, 2, 2, 3, 1, 3, 1, 1},
    {0, 2, 1, 4, 0, 4, 1, 1, 1, 1, 1, 0, 0, 2, 1, 1, 2, 3, 2, 1},
    {0, 2, 1, 4, 1, 1, 1, 0, 1, 4, 2, 0, 2, 0, 2, 4, 0, 3, 1, 1},
    {0, 2, 1, 4, 1, 1, 2, 4, 1, 4, 1, 0, 2, 0, 1, 1, 0, 3, 2, 0},
    {0, 2, 1, 4, 1, 2, 1, 4, 0, 3, 2, 0, 2, 0, 1, 1, 0, 2, 1, 2},
    {0, 2, 1, 4, 1, 3, 1, 2, 1, 4, 1, 0, 0, 3, 1, 0, 0, 4, 1, 1},
    {0, 2, 1, 4, 1, 3, 1, 3, 0, 1, 1, 2, 0, 4, 1, 0, 2, 2, 2, 3},
    {0, 2, 1, 4, 1, 3, 2, 4, 2, 4, 2, 3, 0, 2, 1, 4, 0, 1, 1, 0},
    {0, 2, 1, 4, 1, 4, 1, 2, 2, 3, 1, 0, 1, 0, 1, 1, 0, 4, 1, 3},
    {0, 2, 1, 4, 2, 0, 2, 0, 1, 3, 1, 0, 0, 1, 2, 4, 0, 1, 1, 0},
    {0, 2, 1, 4, 2, 0, 2, 0, 1, 4, 1, 0, 1, 2, 1, 2, 0, 1, 1, 3},
    {0, 2, 1, 4, 2, 0, 2, 0, 1, 4, 1, 0, 2, 2, 2, 2, 0, 1, 2, 3},
    {0, 2, 1, 4, 2, 0, 2, 0, 1, 4, 2, 3, 2, 3, 1, 0, 0, 1, 2, 4},
    {0, 2, 1, 4, 2, 0, 2, 4, 1, 3, 1, 3, 0, 1, 2, 3, 0, 2, 1, 0},
    {0, 2, 1, 4, 2, 0, 2, 4, 1, 4, 1, 0, 2, 3, 2, 0, 0, 1, 2, 3},
    {0, 2, 1, 4, 2, 0, 2, 4, 1, 4, 2, 0, 1, 3, 1, 0, 0, 1, 1, 3},
    {0, 2, 1, 4, 2, 2, 2, 1, 1, 4, 1, 0, 2, 0, 2, 0, 0, 3, 2, 1},
    {0, 2, 1, 4, 2, 3, 2, 0, 0, 1, 1, 0, 0, 4, 1, 2, 1, 2, 1, 3},
    {0, 2, 1, 4, 2, 3, 2, 3, 1, 4, 2, 1, 2, 0, 2, 0, 0, 3, 2, 4},
    {0, 2, 2, 0, 0, 0, 1, 2, 2, 3, 2, 3, 0, 4, 1, 1, 1, 0, 1, 3},
    {0, 2, 2, 0, 0, 0, 1, 3, 2, 3, 2, 1, 0, 4, 2, 3, 1, 0, 1, 3},
    {0, 2, 2, 0, 0, 3, 1, 0, 2, 1, 1, 4, 1, 0, 1, 1, 2, 4, 2, 1},
    {0, 2, 2, 0, 0, 3, 1, 0, 2, 1, 2, 4, 1, 0, 1, 1, 0, 3, 2, 0},
    {0, 2, 2, 0, 0, 3, 2, 4, 1, 1, 1, 0, 2, 0, 1, 1, 2, 4, 2, 1},
    {0, 2, 2, 0, 0, 4, 1, 0, 2, 1, 2, 3, 0, 4, 2, 4, 1, 0, 1, 1},
    {0, 2, 2, 0, 0, 4, 1, 3, 2, 1, 1, 0, 1, 3, 2, 1, 1, 0, 1, 1},
    {0, 2, 2, 0, 1, 0, 1, 3, 2, 3, 2, 4, 0, 1, 1, 0, 0, 0, 1, 3},
    {0, 2, 2, 0, 1, 0, 1, 3, 2, 4, 2, 4, 1, 3, 1, 4, 0, 1, 1, 0},
    {0, 2, 2, 0, 1, 0, 1, 4, 2, 3, 2, 4, 0, 1, 1, 0, 0, 1, 1, 0},
    {0, 2, 2, 0, 1, 0, 1, 4, 2, 4, 2, 3, 0, 1, 2, 3, 0, 1, 1, 0},
    {0, 2, 2, 0, 1, 1, 2, 3, 2, 3, 1, 0, 0, 4, 1, 1, 1, 0, 1, 3},
    {0, 2, 2, 0, 1, 1, 2, 3, 2, 3, 1, 1, 0, 4, 1, 3, 1, 0, 1, 0},
    {0, 2, 2, 0, 1, 3, 1, 3, 2, 4, 1, 0, 0, 3, 1, 4, 1, 0, 1, 1},
    {0, 2, 2, 0, 1, 4, 1, 4, 0, 1, 2, 4, 2, 2, 2, 2, 2, 0, 2, 3},
    {0, 2, 2, 0, 2, 0, 1, 3, 1, 1, 1, 1, 1, 4, 1, 4, 0, 4, 2, 1},
    {0, 2, 2, 0, 2, 4, 1, 0, 1, 3, 2, 0, 2, 0, 2, 1, 0, 4, 2, 3},
    {0, 2, 2, 1, 0, 2, 2, 0, 2, 3, 2, 3, 0, 4, 1, 1, 1, 1, 1, 3},
    {0, 2, 2, 1, 0, 2, 2, 3, 1, 3, 1, 0, 0, 4, 2, 0, 2, 1, 1, 3},
    {0, 2, 2, 1, 0, 2, 2, 4, 2, 4, 1, 0, 1, 1, 1, 4, 0, 3, 2, 0},
    {0, 2, 2, 1, 0, 3, 1, 0, 2, 1, 2, 0, 1, 0, 1, 4, 1, 4, 1, 1},
    {0, 2, 2, 1, 0, 3, 1, 1, 1, 4, 1, 4, 1, 1, 2, 0, 2, 0, 2, 4},
    {0, 2, 2, 1, 0, 3, 1, 1, 2, 1, 1, 4, 1, 0, 1, 0, 1, 3, 1, 3},
    {0, 2, 2, 1, 0, 3, 1, 1, 2, 1, 2, 4, 1, 4, 1, 0, 0, 2, 2, 1},
    {0, 2, 2, 1, 0, 3, 1, 4, 2, 1, 1, 0, 1, 0, 1, 1, 1, 4, 2, 0},
    {0, 2, 2, 1, 0, 3, 1, 4, 2, 1, 2, 0, 1, 4, 1, 1, 0, 2, 2, 1},
    {0, 2, 2, 1, 0, 3, 2, 0, 1, 4, 1, 0, 2, 0, 1, 4, 0, 3, 2, 0},
    {0, 2, 2, 1, 0, 3, 2, 2, 1, 3, 1, 0, 0, 4, 2, 0, 2, 0, 2, 3},
    {0, 2, 2, 1, 0, 3, 2, 4, 2, 1, 1, 0, 1, 0, 1, 1, 0, 2, 2, 3},
    {0, 2, 2, 1, 0, 3, 2, 4, 2, 1, 1, 4, 1, 0, 1, 1, 0, 2, 2, 0},
    {0, 2, 2, 1, 0, 4, 1, 1, 2, 1, 2, 0, 0, 2, 2, 1, 1, 3, 1, 0},
    {0, 2, 2, 1, 0, 4, 1, 1, 2, 1, 2, 3, 0, 2, 2, 4, 1, 0, 1, 0},
    {0, 2, 2, 1, 0, 4, 1, 1, 2, 1, 2, 3, 2, 4, 2, 4, 1, 0, 1, 0},
    {0, 2, 2, 1, 0, 4, 2, 0, 1, 1, 1, 3, 1, 4, 2, 1, 2, 0, 1, 1},
    {0, 2, 2, 1, 0, 4, 2, 3, 1, 3, 1, 0, 0, 4, 2, 0, 2, 0, 1, 1},
    {0, 2, 2, 1, 2, 1, 1, 0, 1, 3, 1, 3, 0, 4, 2, 0, 2, 0, 2, 3},
    {0, 2, 2, 1, 2, 1, 1, 3, 2, 3, 2, 3, 0, 4, 1, 0, 1, 0, 2, 0},
    {0, 2, 2, 1, 2, 2, 2, 0, 1, 3, 1, 0, 0, 4, 2, 0, 2, 0, 1, 3},
    {0, 2, 2, 1, 2, 3, 2, 3, 1, 4, 1, 4, 2, 0, 2, 4, 0, 3, 2, 0},
    {0, 2, 2, 2, 2, 4, 2, 0, 0, 1, 2, 2, 1, 2, 1, 4, 0, 3, 2, 2},
    {0, 2, 2, 3, 0, 2, 1, 3, 1, 3, 1, 1, 0, 4, 2, 0, 2, 1, 2, 3},
    {0, 2, 2, 3, 0, 2, 2, 0, 1, 3, 1, 1, 0, 4, 2, 1, 2, 0, 1, 3},
    {0, 2, 2, 3, 0, 2, 2, 3, 1, 3, 1, 0, 0, 4, 2, 1, 2, 0, 1, 3},
    {0, 2, 2, 3, 0, 2, 2, 3, 2, 3, 1, 1, 0, 4, 2, 0, 1, 0, 1, 3},
    {0, 2, 2, 3, 0, 3, 1, 4, 2, 1, 2, 1, 1, 4, 1, 1, 0, 2, 2, 0},
    {0, 2, 2, 3, 0, 4, 1, 0, 2, 1, 1, 1, 1, 3, 2, 0, 1, 0, 2, 1},
    {0, 2, 2, 3, 0, 4, 1, 0, 2, 1, 2, 1, 0, 2, 2, 3, 1, 3, 1, 1},
    {0, 2, 2, 3, 0, 4, 1, 0, 2, 1, 2, 1, 2, 4, 2, 3, 1, 0, 1, 1},
    {0, 2, 2, 3, 0, 4, 1, 1, 1, 1, 2, 0, 2, 4, 2, 4, 2, 0, 2, 1},
    {0, 2, 2, 3, 0, 4, 1, 1, 2, 1, 2, 0, 0, 4, 1, 3, 1, 0, 1, 0},
    {0, 2, 2, 3, 0, 4, 1, 3, 1, 1, 1, 1, 0, 2, 1, 0, 2, 0, 2, 1},
    {0, 2, 2, 3, 0, 4, 1, 3, 2, 1, 1, 1, 0, 0, 1, 2, 1, 0, 2, 1},
    {0, 2, 2, 3, 0, 4, 2, 0, 1, 1, 1, 0, 2, 2, 2, 0, 2, 0, 1, 1},
    {0, 2, 2, 3, 0, 4, 2, 0, 1, 1, 1, 0, 2, 3, 2, 1, 2, 0, 1, 1},
    {0, 2, 2, 3, 0, 4, 2, 0, 1, 1, 1, 1, 2, 4, 2, 4, 2, 0, 2, 1},
    {0, 2, 2, 3, 1, 0, 1, 0, 1, 4, 2, 4, 0, 0, 1, 1, 2, 3, 1, 4},
    {0, 2, 2, 3, 1, 0, 1, 0, 2, 3, 2, 0, 0, 1, 2, 4, 2, 2, 2, 2},
    {0, 2, 2, 3, 1, 0, 1, 0, 2, 3, 2, 4, 0, 1, 1, 3, 2, 1, 2, 1},
    {0, 2, 2, 3, 1, 0, 1, 0, 2, 4, 2, 0, 0, 1, 1, 4, 0, 1, 1, 3},
    {0, 2, 2, 3, 1, 0, 1, 3, 2, 3, 2, 0, 0, 1, 1, 4, 0, 2, 2, 1},
    {0, 2, 2, 3, 1, 0, 1, 3, 2, 3, 2, 4, 0, 1, 1, 0, 2, 4, 2, 0},
    {0, 2, 2, 3, 1, 0, 1, 3, 2, 4, 1, 0, 0, 1, 2, 0, 0, 1, 2, 0},
    {0, 2, 2, 3, 1, 0, 1, 4, 2, 4, 2, 0, 0, 4, 2, 4, 0, 1, 1, 0},
    {0, 2, 2, 3, 1, 0, 1, 4, 2, 4, 2, 4, 0, 2, 1, 1, 0, 1, 1, 3},
    {0, 2, 2, 3, 1, 0, 1, 4, 2, 4, 2, 4, 2, 1, 2, 1, 0, 1, 1, 0},
    {0, 2, 2, 3, 1, 0, 1, 4, 2, 4, 2, 4, 2, 1, 2, 3, 0, 1, 1, 0},
    {0, 2, 2, 3, 1, 0, 2, 4, 2, 4, 2, 0, 2, 3, 1, 0, 0, 1, 1, 4},
    {0, 2, 2, 3, 1, 0, 2, 4, 2, 4, 2, 0, 2, 3, 1, 4, 0, 1, 1, 0},
    {0, 2, 2, 3, 1, 1, 2, 0, 2, 3, 1, 0, 0, 4, 1, 1, 1, 0, 1, 3},
    {0, 2, 2, 3, 1, 3, 1, 4, 2, 4, 1, 0, 0, 2, 2, 4, 0, 1, 2, 0},
    {0, 2, 2, 3, 1, 4, 1, 0, 1, 0, 2, 0, 0, 1, 1, 3, 2, 3, 2, 4},
    {0, 2, 2, 3, 2, 0, 1, 3, 1, 3, 2, 4, 0, 1, 2, 0, 2, 4, 1, 0},
    {0, 2, 2, 3, 2, 0, 1, 4, 1, 4, 1, 0, 0, 2, 2, 3, 0, 1, 2, 4},
    {0, 2, 2, 3, 2, 2, 2, 3, 0, 4, 1, 2, 0, 1, 1, 3, 1, 3, 1, 0},
    {0, 2, 2, 3, 2, 3, 1, 2, 0, 1, 1, 3, 0, 3, 2, 4, 0, 0, 2, 2},
    {0, 2, 2, 3, 2, 3, 2, 4, 2, 4, 1, 3, 0, 1, 1, 0, 1, 0, 1, 4},
    {0, 2, 2, 3, 2, 4, 1, 2, 1, 3, 2, 0, 2, 0, 2, 1, 0, 4, 2, 3},
    {0, 2, 2, 3, 2, 4, 1, 3, 1, 3, 1, 4, 0, 1, 2, 0, 0, 2, 2, 3},
    {0, 2, 2, 4, 0, 0, 2, 3, 2, 4, 2, 0, 1, 0, 1, 4, 0, 3, 2, 1},
    {0, 2, 2, 4, 0, 2, 2, 0, 2, 4, 1, 1, 1, 0, 1, 4, 0, 3, 2, 1},
    {0, 2, 2, 4, 0, 3, 1, 0, 2, 1, 2, 0, 1, 0, 1, 4, 0, 3, 1, 2},
    {0, 2, 2, 4, 0, 3, 1, 1, 1, 1, 1, 4, 2, 0, 2, 1, 0, 2, 1, 0},
    {0, 2, 2, 4, 0, 3, 1, 1, 2, 1, 2, 1, 1, 0, 1, 0, 0, 2, 2, 1},
    {0, 2, 2, 4, 0, 3, 1, 4, 2, 1, 2, 0, 1, 0, 1, 0, 0, 3, 2, 2},
    {0, 2, 2, 4, 0, 4, 2, 0, 1, 1, 1, 1, 0, 2, 1, 3, 2, 3, 2, 1},
    {0, 2, 2, 4, 0, 4, 2, 0, 2, 1, 1, 3, 0, 2, 2, 1, 1, 3, 1, 1},
    {0, 2, 2, 4, 0, 4, 2, 1, 2, 1, 2, 0, 0, 2, 2, 1, 1, 3, 1, 1},
    {0, 2, 2, 4, 1, 0, 1, 0, 2, 3, 2, 0, 0, 1, 1, 4, 0, 1, 2, 0},
    {0, 2, 2, 4, 1, 0, 1, 0, 2, 4, 2, 0, 1, 2, 1, 2, 0, 1, 1, 3},
    {0, 2, 2, 4, 1, 0, 1, 0, 2, 4, 2, 0, 2, 2, 2, 2, 0, 1, 2, 3},
    {0, 2, 2, 4, 1, 0, 1, 4, 2, 3, 2, 3, 0, 1, 1, 3, 0, 2, 2, 0},
    {0, 2, 2, 4, 1, 0, 1, 4, 2, 4, 1, 0, 2, 3, 2, 0, 0, 1, 2, 3},
    {0, 2, 2, 4, 1, 0, 1, 4, 2, 4, 2, 0, 1, 3, 1, 0, 0, 1, 1, 3},
    {0, 2, 2, 4, 1, 2, 1, 1, 2, 4, 2, 0, 1, 0, 1, 0, 0, 3, 1, 1},
    {0, 2, 2, 4, 1, 3, 1, 0, 0, 1, 2, 0, 0, 4, 2, 2, 2, 2, 2, 3},
    {0, 2, 2, 4, 1, 3, 1, 3, 2, 4, 1, 1, 1, 0, 1, 0, 0, 3, 1, 4},
    {0, 2, 2, 4, 2, 1, 1, 4, 2, 4, 2, 0, 1, 0, 2, 1, 0, 3, 1, 0},
    {0, 2, 2, 4, 2, 1, 2, 0, 2, 4, 1, 0, 1, 0, 1, 4, 0, 3, 2, 1},
    {0, 2, 2, 4, 2, 2, 2, 4, 0, 3, 1, 0, 1, 0, 2, 1, 0, 2, 2, 2},
    {0, 2, 2, 4, 2, 3, 2, 2, 2, 4, 2, 0, 0, 3, 2, 0, 0, 4, 2, 1},
    {0, 2, 2, 4, 2, 3, 2, 3, 0, 1, 2, 2, 0, 4, 2, 0, 1, 2, 1, 3},
    {0, 2, 2, 4, 2, 4, 2, 2, 1, 3, 2, 0, 2, 0, 2, 1, 0, 4, 2, 3},
    {0, 3, 1, 0, 0, 1, 2, 2, 2, 4, 2, 4, 1, 1, 1, 3, 0, 4, 1, 0},
    {0, 3, 1, 0, 0, 2, 2, 0, 2, 0, 1, 4, 1, 1, 1, 1, 1, 4, 2, 1},
    {0, 3, 1, 0, 0, 2, 2, 1, 1, 0, 1, 4, 2, 1, 2, 0, 1, 4, 1, 1},
    {0, 3, 1, 0, 0, 2, 2, 1, 2, 1, 1, 4, 2, 4, 2, 4, 1, 0, 1, 1},
    {0, 3, 1, 0, 0, 3, 1, 2, 0, 4, 1, 1, 2, 2, 2, 0, 1, 1, 2, 2},
    {0, 3, 1, 0, 0, 3, 1, 2, 0, 4, 2, 0, 1, 2, 2, 2, 2, 1, 1, 0},
    {0, 3, 1, 0, 0, 4, 1, 1, 0, 3, 1, 0, 2, 1, 2, 2, 1, 0, 2, 1},
    {0, 3, 1, 0, 0, 4, 1, 2, 1, 2, 2, 0, 1, 1, 1, 1, 2, 0, 2, 1},
    {0, 3, 1, 0, 0, 4, 1, 2, 1, 3, 1, 3, 2, 1, 2, 0, 1, 0, 2, 1},
    {0, 3, 1, 0, 0, 4, 2, 0, 1, 3, 1, 3, 1, 1, 1, 1, 2, 0, 1, 2},
    {0, 3, 1, 0, 0, 4, 2, 1, 1, 0, 1, 1, 2, 2, 2, 2, 2, 1, 1, 2},
    {0, 3, 1, 0, 0, 4, 2, 1, 1, 2, 2, 0, 1, 1, 1, 1, 2, 0, 1, 2},
    {0, 3, 1, 0, 1, 3, 1, 0, 1, 0, 1, 1, 2, 4, 2, 0, 0, 2, 2, 2},
    {0, 3, 1, 0, 1, 4, 2, 0, 2, 0, 2, 2, 1, 2, 2, 4, 0, 1, 1, 4},
    {0, 3, 1, 0, 2, 0, 2, 2, 0, 1, 2, 0, 1, 2, 1, 4, 1, 4, 1, 2},
    {0, 3, 1, 0, 2, 0, 2, 4, 2, 2, 1, 4, 1, 4, 2, 2, 0, 1, 2, 0},
    {0, 3, 1, 0, 2, 1, 1, 4, 2, 0, 2, 4, 1, 4, 2, 0, 0, 2, 2, 1},
    {0, 3, 1, 0, 2, 2, 1, 2, 1, 0, 2, 4, 2, 4, 2, 1, 0, 2, 1, 4},
    {0, 3, 1, 0, 2, 3, 2, 0, 0, 4, 2, 0, 1, 2, 1, 2, 2, 0, 2, 1},
    {0, 3, 1, 1, 0, 2, 1, 4, 2, 0, 2, 1, 1, 1, 2, 4, 0, 3, 1, 0},
    {0, 3, 1, 1, 0, 2, 2, 0, 1, 1, 2, 1, 1, 4, 1, 4, 2, 0, 2, 4},
    {0, 3, 1, 1, 0, 2, 2, 4, 2, 0, 2, 1, 1, 1, 1, 0, 0, 3, 1, 0},
    {0, 3, 1, 1, 0, 2, 2, 4, 2, 0, 2, 1, 1, 1, 1, 0, 2, 4, 2, 0},
    {0, 3, 1, 1, 0, 3, 1, 0, 0, 4, 2, 0, 1, 2, 1, 2, 2, 1, 2, 2},
    {0, 3, 1, 1, 0, 3, 1, 1, 0, 4, 2, 2, 1, 2, 1, 2, 2, 1, 2, 0},
    {0, 3, 1, 1, 0, 3, 2, 4, 0, 4, 1, 2, 1, 2, 2, 1, 2, 0, 2, 2},
    {0, 3, 1, 1, 0, 4, 1, 2, 0, 3, 1, 0, 1, 1, 2, 2, 2, 0, 2, 1},
    {0, 3, 1, 1, 0, 4, 2, 0, 1, 2, 2, 1, 1, 1, 1, 0, 2, 0, 1, 2},
    {0, 3, 1, 1, 0, 4, 2, 1, 0, 3, 1, 4, 1, 1, 1, 2, 2, 0, 2, 0},
    {0, 3, 1, 1, 0, 4, 2, 2, 2, 2, 1, 0, 1, 1, 2, 0, 2, 0, 2, 1},
    {0, 3, 1, 1, 1, 2, 1, 2, 0, 2, 2, 0, 2, 4, 2, 0, 0, 4, 1, 1},
    {0, 3, 1, 1, 1, 3, 1, 3, 1, 4, 1, 4, 0, 2, 2, 0, 2, 0, 2, 4},
    {0, 3, 1, 1, 1, 4, 1, 2, 0, 1, 2, 4, 2, 2, 1, 0, 0, 3, 2, 2},
    {0, 3, 1, 1, 1, 4, 1, 4, 0, 4, 1, 0, 2, 2, 2, 2, 1, 0, 1, 2},
    {0, 3, 1, 1, 2, 0, 2, 2, 2, 4, 1, 4, 1, 1, 2, 0, 0, 4, 2, 1},
    {0, 3, 1, 2, 0, 0, 2, 2, 1, 1, 2, 4, 2, 2, 1, 1, 2, 0, 2, 0},
    {0, 3, 1, 2, 0, 1, 1, 0, 1, 1, 1, 1, 2, 4, 2, 4, 1, 0, 1, 4},
    {0, 3, 1, 2, 0, 3, 1, 2, 0, 4, 1, 1, 2, 2, 2, 0, 1, 0, 2, 2},
    {0, 3, 1, 2, 0, 3, 1, 4, 2, 1, 2, 4, 1, 4, 2, 1, 0, 2, 1, 0},
    {0, 3, 1, 2, 0, 3, 2, 2, 0, 4, 2, 2, 1, 2, 1, 0, 2, 0, 2, 1},
    {0, 3, 1, 2, 0, 3, 2, 2, 0, 4, 2, 2, 2, 2, 2, 1, 1, 0, 1, 0},
    {0, 3, 1, 2, 0, 4, 1, 1, 0, 1, 1, 3, 2, 1, 2, 0, 1, 0, 1, 0},
    {0, 3, 1, 2, 0, 4, 2, 0, 0, 3, 1, 4, 1, 1, 1, 1, 2, 0, 2, 1},
    {0, 3, 1, 2, 0, 4, 2, 0, 0, 4, 2, 3, 1, 1, 1, 0, 2, 0, 2, 2},
    {0, 3, 1, 2, 1, 0, 2, 2, 0, 1, 1, 0, 2, 2, 1, 4, 1, 4, 2, 0},
    {0, 3, 1, 2, 1, 0, 2, 4, 0, 1, 1, 0, 2, 4, 2, 0, 0, 1, 1, 0},
    {0, 3, 1, 2, 1, 3, 1, 3, 0, 4, 1, 1, 1, 2, 1, 0, 2, 0, 2, 0},
    {0, 3, 1, 2, 2, 0, 2, 0, 0, 1, 1, 4, 1, 2, 1, 0, 1, 3, 1, 3},
    {0, 3, 1, 2, 2, 0, 2, 0, 0, 1, 2, 2, 1, 2, 1, 4, 1, 4, 1, 0},
    {0, 3, 1, 2, 2, 0, 2, 0, 0, 1, 2, 4, 1, 2, 1, 0, 2, 3, 2, 2},
    {0, 3, 1, 2, 2, 0, 2, 0, 0, 1, 2, 4, 1, 2, 1, 0, 2, 3, 2, 4},
    {0, 3, 1, 2, 2, 0, 2, 2, 0, 1, 1, 4, 1, 2, 1, 0, 0, 2, 2, 3},
    {0, 3, 1, 2, 2, 0, 2, 2, 0, 1, 1, 4, 1, 2, 2, 0, 0, 3, 1, 3},
    {0, 3, 1, 2, 2, 0, 2, 2, 0, 4, 2, 1, 1, 1, 1, 1, 1, 2, 2, 0},
    {0, 3, 1, 2, 2, 0, 2, 4, 0, 1, 1, 0, 1, 2, 2, 0, 2, 3, 2, 3},
    {0, 3, 1, 2, 2, 0, 2, 4, 1, 1, 1, 2, 1, 4, 1, 4, 0, 1, 2, 0},
    {0, 3, 1, 2, 2, 1, 1, 0, 0, 4, 2, 1, 2, 2, 2, 0, 1, 0, 2, 2},
    {0, 3, 1, 2, 2, 1, 1, 0, 0, 4, 2, 2, 1, 2, 1, 1, 2, 0, 2, 0},
    {0, 3, 1, 2, 2, 2, 2, 2, 0, 3, 1, 0, 1, 4, 1, 4, 0, 1, 2, 4},
    {0, 3, 1, 2, 2, 2, 2, 4, 0, 3, 1, 2, 1, 4, 1, 4, 0, 1, 2, 0},
    {0, 3, 1, 2, 2, 3, 1, 0, 0, 4, 1, 0, 1, 2, 2, 0, 2, 0, 2, 1},
    {0, 3, 1, 2, 2, 3, 2, 1, 0, 4, 2, 1, 1, 2, 1, 0, 2, 0, 2, 0},
    {0, 3, 1, 2, 2, 3, 2, 2, 0, 4, 2, 1, 1, 2, 1, 0, 2, 0, 2, 0},
    {0, 3, 1, 2, 2, 3, 2, 3, 0, 4, 2, 1, 1, 2, 1, 0, 2, 0, 2, 0},
    {0, 3, 1, 2, 2, 4, 2, 2, 0, 1, 2, 0, 1, 2, 1, 0, 0, 3, 1, 2},
    {0, 3, 1, 3, 0, 2, 2, 1, 1, 0, 2, 0, 2, 4, 1, 1, 0, 2, 2, 1},
    {0, 3, 1, 3, 1, 0, 1, 2, 0, 1, 2, 2, 2, 2, 1, 4, 1, 1, 1, 3},
    {0, 3, 1, 4, 0, 1, 2, 4, 2, 1, 2, 1, 2, 4, 1, 0, 1, 0, 2, 2},
    {0, 3, 1, 4, 0, 2, 1, 0, 1, 0, 2, 1, 2, 1, 2, 0, 0, 2, 1, 0},
    {0, 3, 1, 4, 0, 2, 2, 0, 2, 0, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2},
    {0, 3, 1, 4, 0, 3, 1, 0, 1, 0, 2, 4, 2, 4, 2, 1, 0, 2, 1, 1},
    {0, 3, 1, 4, 0, 3, 1, 0, 2, 0, 2, 4, 1, 4, 2, 1, 0, 2, 1, 1},
    {0, 3, 1, 4, 0, 3, 1, 1, 2, 0, 1, 1, 1, 4, 2, 0, 0, 2, 2, 4},
    {0, 3, 1, 4, 1, 1, 2, 0, 2, 0, 2, 4, 1, 4, 1, 0, 0, 2, 1, 1},
    {0, 3, 1, 4, 2, 0, 1, 2, 0, 3, 2, 0, 1, 4, 2, 2, 0, 1, 2, 4},
    {0, 3, 1, 4, 2, 0, 2, 2, 0, 1, 2, 0, 1, 2, 1, 2, 0, 3, 1, 4},
    {0, 3, 1, 4, 2, 0, 2, 2, 0, 1, 2, 0, 1, 2, 1, 2, 1, 1, 1, 4},
    {0, 3, 1, 4, 2, 0, 2, 2, 0, 1, 2, 3, 1, 4, 2, 0, 0, 1, 1, 0},
    {0, 3, 1, 4, 2, 0, 2, 2, 2, 2, 2, 4, 1, 4, 1, 0, 0, 1, 2, 0},
    {0, 3, 1, 4, 2, 0, 2, 4, 0, 3, 1, 1, 1, 4, 2, 0, 0, 1, 1, 2},
    {0, 3, 1, 4, 2, 0, 2, 4, 2, 1, 2, 1, 1, 4, 2, 0, 0, 1, 2, 2},
    {0, 3, 1, 4, 2, 1, 2, 0, 1, 0, 2, 4, 2, 4, 2, 1, 0, 2, 1, 0},
    {0, 3, 1, 4, 2, 1, 2, 4, 2, 0, 2, 1, 1, 4, 2, 0, 0, 2, 1, 0},
    {0, 3, 1, 4, 2, 2, 2, 2, 0, 3, 1, 4, 1, 4, 1, 0, 0, 1, 2, 4},
    {0, 3, 2, 0, 0, 1, 1, 2, 1, 4, 1, 4, 2, 1, 2, 3, 0, 4, 2, 0},
    {0, 3, 2, 0, 0, 2, 1, 0, 1, 0, 2, 4, 2, 1, 2, 1, 2, 4, 1, 1},
    {0, 3, 2, 0, 0, 2, 1, 1, 1, 1, 2, 4, 1, 4, 1, 4, 2, 0, 2, 1},
    {0, 3, 2, 0, 0, 2, 1, 1, 2, 0, 2, 4, 1, 1, 1, 0, 2, 4, 2, 1},
    {0, 3, 2, 0, 0, 3, 2, 2, 0, 4, 1, 0, 2, 2, 1, 2, 1, 1, 2, 0},
    {0, 3, 2, 0, 0, 3, 2, 2, 0, 4, 2, 1, 1, 2, 1, 0, 2, 1, 1, 2},
    {0, 3, 2, 0, 0, 4, 1, 0, 2, 3, 2, 3, 2, 1, 2, 1, 1, 0, 2, 2},
    {0, 3, 2, 0, 0, 4, 1, 1, 2, 0, 2, 1, 1, 2, 1, 2, 1, 1, 2, 2},
    {0, 3, 2, 0, 0, 4, 1, 1, 2, 2, 1, 0, 2, 1, 2, 1, 1, 0, 2, 2},
    {0, 3, 2, 0, 0, 4, 2, 1, 0, 3, 2, 0, 1, 1, 1, 2, 2, 0, 1, 1},
    {0, 3, 2, 0, 0, 4, 2, 2, 2, 2, 1, 0, 2, 1, 2, 1, 1, 0, 1, 1},
    {0, 3, 2, 0, 1, 0, 1, 2, 0, 1, 1, 0, 2, 2, 2, 4, 2, 4, 2, 2},
    {0, 3, 2, 0, 1, 0, 1, 4, 1, 2, 2, 4, 2, 4, 1, 2, 0, 1, 1, 0},
    {0, 3, 2, 0, 1, 1, 2, 4, 1, 0, 1, 4, 2, 4, 1, 0, 0, 2, 1, 1},
    {0, 3, 2, 0, 1, 2, 2, 2, 2, 0, 1, 4, 1, 4, 1, 1, 0, 2, 2, 4},
    {0, 3, 2, 0, 1, 3, 1, 0, 0, 4, 1, 0, 2, 2, 2, 2, 1, 0, 1, 1},
    {0, 3, 2, 0, 2, 3, 2, 0, 2, 0, 2, 1, 1, 4, 1, 0, 0, 2, 1, 2},
    {0, 3, 2, 0, 2, 4, 1, 0, 1, 0, 1, 2, 2, 2, 1, 4, 0, 1, 2, 4},
    {0, 3, 2, 0, 2, 4, 1, 2, 1, 3, 1, 3, 0, 1, 1, 0, 1, 0, 1, 4},
    {0, 3, 2, 1, 0, 0, 2, 0, 1, 0, 1, 4, 2, 4, 2, 4, 0, 2, 1, 1},
    {0, 3, 2, 1, 0, 2, 1, 0, 2, 1, 1, 1, 2, 4, 2, 4, 1, 0, 1, 4},
    {0, 3, 2, 1, 0, 2, 1, 4, 1, 0, 1, 1, 2, 1, 2, 0, 0, 3, 2, 0},
    {0, 3, 2, 1, 0, 2, 1, 4, 1, 0, 1, 1, 2, 1, 2, 0, 1, 4, 1, 0},
    {0, 3, 2, 1, 0, 2, 2, 4, 1, 0, 1, 1, 2, 1, 1, 4, 0, 3, 2, 0},
    {0, 3, 2, 1, 0, 3, 1, 4, 0, 4, 2, 2, 2, 2, 1, 1, 1, 0, 1, 2},
    {0, 3, 2, 1, 0, 3, 2, 0, 0, 4, 1, 0, 2, 2, 2, 2, 1, 1, 1, 2},
    {0, 3, 2, 1, 0, 3, 2, 1, 0, 4, 1, 2, 2, 2, 2, 2, 1, 1, 1, 0},
    {0, 3, 2, 1, 0, 4, 1, 0, 2, 2, 1, 1, 2, 1, 2, 0, 1, 0, 2, 2},
    {0, 3, 2, 1, 0, 4, 1, 1, 0, 3, 2, 4, 2, 1, 2, 2, 1, 0, 1, 0},
    {0, 3, 2, 1, 0, 4, 1, 2, 1, 2, 2, 0, 2, 1, 1, 0, 1, 0, 1, 1},
    {0, 3, 2, 1, 0, 4, 2, 2, 0, 3, 2, 0, 2, 1, 1, 2, 1, 0, 1, 1},
    {0, 3, 2, 1, 1, 0, 1, 2, 1, 4, 2, 4, 2, 1, 1, 0, 0, 4, 1, 1},
    {0, 3, 2, 1, 2, 2, 2, 2, 0, 2, 1, 0, 1, 4, 1, 0, 0, 4, 2, 1},
    {0, 3, 2, 1, 2, 3, 2, 3, 2, 4, 2, 4, 0, 2, 1, 0, 1, 0, 1, 4},
    {0, 3, 2, 1, 2, 4, 2, 2, 0, 1, 1, 4, 1, 2, 2, 0, 0, 3, 1, 2},
    {0, 3, 2, 1, 2, 4, 2, 4, 0, 4, 2, 0, 1, 2, 1, 2, 2, 0, 2, 2},
    {0, 3, 2, 2, 0, 0, 1, 2, 2, 1, 1, 4, 1, 2, 2, 1, 1, 0, 1, 0},
    {0, 3, 2, 2, 0, 1, 2, 0, 2, 1, 2, 1, 1, 4, 1, 4, 2, 0, 2, 4},
    {0, 3, 2, 2, 0, 3, 1, 2, 0, 4, 1, 2, 1, 2, 1, 1, 2, 0, 2, 0},
    {0, 3, 2, 2, 0, 3, 1, 2, 0, 4, 1, 2, 2, 2, 2, 0, 1, 0, 1, 1},
    {0, 3, 2, 2, 0, 3, 2, 2, 0, 4, 2, 1, 1, 2, 1, 0, 2, 0, 1, 2},
    {0, 3, 2, 2, 0, 3, 2, 4, 1, 1, 1, 4, 2, 4, 1, 1, 0, 2, 2, 0},
    {0, 3, 2, 2, 0, 4, 1, 0, 0, 3, 2, 4, 2, 1, 2, 1, 1, 0, 1, 1},
    {0, 3, 2, 2, 0, 4, 1, 0, 0, 4, 1, 3, 2, 1, 2, 0, 1, 0, 1, 2},
    {0, 3, 2, 2, 0, 4, 2, 1, 0, 1, 2, 3, 1, 1, 1, 0, 2, 0, 2, 0},
    {0, 3, 2, 2, 1, 0, 1, 0, 0, 1, 1, 2, 2, 2, 2, 4, 2, 4, 2, 0},
    {0, 3, 2, 2, 1, 0, 1, 0, 0, 1, 1, 4, 2, 2, 2, 0, 1, 3, 1, 2},
    {0, 3, 2, 2, 1, 0, 1, 0, 0, 1, 1, 4, 2, 2, 2, 0, 1, 3, 1, 4},
    {0, 3, 2, 2, 1, 0, 1, 0, 0, 1, 2, 4, 2, 2, 2, 0, 2, 3, 2, 3},
    {0, 3, 2, 2, 1, 0, 1, 2, 0, 1, 2, 4, 2, 2, 1, 0, 0, 3, 2, 3},
    {0, 3, 2, 2, 1, 0, 1, 2, 0, 1, 2, 4, 2, 2, 2, 0, 0, 2, 1, 3},
    {0, 3, 2, 2, 1, 0, 1, 2, 0, 4, 1, 1, 2, 1, 2, 1, 2, 2, 1, 0},
    {0, 3, 2, 2, 1, 0, 1, 4, 0, 1, 2, 0, 2, 2, 1, 0, 1, 3, 1, 3},
    {0, 3, 2, 2, 1, 0, 1, 4, 2, 1, 2, 2, 2, 4, 2, 4, 0, 1, 1, 0},
    {0, 3, 2, 2, 1, 1, 2, 0, 0, 4, 1, 1, 1, 2, 1, 0, 2, 0, 1, 2},
    {0, 3, 2, 2, 1, 1, 2, 0, 0, 4, 1, 2, 2, 2, 2, 1, 1, 0, 1, 0},
    {0, 3, 2, 2, 1, 2, 1, 2, 0, 3, 2, 0, 2, 4, 2, 4, 0, 1, 1, 4},
    {0, 3, 2, 2, 1, 2, 1, 4, 0, 3, 2, 2, 2, 4, 2, 4, 0, 1, 1, 0},
    {0, 3, 2, 2, 1, 3, 1, 1, 0, 4, 1, 1, 2, 2, 2, 0, 1, 0, 1, 0},
    {0, 3, 2, 2, 1, 3, 1, 2, 0, 4, 1, 1, 2, 2, 2, 0, 1, 0, 1, 0},
    {0, 3, 2, 2, 1, 3, 1, 3, 0, 4, 1, 1, 2, 2, 2, 0, 1, 0, 1, 0},
    {0, 3, 2, 2, 1, 3, 2, 0, 0, 4, 2, 0, 2, 2, 1, 0, 1, 0, 1, 1},
    {0, 3, 2, 2, 1, 4, 1, 2, 0, 1, 1, 0, 2, 2, 2, 0, 0, 3, 2, 2},
    {0, 3, 2, 2, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 1, 4, 1, 1, 1, 1},
    {0, 3, 2, 2, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 2, 4, 2, 4, 1, 0},
    {0, 3, 2, 2, 2, 0, 1, 4, 0, 1, 2, 0, 1, 4, 1, 0, 0, 1, 2, 0},
    {0, 3, 2, 2, 2, 3, 2, 3, 0, 4, 2, 1, 2, 2, 2, 0, 1, 0, 1, 0},
    {0, 3, 2, 3, 0, 2, 1, 1, 2, 0, 1, 0, 1, 4, 2, 1, 0, 2, 1, 1},
    {0, 3, 2, 3, 2, 0, 2, 2, 0, 1, 1, 2, 1, 2, 2, 4, 2, 1, 2, 3},
    {0, 3, 2, 4, 0, 1, 1, 4, 1, 1, 1, 1, 1, 4, 2, 0, 2, 0, 1, 2},
    {0, 3, 2, 4, 0, 2, 1, 0, 1, 0, 1, 1, 2, 1, 2, 1, 2, 2, 2, 2},
    {0, 3, 2, 4, 0, 2, 1, 4, 2, 0, 2, 0, 1, 4, 1, 0, 0, 2, 1, 1},
    {0, 3, 2, 4, 0, 3, 2, 0, 2, 0, 1, 4, 1, 4, 1, 1, 0, 2, 2, 1},
    {0, 3, 2, 4, 0, 3, 2, 1, 1, 0, 2, 1, 2, 4, 1, 0, 0, 2, 1, 4},
    {0, 3, 2, 4, 1, 0, 1, 2, 0, 1, 1, 0, 2, 2, 2, 2, 0, 3, 2, 4},
    {0, 3, 2, 4, 1, 0, 1, 2, 0, 1, 1, 0, 2, 2, 2, 2, 2, 1, 2, 4},
    {0, 3, 2, 4, 1, 0, 1, 2, 0, 1, 1, 3, 2, 4, 1, 0, 0, 1, 2, 0},
    {0, 3, 2, 4, 1, 0, 1, 2, 1, 2, 1, 4, 2, 4, 2, 0, 0, 1, 1, 0},
    {0, 3, 2, 4, 1, 0, 1, 4, 1, 1, 1, 1, 2, 4, 1, 0, 0, 1, 1, 2},
    {0, 3, 2, 4, 1, 0, 2, 2, 0, 3, 1, 0, 2, 4, 1, 2, 0, 1, 1, 4},
    {0, 3, 2, 4, 1, 1, 1, 0, 2, 0, 1, 4, 1, 4, 1, 1, 0, 2, 2, 0},
    {0, 3, 2, 4, 1, 1, 1, 4, 1, 0, 1, 1, 2, 4, 1, 0, 0, 2, 2, 0},
    {0, 3, 2, 4, 1, 2, 1, 2, 0, 3, 2, 4, 2, 4, 2, 0, 0, 1, 1, 4},
    {0, 3, 2, 4, 1, 3, 1, 1, 1, 0, 1, 0, 2, 4, 2, 0, 0, 2, 1, 1},
    {0, 3, 2, 4, 2, 1, 1, 0, 1, 0, 1, 4, 2, 4, 2, 0, 0, 2, 2, 1},
    {0, 4, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 3, 1, 2, 1, 3, 1, 4},
    {0, 4, 1, 0, 0, 2, 1, 3, 2, 0, 2, 1, 1, 3, 1, 1, 1, 1, 2, 0},
    {0, 4, 1, 0, 0, 2, 2, 3, 2, 0, 2, 1, 2, 3, 1, 1, 1, 1, 2, 0},
    {0, 4, 1, 0, 0, 3, 2, 2, 0, 3, 2, 0, 2, 0, 2, 0, 1, 1, 1, 1},
    {0, 4, 1, 0, 0, 3, 2, 2, 1, 0, 1, 2, 2, 1, 1, 1, 2, 2, 2, 1},
    {0, 4, 1, 0, 0, 4, 2, 2, 2, 0, 2, 3, 0, 2, 2, 1, 1, 3, 1, 3},
    {0, 4, 1, 0, 1, 1, 2, 3, 2, 0, 1, 3, 0, 2, 2, 1, 1, 3, 2, 0},
    {0, 4, 1, 0, 1, 4, 1, 2, 0, 1, 2, 2, 2, 2, 2, 0, 0, 3, 2, 4},
    {0, 4, 1, 0, 1, 4, 1, 3, 1, 0, 2, 3, 0, 2, 1, 1, 2, 3, 2, 0},
    {0, 4, 1, 0, 1, 4, 1, 4, 2, 0, 1, 1, 0, 2, 2, 0, 1, 3, 1, 3},
    {0, 4, 1, 0, 2, 0, 1, 2, 1, 4, 1, 4, 0, 1, 2, 0, 1, 3, 1, 3},
    {0, 4, 1, 0, 2, 0, 2, 2, 0, 1, 2, 0, 0, 1, 1, 0, 1, 2, 1, 3},
    {0, 4, 1, 0, 2, 0, 2, 3, 0, 1, 1, 1, 0, 1, 2, 0, 1, 3, 1, 2},
    {0, 4, 1, 0, 2, 1, 2, 0, 1, 0, 1, 3, 0, 2, 2, 1, 2, 3, 2, 3},
    {0, 4, 1, 0, 2, 2, 2, 3, 0, 4, 1, 3, 0, 1, 1, 2, 1, 3, 2, 0},
    {0, 4, 1, 0, 2, 3, 2, 2, 0, 1, 2, 0, 0, 4, 1, 3, 1, 2, 1, 2},
    {0, 4, 1, 1, 0, 2, 1, 0, 0, 3, 1, 2, 1, 0, 1, 4, 2, 2, 2, 0},
    {0, 4, 1, 1, 0, 2, 1, 0, 1, 3, 2, 1, 0, 4, 1, 1, 2, 1, 2, 3},
    {0, 4, 1, 1, 0, 2, 2, 0, 2, 3, 2, 3, 1, 1, 1, 3, 2, 0, 1, 0},
    {0, 4, 1, 1, 0, 2, 2, 1, 2, 0, 1, 3, 1, 3, 2, 0, 1, 1, 1, 0},
    {0, 4, 1, 1, 0, 2, 2, 1, 2, 0, 2, 3, 0, 4, 2, 1, 1, 1, 1, 0},
    {0, 4, 1, 1, 0, 2, 2, 1, 2, 3, 1, 0, 0, 4, 1, 1, 1, 1, 2, 3},
    {0, 4, 1, 1, 0, 3, 1, 0, 1, 4, 1, 4, 2, 0, 1, 2, 1, 1, 2, 0},
    {0, 4, 1, 1, 0, 3, 1, 2, 0, 3, 1, 0, 2, 0, 2, 1, 1, 1, 1, 0},
    {0, 4, 1, 1, 0, 3, 1, 2, 1, 4, 1, 4, 2, 0, 2, 0, 1, 1, 1, 0},
    {0, 4, 1, 1, 0, 3, 1, 4, 0, 3, 2, 1, 2, 0, 2, 0, 1, 2, 1, 0},
    {0, 4, 1, 1, 0, 3, 2, 0, 1, 2, 1, 0, 2, 0, 2, 1, 1, 1, 1, 2},
    {0, 4, 1, 1, 0, 3, 2, 1, 2, 2, 2, 0, 2, 0, 2, 2, 1, 1, 1, 0},
    {0, 4, 1, 1, 0, 3, 2, 2, 1, 2, 2, 1, 2, 0, 2, 0, 1, 1, 1, 0},
    {0, 4, 1, 1, 0, 3, 2, 2, 2, 4, 2, 4, 2, 0, 2, 0, 1, 1, 1, 0},
    {0, 4, 1, 1, 0, 4, 1, 0, 0, 3, 1, 2, 2, 0, 2, 2, 1, 2, 2, 1},
    {0, 4, 1, 1, 0, 4, 1, 1, 2, 1, 2, 3, 0, 2, 2, 0, 1, 3, 1, 3},
    {0, 4, 1, 1, 0, 4, 1, 3, 2, 1, 2, 3, 0, 2, 1, 0, 1, 3, 2, 0},
    {0, 4, 1, 1, 1, 1, 1, 0, 0, 3, 1, 2, 1, 0, 2, 2, 2, 2, 2, 0},
    {0, 4, 1, 1, 1, 1, 1, 0, 1, 0, 2, 3, 0, 2, 1, 3, 2, 3, 2, 0},
    {0, 4, 1, 1, 1, 1, 1, 2, 0, 3, 1, 0, 2, 0, 2, 2, 1, 2, 2, 0},
    {0, 4, 1, 1, 1, 1, 1, 2, 0, 3, 2, 2, 2, 0, 2, 0, 1, 2, 1, 0},
    {0, 4, 1, 1, 1, 2, 1, 3, 0, 4, 2, 0, 0, 1, 2, 3, 2, 3, 1, 0},
    {0, 4, 1, 1, 1, 3, 1, 3, 0, 4, 1, 1, 0, 3, 1, 0, 1, 2, 2, 0},
    {0, 4, 1, 1, 2, 1, 1, 2, 0, 3, 2, 0, 2, 0, 2, 2, 1, 2, 1, 0},
    {0, 4, 1, 1, 2, 4, 2, 3, 1, 3, 1, 4, 0, 1, 1, 0, 0, 2, 1, 3},
    {0, 4, 1, 2, 0, 0, 1, 1, 1, 1, 1, 3, 1, 0, 1, 0, 2, 2, 2, 2},
    {0, 4, 1, 2, 0, 3, 1, 0, 0, 3, 1, 1, 1, 0, 2, 2, 2, 1, 2, 0},
    {0, 4, 1, 2, 0, 3, 1, 0, 0, 3, 1, 1, 2, 0, 2, 2, 1, 1, 2, 0},
    {0, 4, 1, 2, 0, 3, 1, 0, 0, 4, 1, 1, 1, 2, 2, 1, 2, 1, 2, 0},
    {0, 4, 1, 2, 0, 3, 2, 0, 0, 3, 1, 0, 2, 0, 2, 1, 1, 1, 1, 0},
    {0, 4, 1, 2, 0, 3, 2, 0, 1, 2, 2, 1, 2, 0, 1, 1, 1, 1, 1, 0},
    {0, 4, 1, 2, 0, 3, 2, 0, 1, 3, 1, 2, 2, 0, 2, 1, 1, 1, 1, 1},
    {0, 4, 1, 2, 0, 3, 2, 1, 0, 4, 1, 2, 2, 0, 2, 2, 1, 1, 1, 1},
    {0, 4, 1, 2, 0, 4, 1, 0, 0, 3, 1, 1, 2, 0, 2, 2, 1, 2, 2, 1},
    {0, 4, 1, 2, 0, 4, 1, 2, 0, 3, 1, 1, 1, 0, 2, 2, 2, 2, 2, 0},
    {0, 4, 1, 2, 0, 4, 1, 2, 0, 3, 2, 1, 2, 0, 2, 2, 1, 2, 1, 1},
    {0, 4, 1, 2, 0, 4, 2, 2, 0, 3, 2, 2, 2, 0, 1, 0, 1, 2, 2, 1},
    {0, 4, 1, 2, 0, 4, 2, 4, 0, 3, 2, 1, 2, 0, 2, 2, 1, 2, 1, 0},
    {0, 4, 1, 2, 1, 0, 2, 2, 0, 1, 1, 3, 0, 1, 1, 0, 2, 3, 2, 0},
    {0, 4, 1, 2, 1, 0, 2, 2, 0, 1, 1, 3, 0, 4, 1, 0, 2, 2, 2, 3},
    {0, 4, 1, 2, 1, 0, 2, 3, 0, 1, 1, 0, 0, 1, 1, 0, 2, 3, 2, 0},
    {0, 4, 1, 2, 1, 1, 1, 0, 0, 3, 2, 0, 2, 0, 2, 2, 1, 2, 1, 1},
    {0, 4, 1, 2, 1, 2, 1, 1, 0, 0, 2, 3, 2, 0, 2, 0, 2, 1, 2, 1},
    {0, 4, 1, 2, 1, 2, 2, 1, 0, 0, 2, 3, 2, 0, 2, 0, 2, 1, 1, 1},
    {0, 4, 1, 2, 1, 3, 1, 3, 0, 3, 2, 0, 2, 0, 2, 2, 1, 2, 1, 1},
    {0, 4, 1, 2, 1, 4, 1, 3, 2, 3, 2, 4, 0, 1, 2, 0, 0, 2, 2, 3},
    {0, 4, 1, 2, 1, 4, 1, 4, 0, 3, 1, 1, 2, 0, 2, 0, 1, 2, 1, 0},
    {0, 4, 1, 2, 2, 0, 1, 3, 1, 2, 2, 0, 0, 1, 2, 3, 1, 3, 1, 0},
    {0, 4, 1, 2, 2, 0, 2, 0, 0, 1, 1, 3, 1, 4, 1, 4, 1, 2, 1, 0},
    {0, 4, 1, 2, 2, 0, 2, 0, 0, 1, 2, 3, 2, 4, 2, 3, 1, 2, 1, 0},
    {0, 4, 1, 2, 2, 0, 2, 0, 0, 1, 2, 3, 2, 4, 2, 4, 1, 2, 1, 0},
    {0, 4, 1, 2, 2, 0, 2, 2, 0, 1, 1, 3, 0, 1, 1, 0, 1, 3, 2, 0},
    {0, 4, 1, 2, 2, 0, 2, 2, 0, 1, 1, 3, 0, 4, 1, 2, 1, 2, 2, 3},
    {0, 4, 1, 2, 2, 0, 2, 2, 0, 1, 2, 3, 2, 3, 1, 0, 1, 2, 2, 0},
    {0, 4, 1, 2, 2, 0, 2, 3, 1, 1, 1, 2, 0, 1, 2, 0, 1, 3, 1, 3},
    {0, 4, 1, 2, 2, 1, 1, 0, 0, 3, 2, 0, 2, 0, 2, 2, 1, 2, 2, 1},
    {0, 4, 1, 2, 2, 1, 2, 0, 0, 3, 2, 2, 2, 0, 2, 1, 1, 2, 1, 0},
    {0, 4, 1, 2, 2, 2, 2, 2, 0, 1, 1, 0, 1, 0, 1, 3, 2, 3, 2, 3},
    {0, 4, 1, 2, 2, 2, 2, 2, 1, 3, 1, 0, 0, 1, 2, 0, 2, 0, 1, 3},
    {0, 4, 1, 2, 2, 3, 2, 0, 0, 1, 2, 2, 0, 4, 1, 2, 1, 2, 1, 3},
    {0, 4, 1, 2, 2, 4, 2, 4, 0, 3, 2, 0, 2, 0, 2, 1, 1, 2, 1, 0},
    {0, 4, 1, 3, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 2, 2, 3, 2, 3},
    {0, 4, 1, 3, 0, 2, 1, 0, 1, 0, 2, 1, 1, 4, 1, 0, 2, 1, 2, 0},
    {0, 4, 1, 3, 0, 2, 2, 0, 2, 0, 2, 1, 0, 4, 1, 3, 1, 1, 1, 1},
    {0, 4, 1, 3, 0, 2, 2, 0, 2, 3, 2, 1, 0, 4, 1, 3, 1, 1, 1, 1},
    {0, 4, 1, 3, 0, 2, 2, 1, 2, 0, 1, 1, 1, 3, 2, 0, 1, 1, 1, 0},
    {0, 4, 1, 3, 0, 3, 1, 1, 2, 1, 2, 0, 1, 4, 1, 4, 0, 2, 2, 1},
    {0, 4, 1, 3, 0, 4, 1, 3, 1, 0, 2, 3, 0, 2, 1, 1, 2, 3, 2, 0},
    {0, 4, 1, 3, 1, 0, 1, 2, 0, 1, 2, 2, 0, 4, 1, 3, 2, 2, 2, 3},
    {0, 4, 1, 3, 1, 0, 1, 2, 1, 3, 1, 0, 0, 3, 1, 1, 2, 1, 1, 0},
    {0, 4, 1, 3, 1, 1, 2, 0, 1, 0, 1, 1, 0, 2, 1, 0, 2, 3, 2, 3},
    {0, 4, 1, 3, 1, 4, 1, 4, 2, 0, 2, 0, 0, 2, 1, 1, 1, 3, 1, 0},
    {0, 4, 1, 3, 2, 0, 1, 2, 0, 1, 2, 0, 1, 3, 2, 2, 1, 2, 1, 0},
    {0, 4, 1, 3, 2, 0, 1, 2, 1, 2, 2, 0, 0, 1, 2, 3, 1, 3, 1, 0},
    {0, 4, 1, 3, 2, 0, 2, 0, 2, 4, 2, 2, 0, 1, 2, 2, 1, 3, 1, 0},
    {0, 4, 1, 3, 2, 0, 2, 0, 2, 4, 2, 4, 0, 1, 2, 2, 1, 3, 1, 0},
    {0, 4, 1, 3, 2, 0, 2, 2, 0, 1, 2, 0, 1, 1, 1, 1, 1, 2, 1, 2},
    {0, 4, 1, 3, 2, 0, 2, 2, 0, 1, 2, 3, 0, 1, 2, 0, 1, 3, 1, 0},
    {0, 4, 1, 3, 2, 0, 2, 3, 0, 1, 1, 0, 0, 1, 1, 2, 1, 2, 2, 0},
    {0, 4, 1, 3, 2, 0, 2, 3, 1, 2, 1, 0, 0, 1, 1, 2, 1, 3, 2, 0},
    {0, 4, 1, 3, 2, 0, 2, 3, 2, 2, 1, 0, 0, 1, 2, 2, 1, 3, 2, 0},
    {0, 4, 1, 3, 2, 3, 2, 0, 0, 1, 2, 2, 0, 4, 1, 0, 1, 2, 1, 2},
    {0, 4, 1, 4, 0, 2, 1, 3, 0, 1, 2, 0, 1, 1, 1, 1, 2, 2, 2, 3},
    {0, 4, 1, 4, 0, 4, 1, 0, 0, 3, 2, 2, 1, 1, 1, 2, 2, 2, 2, 0},
    {0, 4, 1, 4, 2, 4, 2, 2, 0, 1, 2, 0, 1, 2, 1, 0, 0, 3, 1, 4},
    {0, 4, 2, 0, 0, 1, 2, 0, 2, 1, 2, 1, 0, 3, 2, 2, 2, 3, 2, 4},
    {0, 4, 2, 0, 0, 2, 1, 1, 1, 0, 1, 3, 0, 2, 2, 0, 2, 1, 2, 1},
    {0, 4, 2, 0, 0, 2, 1, 3, 1, 0, 1, 1, 1, 3, 2, 1, 2, 1, 1, 0},
    {0, 4, 2, 0, 0, 2, 2, 3, 1, 0, 1, 1, 2, 3, 2, 1, 2, 1, 1, 0},
    {0, 4, 2, 0, 0, 3, 1, 2, 0, 3, 1, 0, 1, 0, 1, 0, 2, 1, 2, 1},
    {0, 4, 2, 0, 0, 3, 1, 2, 2, 0, 2, 2, 1, 1, 2, 1, 1, 2, 1, 1},
    {0, 4, 2, 0, 0, 4, 1, 2, 1, 0, 1, 3, 0, 2, 1, 1, 2, 3, 2, 3},
    {0, 4, 2, 0, 1, 0, 1, 2, 0, 1, 1, 0, 0, 1, 2, 0, 2, 2, 2, 3},
    {0, 4, 2, 0, 1, 0, 1, 3, 0, 1, 2, 1, 0, 1, 1, 0, 2, 3, 2, 2},
    {0, 4, 2, 0, 1, 2, 1, 3, 0, 4, 2, 3, 0, 1, 2, 2, 2, 3, 1, 0},
    {0, 4, 2, 0, 1, 3, 1, 2, 0, 1, 1, 0, 0, 4, 2, 3, 2, 2, 2, 2},
    {0, 4, 2, 0, 2, 1, 1, 3, 1, 0, 2, 3, 0, 2, 1, 1, 2, 3, 1, 0},
    {0, 4, 2, 0, 2, 4, 2, 2, 0, 1, 1, 2, 1, 2, 1, 0, 0, 3, 1, 4},
    {0, 4, 2, 0, 2, 4, 2, 3, 2, 0, 1, 3, 0, 2, 2, 1, 1, 3, 1, 0},
    {0, 4, 2, 0, 2, 4, 2, 4, 1, 0, 2, 1, 0, 2, 1, 0, 2, 3, 2, 3},
    {0, 4, 2, 1, 0, 2, 1, 0, 1, 3, 1, 3, 2, 1, 2, 3, 1, 0, 2, 0},
    {0, 4, 2, 1, 0, 2, 1, 1, 1, 0, 1, 3, 0, 4, 1, 1, 2, 1, 2, 0},
    {0, 4, 2, 1, 0, 2, 1, 1, 1, 0, 2, 3, 2, 3, 1, 0, 2, 1, 2, 0},
    {0, 4, 2, 1, 0, 2, 1, 1, 1, 3, 2, 0, 0, 4, 2, 1, 2, 1, 1, 3},
    {0, 4, 2, 1, 0, 2, 2, 0, 0, 3, 2, 2, 2, 0, 2, 4, 1, 2, 1, 0},
    {0, 4, 2, 1, 0, 2, 2, 0, 2, 3, 1, 1, 0, 4, 2, 1, 1, 1, 1, 3},
    {0, 4, 2, 1, 0, 3, 1, 0, 1, 0, 1, 2, 2, 1, 2, 2, 2, 2, 1, 1},
    {0, 4, 2, 1, 0, 3, 1, 0, 2, 2, 2, 0, 1, 0, 1, 1, 2, 1, 2, 2},
    {0, 4, 2, 1, 0, 3, 1, 1, 1, 2, 1, 0, 1, 0, 1, 2, 2, 1, 2, 0},
    {0, 4, 2, 1, 0, 3, 1, 2, 1, 4, 1, 4, 1, 0, 1, 0, 2, 1, 2, 0},
    {0, 4, 2, 1, 0, 3, 1, 2, 2, 2, 1, 1, 1, 0, 1, 0, 2, 1, 2, 0},
    {0, 4, 2, 1, 0, 3, 2, 0, 2, 4, 2, 4, 1, 0, 2, 2, 2, 1, 1, 0},
    {0, 4, 2, 1, 0, 3, 2, 2, 0, 3, 2, 0, 1, 0, 1, 1, 2, 1, 2, 0},
    {0, 4, 2, 1, 0, 3, 2, 2, 2, 4, 2, 4, 1, 0, 1, 0, 2, 1, 2, 0},
    {0, 4, 2, 1, 0, 3, 2, 4, 0, 3, 1, 1, 1, 0, 1, 0, 2, 2, 2, 0},
    {0, 4, 2, 1, 0, 4, 2, 0, 0, 3, 2, 2, 1, 0, 1, 2, 2, 2, 1, 1},
    {0, 4, 2, 1, 0, 4, 2, 1, 1, 1, 1, 3, 0, 2, 1, 0, 2, 3, 2, 3},
    {0, 4, 2, 1, 0, 4, 2, 3, 1, 1, 1, 3, 0, 2, 2, 0, 2, 3, 1, 0},
    {0, 4, 2, 1, 1, 1, 2, 2, 0, 3, 1, 0, 1, 0, 1, 2, 2, 2, 2, 0},
    {0, 4, 2, 1, 2, 1, 2, 0, 0, 3, 2, 2, 2, 0, 1, 2, 1, 2, 1, 0},
    {0, 4, 2, 1, 2, 1, 2, 0, 2, 0, 1, 3, 0, 2, 2, 3, 1, 3, 1, 0},
    {0, 4, 2, 1, 2, 1, 2, 2, 0, 3, 1, 2, 1, 0, 1, 0, 2, 2, 2, 0},
    {0, 4, 2, 1, 2, 1, 2, 2, 0, 3, 2, 0, 1, 0, 1, 2, 2, 2, 1, 0},
    {0, 4, 2, 1, 2, 2, 2, 3, 0, 4, 1, 0, 0, 1, 1, 3, 1, 3, 2, 0},
    {0, 4, 2, 1, 2, 3, 2, 3, 0, 4, 2, 1, 0, 3, 2, 0, 2, 2, 1, 0},
    {0, 4, 2, 2, 0, 0, 2, 1, 2, 1, 2, 3, 2, 0, 2, 0, 1, 2, 1, 2},
    {0, 4, 2, 2, 0, 3, 1, 0, 0, 3, 2, 0, 1, 0, 1, 1, 2, 1, 2, 0},
    {0, 4, 2, 2, 0, 3, 1, 0, 2, 2, 1, 1, 1, 0, 2, 1, 2, 1, 2, 0},
    {0, 4, 2, 2, 0, 3, 1, 0, 2, 3, 2, 2, 1, 0, 1, 1, 2, 1, 2, 1},
    {0, 4, 2, 2, 0, 3, 1, 1, 0, 4, 2, 2, 1, 0, 1, 2, 2, 1, 2, 1},
    {0, 4, 2, 2, 0, 3, 2, 0, 0, 3, 2, 1, 1, 0, 1, 2, 2, 1, 1, 0},
    {0, 4, 2, 2, 0, 3, 2, 0, 0, 3, 2, 1, 2, 0, 1, 2, 1, 1, 1, 0},
    {0, 4, 2, 2, 0, 3, 2, 0, 0, 4, 2, 1, 2, 2, 1, 1, 1, 1, 1, 0},
    {0, 4, 2, 2, 0, 4, 1, 2, 0, 3, 1, 2, 1, 0, 2, 0, 2, 2, 1, 1},
    {0, 4, 2, 2, 0, 4, 1, 4, 0, 3, 1, 1, 1, 0, 1, 2, 2, 2, 2, 0},
    {0, 4, 2, 2, 0, 4, 2, 0, 0, 3, 2, 1, 1, 0, 1, 2, 2, 2, 1, 1},
    {0, 4, 2, 2, 0, 4, 2, 2, 0, 3, 1, 1, 1, 0, 1, 2, 2, 2, 2, 1},
    {0, 4, 2, 2, 0, 4, 2, 2, 0, 3, 2, 1, 2, 0, 1, 2, 1, 2, 1, 0},
    {0, 4, 2, 2, 1, 0, 1, 0, 0, 1, 1, 3, 1, 4, 1, 3, 2, 2, 2, 0},
    {0, 4, 2, 2, 1, 0, 1, 0, 0, 1, 1, 3, 1, 4, 1, 4, 2, 2, 2, 0},
    {0, 4, 2, 2, 1, 0, 1, 0, 0, 1, 2, 3, 2, 4, 2, 4, 2, 2, 2, 0},
    {0, 4, 2, 2, 1, 0, 1, 2, 0, 1, 1, 3, 1, 3, 2, 0, 2, 2, 1, 0},
    {0, 4, 2, 2, 1, 0, 1, 2, 0, 1, 2, 3, 0, 1, 2, 0, 2, 3, 1, 0},
    {0, 4, 2, 2, 1, 0, 1, 2, 0, 1, 2, 3, 0, 4, 2, 2, 2, 2, 1, 3},
    {0, 4, 2, 2, 1, 0, 1, 3, 2, 1, 2, 2, 0, 1, 1, 0, 2, 3, 2, 3},
    {0, 4, 2, 2, 1, 0, 2, 3, 2, 2, 1, 0, 0, 1, 1, 3, 2, 3, 2, 0},
    {0, 4, 2, 2, 1, 1, 1, 0, 0, 3, 1, 2, 1, 0, 1, 1, 2, 2, 2, 0},
    {0, 4, 2, 2, 1, 1, 2, 0, 0, 3, 1, 0, 1, 0, 1, 2, 2, 2, 1, 1},
    {0, 4, 2, 2, 1, 2, 1, 2, 0, 1, 2, 0, 2, 0, 2, 3, 1, 3, 1, 3},
    {0, 4, 2, 2, 1, 2, 1, 2, 2, 3, 2, 0, 0, 1, 1, 0, 1, 0, 2, 3},
    {0, 4, 2, 2, 1, 3, 1, 0, 0, 1, 1, 2, 0, 4, 2, 2, 2, 2, 2, 3},
    {0, 4, 2, 2, 1, 4, 1, 4, 0, 3, 1, 0, 1, 0, 1, 1, 2, 2, 2, 0},
    {0, 4, 2, 2, 2, 0, 1, 2, 0, 1, 2, 3, 0, 1, 2, 0, 1, 3, 1, 0},
    {0, 4, 2, 2, 2, 0, 1, 2, 0, 1, 2, 3, 0, 4, 2, 0, 1, 2, 1, 3},
    {0, 4, 2, 2, 2, 0, 1, 3, 0, 1, 2, 0, 0, 1, 2, 0, 1, 3, 1, 0},
    {0, 4, 2, 2, 2, 1, 2, 0, 0, 3, 1, 0, 1, 0, 1, 2, 2, 2, 2, 1},
    {0, 4, 2, 2, 2, 2, 1, 1, 0, 0, 1, 3, 1, 0, 1, 0, 1, 1, 2, 1},
    {0, 4, 2, 2, 2, 2, 2, 1, 0, 0, 1, 3, 1, 0, 1, 0, 1, 1, 1, 1},
    {0, 4, 2, 2, 2, 3, 2, 3, 0, 3, 1, 0, 1, 0, 1, 2, 2, 2, 2, 1},
    {0, 4, 2, 2, 2, 4, 2, 3, 1, 3, 1, 4, 0, 1, 1, 0, 0, 2, 1, 3},
    {0, 4, 2, 2, 2, 4, 2, 4, 0, 3, 2, 1, 1, 0, 1, 0, 2, 2, 2, 0},
    {0, 4, 2, 3, 0, 0, 2, 1, 2, 0, 2, 0, 2, 1, 2, 2, 1, 3, 1, 3},
    {0, 4, 2, 3, 0, 2, 1, 0, 1, 0, 1, 1, 0, 4, 2, 3, 2, 1, 2, 1},
    {0, 4, 2, 3, 0, 2, 1, 0, 1, 3, 1, 1, 0, 4, 2, 3, 2, 1, 2, 1},
    {0, 4, 2, 3, 0, 2, 1, 1, 1, 0, 2, 1, 2, 3, 1, 0, 2, 1, 2, 0},
    {0, 4, 2, 3, 0, 2, 2, 0, 2, 0, 1, 1, 2, 4, 2, 0, 1, 1, 1, 0},
    {0, 4, 2, 3, 0, 3, 2, 1, 1, 1, 1, 0, 2, 4, 2, 4, 0, 2, 1, 1},
    {0, 4, 2, 3, 1, 0, 1, 0, 1, 4, 1, 2, 0, 1, 1, 2, 2, 3, 2, 0},
    {0, 4, 2, 3, 1, 0, 1, 0, 1, 4, 1, 4, 0, 1, 1, 2, 2, 3, 2, 0},
    {0, 4, 2, 3, 1, 0, 1, 1, 2, 3, 1, 1, 0, 0, 2, 0, 1, 2, 2, 2},
    {0, 4, 2, 3, 1, 0, 1, 2, 0, 1, 1, 0, 2, 1, 2, 1, 2, 2, 2, 2},
    {0, 4, 2, 3, 1, 0, 1, 2, 0, 1, 1, 3, 0, 1, 1, 0, 2, 3, 2, 0},
    {0, 4, 2, 3, 1, 0, 1, 3, 0, 1, 2, 0, 0, 1, 2, 2, 2, 2, 1, 0},
    {0, 4, 2, 3, 1, 0, 1, 3, 1, 2, 2, 0, 0, 1, 1, 2, 2, 3, 1, 0},
    {0, 4, 2, 3, 1, 0, 1, 3, 2, 2, 2, 0, 0, 1, 2, 2, 2, 3, 1, 0},
    {0, 4, 2, 3, 1, 0, 2, 2, 0, 1, 1, 0, 2, 3, 1, 2, 2, 2, 2, 0},
    {0, 4, 2, 3, 1, 0, 2, 2, 2, 2, 1, 0, 0, 1, 1, 3, 2, 3, 2, 0},
    {0, 4, 2, 3, 1, 3, 1, 0, 0, 1, 1, 2, 0, 4, 2, 0, 2, 2, 2, 2},
    {0, 4, 2, 3, 2, 0, 1, 3, 1, 1, 1, 1, 0, 1, 2, 0, 1, 3, 1, 2},
    {0, 4, 2, 3, 2, 0, 2, 2, 0, 1, 1, 2, 0, 4, 2, 3, 1, 2, 1, 3},
    {0, 4, 2, 3, 2, 0, 2, 2, 2, 3, 2, 0, 0, 3, 2, 1, 1, 1, 2, 0},
    {0, 4, 2, 3, 2, 1, 1, 0, 2, 0, 2, 1, 0, 2, 2, 0, 1, 3, 1, 3},
    {0, 4, 2, 3, 2, 4, 2, 4, 1, 0, 1, 0, 0, 2, 2, 1, 2, 3, 2, 0},
    {0, 4, 2, 4, 0, 2, 2, 3, 0, 1, 1, 0, 2, 1, 2, 1, 1, 2, 1, 3},
    {0, 4, 2, 4, 0, 4, 2, 0, 0, 3, 1, 2, 2, 1, 2, 2, 1, 2, 1, 0},
    {0, 4, 2, 4, 1, 4, 1, 2, 0, 1, 1, 0, 2, 2, 2, 0, 0, 3, 2, 4},
    {1, 0, 1, 1, 0, 2, 1, 4, 1, 4, 2, 1, 2, 1, 2, 4, 0, 3, 1, 0},
    {1, 0, 1, 1, 0, 3, 2, 4, 1, 1, 1, 4, 2, 4, 2, 1, 0, 2, 1, 0},
    {1, 0, 1, 1, 0, 4, 1, 3, 0, 2, 1, 0, 1, 2, 1, 2, 1, 1, 2, 1},
    {1, 0, 1, 1, 0, 4, 1, 3, 2, 1, 2, 1, 0, 2, 2, 3, 1, 3, 1, 0},
    {1, 0, 1, 1, 0, 4, 1, 3, 2, 1, 2, 3, 0, 2, 1, 0, 1, 3, 2, 1},
    {1, 0, 1, 2, 0, 3, 2, 2, 0, 4, 2, 1, 2, 2, 1, 1, 1, 1, 1, 0},
    {1, 0, 1, 2, 2, 2, 2, 2, 0, 4, 1, 3, 0, 1, 2, 3, 1, 3, 1, 0},
    {1, 0, 1, 2, 2, 2, 2, 3, 0, 4, 1, 3, 0, 1, 1, 0, 1, 3, 2, 2},
    {1, 0, 1, 2, 2, 3, 2, 2, 0, 1, 1, 3, 0, 4, 1, 0, 1, 2, 1, 3},
    {1, 0, 1, 2, 2, 4, 2, 0, 0, 1, 2, 4, 1, 2, 1, 4, 0, 3, 2, 2},
    {1, 0, 1, 3, 0, 2, 1, 0, 2, 3, 2, 1, 0, 4, 1, 1, 1, 1, 2, 3},
    {1, 0, 1, 3, 0, 4, 2, 3, 1, 1, 1, 0, 0, 2, 1, 1, 2, 3, 2, 1},
    {1, 0, 1, 3, 1, 3, 1, 2, 0, 1, 2, 2, 0, 4, 2, 3, 2, 2, 1, 0},
    {1, 0, 1, 3, 2, 4, 2, 3, 1, 3, 2, 4, 0, 1, 1, 0, 0, 2, 1, 4},
    {1, 0, 1, 4, 0, 2, 1, 1, 1, 4, 2, 1, 2, 1, 2, 4, 0, 3, 1, 0},
    {1, 0, 1, 4, 0, 2, 2, 0, 2, 4, 2, 1, 1, 1, 1, 4, 0, 3, 1, 1},
    {1, 0, 1, 4, 0, 2, 2, 4, 2, 4, 2, 1, 1, 1, 1, 0, 0, 3, 1, 1},
    {1, 0, 1, 4, 0, 3, 2, 4, 1, 1, 1, 0, 2, 4, 2, 1, 0, 2, 1, 1},
    {1, 0, 1, 4, 1, 3, 2, 4, 2, 4, 2, 3, 0, 2, 1, 0, 0, 1, 1, 3},
    {1, 0, 1, 4, 1, 4, 2, 3, 2, 3, 1, 0, 0, 1, 1, 3, 0, 2, 2, 4},
    {1, 0, 2, 1, 0, 2, 1, 3, 2, 3, 1, 0, 0, 4, 1, 1, 1, 1, 2, 3},
    {1, 0, 2, 1, 0, 2, 1, 4, 1, 4, 1, 1, 2, 1, 2, 4, 0, 3, 1, 0},
    {1, 0, 2, 1, 0, 2, 1, 4, 2, 4, 1, 0, 1, 1, 2, 4, 0, 3, 1, 1},
    {1, 0, 2, 1, 0, 2, 2, 3, 2, 3, 1, 0, 0, 4, 1, 3, 1, 1, 1, 1},
    {1, 0, 2, 1, 0, 2, 2, 4, 2, 4, 1, 0, 1, 1, 1, 1, 0, 3, 1, 4},
    {1, 0, 2, 1, 0, 4, 2, 3, 1, 1, 1, 3, 0, 2, 1, 0, 2, 3, 1, 1},
    {1, 0, 2, 2, 0, 4, 1, 1, 0, 3, 2, 1, 2, 1, 1, 2, 1, 2, 2, 0},
    {1, 0, 2, 2, 2, 3, 1, 2, 0, 1, 2, 3, 0, 4, 1, 0, 1, 2, 1, 3},
    {1, 0, 2, 2, 2, 4, 1, 2, 0, 1, 2, 4, 1, 2, 1, 4, 0, 3, 1, 0},
    {1, 0, 2, 3, 0, 2, 2, 1, 2, 3, 1, 1, 0, 4, 1, 0, 1, 1, 1, 3},
    {1, 0, 2, 3, 1, 3, 2, 4, 2, 4, 1, 0, 0, 2, 1, 3, 0, 1, 1, 4},
    {1, 0, 2, 3, 1, 4, 1, 3, 2, 3, 1, 4, 0, 1, 1, 0, 0, 2, 2, 4},
    {1, 0, 2, 3, 2, 4, 1, 3, 1, 3, 1, 4, 0, 1, 2, 0, 0, 2, 2, 4},
    {1, 0, 2, 3, 2, 4, 1, 3, 1, 3, 1, 4, 0, 1, 2, 4, 0, 2, 1, 0},
    {1, 0, 2, 3, 2, 4, 2, 4, 1, 3, 1, 4, 0, 1, 1, 3, 0, 2, 1, 0},
    {1, 0, 2, 4, 0, 2, 1, 4, 1, 4, 2, 1, 2, 1, 1, 0, 0, 3, 1, 1},
    {1, 0, 2, 4, 1, 3, 1, 4, 2, 4, 1, 0, 0, 2, 2, 3, 0, 1, 1, 3},
    {1, 0, 2, 4, 1, 3, 1, 4, 2, 4, 2, 3, 0, 2, 1, 0, 0, 1, 1, 3},
    {1, 0, 2, 4, 2, 3, 1, 4, 1, 4, 1, 3, 0, 2, 2, 3, 0, 1, 1, 0},
    {1, 1, 1, 0, 0, 2, 1, 1, 2, 0, 2, 3, 0, 4, 2, 0, 2, 3, 1, 3},
    {1, 1, 1, 0, 0, 2, 1, 2, 0, 3, 1, 1, 2, 0, 1, 4, 1, 2, 1, 0},
    {1, 1, 1, 0, 0, 2, 1, 3, 2, 0, 1, 4, 0, 3, 1, 1, 1, 3, 2, 0},
    {1, 1, 1, 0, 0, 2, 2, 3, 2, 0, 2, 0, 0, 4, 1, 1, 2, 3, 1, 3},
    {1, 1, 1, 1, 0, 1, 1, 2, 2, 4, 1, 0, 1, 2, 2, 4, 0, 3, 2, 2},
    {1, 1, 1, 1, 0, 1, 1, 4, 1, 3, 1, 0, 0, 3, 1, 0, 0, 2, 2, 2},
    {1, 1, 1, 1, 0, 1, 2, 2, 1, 3, 1, 0, 0, 4, 1, 2, 2, 2, 1, 3},
    {1, 1, 1, 1, 0, 1, 2, 3, 0, 2, 1, 0, 0, 4, 1, 3, 2, 2, 1, 0},
    {1, 1, 1, 1, 0, 1, 2, 4, 2, 4, 1, 3, 0, 2, 1, 4, 1, 3, 1, 0},
    {1, 1, 1, 1, 0, 2, 1, 3, 2, 4, 2, 1, 1, 3, 2, 4, 0, 0, 1, 4},
    {1, 1, 1, 1, 0, 2, 1, 3, 2, 4, 2, 4, 0, 1, 1, 0, 1, 3, 1, 4},
    {1, 1, 1, 1, 0, 2, 2, 1, 2, 4, 2, 3, 0, 0, 1, 4, 0, 0, 1, 3},
    {1, 1, 1, 1, 0, 2, 2, 3, 2, 3, 2, 4, 0, 0, 1, 3, 2, 0, 2, 0},
    {1, 1, 1, 1, 0, 2, 2, 3, 2, 4, 2, 1, 2, 3, 2, 4, 0, 0, 1, 4},
    {1, 1, 1, 1, 0, 2, 2, 4, 2, 4, 2, 1, 0, 0, 1, 2, 0, 0, 1, 3},
    {1, 1, 1, 1, 0, 3, 1, 2, 1, 4, 1, 0, 2, 2, 2, 2, 0, 1, 1, 4},
    {1, 1, 1, 1, 0, 3, 1, 4, 0, 0, 1, 2, 2, 2, 2, 1, 1, 4, 2, 2},
    {1, 1, 1, 1, 0, 3, 2, 2, 0, 0, 2, 3, 2, 4, 2, 1, 0, 0, 1, 2},
    {1, 1, 1, 1, 0, 3, 2, 4, 0, 1, 2, 2, 1, 4, 1, 4, 2, 2, 1, 0},
    {1, 1, 1, 1, 0, 3, 2, 4, 1, 3, 1, 2, 2, 4, 2, 1, 0, 0, 1, 2},
    {1, 1, 1, 1, 0, 3, 2, 4, 2, 4, 2, 2, 1, 2, 1, 0, 0, 1, 1, 4},
    {1, 1, 1, 1, 0, 4, 2, 2, 0, 4, 2, 2, 0, 0, 1, 3, 2, 3, 2, 3},
    {1, 1, 1, 1, 0, 4, 2, 3, 0, 1, 1, 0, 2, 2, 1, 3, 1, 3, 2, 2},
    {1, 1, 1, 1, 0, 4, 2, 3, 1, 2, 1, 3, 0, 0, 1, 2, 2, 3, 2, 1},
    {1, 1, 1, 1, 0, 4, 2, 3, 2, 4, 2, 4, 0, 0, 2, 2, 2, 3, 2, 1},
    {1, 1, 1, 1, 1, 3, 1, 2, 0, 1, 1, 3, 0, 4, 1, 0, 2, 2, 2, 2},
    {1, 1, 1, 1, 1, 4, 1, 2, 0, 1, 1, 4, 2, 2, 1, 0, 0, 3, 2, 2},
    {1, 1, 1, 1, 1, 4, 1, 2, 0, 1, 1, 4, 2, 2, 2, 2, 0, 3, 1, 0},
    {1, 1, 1, 1, 2, 2, 2, 3, 0, 4, 1, 0, 0, 1, 2, 2, 1, 3, 1, 3},
    {1, 1, 1, 1, 2, 2, 2, 4, 0, 3, 1, 0, 1, 4, 1, 4, 0, 1, 2, 2},
    {1, 1, 1, 1, 2, 3, 2, 2, 0, 1, 2, 3, 0, 4, 1, 0, 1, 2, 1, 2},
    {1, 1, 1, 1, 2, 4, 2, 1, 2, 3, 2, 3, 0, 3, 2, 4, 0, 0, 2, 2},
    {1, 1, 1, 2, 0, 1, 1, 3, 1, 3, 1, 2, 0, 4, 1, 1, 2, 2, 1, 0},
    {1, 1, 1, 2, 0, 3, 1, 4, 0, 0, 1, 1, 2, 2, 2, 1, 0, 2, 1, 3},
    {1, 1, 1, 2, 0, 3, 2, 2, 0, 0, 1, 3, 2, 4, 2, 1, 0, 0, 1, 1},
    {1, 1, 1, 2, 0, 3, 2, 2, 0, 0, 1, 4, 2, 2, 2, 1, 1, 4, 1, 1},
    {1, 1, 1, 2, 0, 3, 2, 2, 0, 0, 2, 4, 2, 2, 1, 4, 0, 3, 2, 1},
    {1, 1, 1, 2, 0, 3, 2, 2, 0, 3, 1, 0, 2, 4, 2, 4, 0, 0, 1, 4},
    {1, 1, 1, 2, 0, 4, 2, 1, 0, 0, 1, 1, 0, 0, 2, 1, 2, 2, 2, 3},
    {1, 1, 1, 2, 0, 4, 2, 2, 0, 0, 1, 3, 0, 4, 1, 1, 2, 2, 2, 1},
    {1, 1, 1, 2, 0, 4, 2, 2, 0, 0, 2, 3, 2, 3, 1, 1, 2, 2, 2, 1},
    {1, 1, 1, 2, 0, 4, 2, 3, 0, 0, 2, 1, 0, 0, 2, 1, 2, 2, 1, 1},
    {1, 1, 1, 2, 0, 4, 2, 3, 0, 4, 1, 3, 0, 0, 1, 3, 2, 3, 2, 1},
    {1, 1, 1, 2, 2, 3, 2, 3, 0, 1, 2, 2, 0, 4, 1, 2, 1, 2, 1, 0},
    {1, 1, 1, 3, 0, 2, 1, 1, 2, 3, 2, 1, 0, 0, 2, 4, 0, 0, 2, 1},
    {1, 1, 1, 3, 0, 2, 2, 1, 2, 3, 1, 1, 0, 0, 2, 4, 2, 4, 2, 3},
    {1, 1, 1, 3, 0, 2, 2, 3, 2, 0, 1, 1, 0, 4, 2, 0, 1, 3, 1, 0},
    {1, 1, 1, 3, 0, 2, 2, 3, 2, 3, 1, 1, 0, 0, 2, 4, 2, 4, 2, 1},
    {1, 1, 1, 3, 0, 2, 2, 4, 2, 3, 1, 1, 0, 0, 2, 1, 0, 0, 2, 1},
    {1, 1, 1, 3, 0, 2, 2, 4, 2, 3, 1, 4, 0, 0, 2, 3, 0, 2, 1, 0},
    {1, 1, 1, 3, 0, 2, 2, 4, 2, 3, 2, 3, 0, 0, 1, 1, 2, 0, 2, 4},
    {1, 1, 1, 3, 0, 2, 2, 4, 2, 3, 2, 3, 0, 0, 1, 1, 2, 4, 2, 1},
    {1, 1, 1, 3, 0, 2, 2, 4, 2, 4, 2, 1, 0, 0, 1, 2, 0, 0, 1, 1},
    {1, 1, 1, 3, 0, 4, 1, 1, 0, 0, 1, 1, 0, 2, 1, 3, 2, 2, 2, 4},
    {1, 1, 1, 3, 0, 4, 1, 2, 1, 2, 2, 1, 0, 0, 1, 1, 2, 3, 2, 3},
    {1, 1, 1, 3, 0, 4, 2, 2, 0, 0, 1, 2, 0, 4, 1, 2, 2, 2, 2, 1},
    {1, 1, 1, 3, 0, 4, 2, 2, 0, 4, 2, 1, 0, 0, 2, 3, 2, 3, 1, 1},
    {1, 1, 1, 3, 0, 4, 2, 3, 0, 4, 2, 0, 0, 0, 1, 2, 2, 3, 2, 2},
    {1, 1, 1, 3, 0, 4, 2, 3, 1, 2, 1, 1, 0, 0, 1, 2, 2, 3, 2, 1},
    {1, 1, 1, 3, 0, 4, 2, 3, 1, 2, 2, 1, 0, 0, 1, 2, 2, 3, 1, 1},
    {1, 1, 1, 4, 0, 1, 1, 3, 2, 4, 1, 0, 0, 2, 1, 1, 1, 3, 1, 4},
    {1, 1, 1, 4, 0, 2, 2, 1, 2, 4, 1, 1, 0, 0, 2, 3, 0, 0, 2, 3},
    {1, 1, 1, 4, 0, 2, 2, 1, 2, 4, 2, 3, 0, 0, 2, 0, 0, 0, 1, 1},
    {1, 1, 1, 4, 0, 2, 2, 1, 2, 4, 2, 4, 0, 2, 2, 3, 0, 0, 1, 3},
    {1, 1, 1, 4, 0, 3, 2, 1, 0, 1, 1, 1, 2, 4, 2, 2, 0, 0, 2, 4},
    {1, 1, 1, 4, 0, 3, 2, 1, 0, 3, 2, 1, 2, 4, 2, 4, 0, 0, 1, 2},
    {1, 1, 1, 4, 0, 3, 2, 1, 1, 2, 2, 4, 2, 4, 1, 1, 0, 0, 2, 2},
    {1, 1, 1, 4, 0, 3, 2, 2, 1, 2, 2, 1, 2, 4, 2, 4, 0, 0, 1, 1},
    {1, 1, 1, 4, 0, 3, 2, 2, 2, 0, 2, 0, 2, 4, 1, 1, 0, 0, 2, 4},
    {1, 1, 1, 4, 0, 3, 2, 2, 2, 0, 2, 0, 2, 4, 2, 4, 0, 0, 1, 1},
    {1, 1, 1, 4, 0, 3, 2, 4, 0, 3, 2, 0, 2, 4, 2, 1, 0, 0, 1, 2},
    {1, 1, 1, 4, 0, 3, 2, 4, 0, 3, 2, 1, 2, 4, 1, 2, 0, 0, 2, 2},
    {1, 1, 1, 4, 0, 3, 2, 4, 2, 0, 2, 4, 2, 4, 1, 1, 0, 0, 2, 2},
    {1, 1, 2, 0, 0, 2, 2, 3, 0, 4, 1, 1, 2, 2, 2, 2, 2, 0, 1, 0},
    {1, 1, 2, 1, 0, 0, 2, 3, 0, 2, 1, 4, 2, 2, 2, 2, 0, 0, 2, 3},
    {1, 1, 2, 1, 0, 0, 2, 3, 2, 3, 2, 2, 0, 4, 2, 4, 1, 2, 1, 1},
    {1, 1, 2, 1, 0, 1, 1, 4, 2, 4, 1, 3, 0, 2, 1, 4, 1, 3, 1, 0},
    {1, 1, 2, 1, 0, 1, 2, 3, 2, 3, 1, 4, 1, 4, 1, 0, 0, 2, 1, 3},
    {1, 1, 2, 2, 0, 1, 2, 2, 2, 4, 2, 4, 0, 0, 1, 4, 0, 4, 1, 3},
    {1, 1, 2, 2, 0, 3, 1, 2, 0, 0, 1, 4, 2, 4, 2, 1, 0, 0, 1, 1},
    {1, 1, 2, 2, 0, 3, 2, 4, 0, 0, 1, 2, 2, 2, 2, 1, 2, 4, 1, 1},
    {1, 1, 2, 2, 0, 3, 2, 4, 2, 3, 2, 3, 2, 4, 1, 1, 0, 0, 2, 1},
    {1, 1, 2, 2, 0, 4, 1, 2, 0, 0, 1, 1, 1, 3, 2, 1, 2, 2, 1, 3},
    {1, 1, 2, 2, 0, 4, 1, 2, 0, 0, 1, 1, 2, 3, 2, 1, 2, 2, 2, 3},
    {1, 1, 2, 2, 0, 4, 1, 2, 0, 0, 2, 3, 0, 4, 2, 2, 2, 2, 1, 1},
    {1, 1, 2, 2, 0, 4, 2, 3, 0, 0, 1, 1, 0, 4, 2, 0, 2, 2, 1, 2},
    {1, 1, 2, 2, 2, 2, 2, 3, 0, 0, 1, 2, 0, 4, 2, 1, 1, 3, 1, 3},
    {1, 1, 2, 2, 2, 4, 2, 1, 0, 3, 2, 4, 1, 2, 1, 1, 0, 0, 1, 2},
    {1, 1, 2, 2, 2, 4, 2, 1, 2, 3, 2, 3, 0, 0, 2, 4, 0, 3, 1, 4},
    {1, 1, 2, 3, 0, 2, 1, 1, 2, 4, 2, 1, 0, 0, 1, 3, 0, 0, 1, 3},
    {1, 1, 2, 3, 0, 2, 1, 3, 2, 3, 2, 4, 0, 0, 1, 4, 0, 2, 1, 1},
    {1, 1, 2, 3, 0, 2, 1, 4, 2, 3, 2, 1, 0, 0, 1, 1, 0, 0, 1, 2},
    {1, 1, 2, 3, 0, 2, 2, 2, 2, 4, 2, 1, 2, 2, 2, 3, 0, 0, 1, 1},
    {1, 1, 2, 4, 0, 2, 1, 4, 2, 4, 2, 3, 2, 3, 2, 1, 0, 0, 1, 1},
    {1, 1, 2, 4, 0, 2, 2, 3, 2, 4, 2, 1, 2, 3, 1, 4, 0, 0, 1, 1},
    {1, 1, 2, 4, 0, 3, 1, 4, 2, 0, 1, 4, 2, 4, 2, 2, 0, 0, 1, 1},
    {1, 1, 2, 4, 0, 3, 2, 2, 2, 2, 1, 4, 2, 4, 2, 1, 0, 0, 1, 1},
    {1, 1, 2, 4, 2, 4, 1, 3, 0, 2, 1, 1, 1, 2, 1, 2, 0, 0, 2, 1},
    {1, 1, 2, 4, 2, 4, 2, 2, 2, 3, 1, 1, 0, 0, 2, 1, 0, 3, 2, 3},
    {1, 2, 1, 0, 0, 2, 2, 3, 2, 3, 2, 1, 0, 4, 1, 0, 1, 1, 1, 1},
    {1, 2, 1, 0, 0, 3, 1, 0, 2, 1, 2, 4, 1, 4, 1, 4, 0, 2, 2, 1},
    {1, 2, 1, 0, 0, 3, 1, 2, 0, 1, 1, 1, 2, 0, 1, 4, 1, 1, 1, 3},
    {1, 2, 1, 0, 0, 4, 2, 0, 0, 2, 2, 1, 0, 3, 1, 0, 2, 3, 2, 3},
    {1, 2, 1, 0, 1, 3, 1, 3, 0, 3, 2, 2, 0, 4, 1, 2, 2, 0, 1, 1},
    {1, 2, 1, 1, 0, 0, 1, 2, 0, 3, 2, 2, 2, 1, 2, 4, 0, 0, 2, 2},
    {1, 2, 1, 1, 0, 0, 1, 2, 0, 3, 2, 4, 2, 1, 2, 1, 2, 0, 2, 4},
    {1, 2, 1, 1, 0, 0, 1, 2, 0, 4, 1, 3, 1, 3, 2, 1, 2, 1, 2, 2},
    {1, 2, 1, 1, 0, 0, 1, 3, 0, 4, 2, 1, 1, 3, 2, 2, 2, 1, 1, 2},
    {1, 2, 1, 1, 0, 0, 1, 3, 0, 4, 2, 2, 0, 4, 1, 0, 2, 1, 2, 1},
    {1, 2, 1, 1, 0, 0, 1, 3, 0, 4, 2, 3, 0, 2, 1, 0, 2, 1, 2, 1},
    {1, 2, 1, 1, 0, 0, 1, 4, 0, 3, 2, 2, 2, 1, 1, 2, 1, 4, 2, 1},
    {1, 2, 1, 1, 0, 0, 1, 4, 0, 4, 2, 3, 0, 0, 2, 2, 2, 3, 1, 2},
    {1, 2, 1, 1, 0, 0, 2, 1, 0, 3, 2, 4, 2, 4, 1, 2, 0, 0, 2, 2},
    {1, 2, 1, 1, 0, 0, 2, 3, 0, 4, 2, 1, 0, 0, 1, 2, 2, 3, 2, 2},
    {1, 2, 1, 1, 0, 0, 2, 4, 0, 3, 2, 1, 2, 1, 1, 4, 0, 3, 2, 1},
    {1, 2, 1, 1, 1, 1, 1, 2, 0, 4, 2, 3, 0, 0, 1, 3, 2, 3, 2, 2},
    {1, 2, 1, 1, 1, 1, 1, 3, 0, 4, 2, 3, 0, 0, 2, 2, 2, 3, 1, 2},
    {1, 2, 1, 1, 1, 3, 1, 2, 0, 3, 2, 2, 2, 4, 2, 4, 0, 0, 1, 2},
    {1, 2, 1, 1, 1, 3, 1, 2, 0, 4, 1, 3, 0, 3, 1, 0, 2, 0, 1, 2},
    {1, 2, 1, 1, 1, 4, 1, 4, 0, 4, 2, 2, 0, 0, 1, 2, 2, 3, 2, 3},
    {1, 2, 1, 1, 1, 4, 2, 4, 0, 3, 1, 0, 2, 0, 1, 2, 0, 4, 2, 0},
    {1, 2, 1, 1, 2, 3, 1, 0, 0, 2, 1, 4, 1, 4, 1, 3, 0, 1, 1, 2},
    {1, 2, 1, 2, 0, 0, 1, 3, 0, 4, 2, 1, 1, 4, 1, 3, 2, 1, 2, 2},
    {1, 2, 1, 2, 0, 0, 1, 3, 0, 4, 2, 1, 2, 3, 1, 1, 2, 1, 2, 2},
    {1, 2, 1, 2, 0, 0, 1, 3, 0, 4, 2, 2, 1, 4, 1, 4, 2, 1, 2, 1},
    {1, 2, 1, 2, 0, 0, 1, 4, 0, 3, 2, 1, 2, 1, 2, 2, 1, 3, 1, 3},
    {1, 2, 1, 2, 0, 0, 2, 1, 0, 4, 1, 1, 2, 0, 2, 1, 2, 1, 2, 3},
    {1, 2, 1, 2, 0, 0, 2, 4, 0, 3, 2, 1, 2, 1, 2, 2, 2, 3, 2, 3},
    {1, 2, 1, 2, 0, 2, 1, 0, 1, 4, 1, 1, 2, 1, 1, 4, 0, 3, 2, 1},
    {1, 2, 1, 2, 0, 2, 1, 4, 1, 4, 1, 1, 2, 1, 1, 0, 0, 3, 2, 1},
    {1, 2, 1, 2, 0, 2, 2, 3, 2, 3, 2, 1, 0, 4, 1, 0, 1, 1, 1, 1},
    {1, 2, 1, 2, 0, 2, 2, 3, 2, 3, 2, 1, 0, 4, 1, 1, 1, 1, 1, 0},
    {1, 2, 1, 2, 0, 4, 1, 0, 1, 1, 1, 3, 0, 2, 1, 1, 2, 3, 2, 3},
    {1, 2, 1, 2, 0, 4, 1, 3, 0, 2, 2, 1, 0, 3, 1, 0, 2, 3, 1, 1},
    {1, 2, 1, 2, 1, 3, 1, 0, 0, 4, 1, 1, 0, 2, 1, 3, 2, 1, 2, 1},
    {1, 2, 1, 2, 1, 3, 1, 1, 0, 2, 1, 3, 0, 4, 1, 0, 2, 1, 2, 1},
    {1, 2, 1, 2, 1, 3, 2, 4, 0, 2, 1, 3, 2, 4, 1, 0, 0, 1, 2, 3},
    {1, 2, 1, 2, 1, 4, 1, 1, 0, 4, 2, 3, 0, 0, 1, 1, 2, 3, 2, 2},
    {1, 2, 1, 2, 2, 0, 2, 0, 0, 4, 2, 3, 0, 0, 1, 3, 2, 3, 2, 1},
    {1, 2, 1, 2, 2, 3, 1, 4, 0, 2, 2, 3, 1, 4, 1, 0, 0, 1, 1, 3},
    {1, 2, 1, 2, 2, 3, 2, 2, 0, 1, 1, 3, 0, 0, 2, 4, 0, 0, 1, 0},
    {1, 2, 1, 2, 2, 3, 2, 2, 0, 1, 2, 3, 0, 0, 1, 4, 0, 3, 1, 3},
    {1, 2, 1, 2, 2, 3, 2, 2, 0, 1, 2, 4, 0, 0, 1, 3, 0, 0, 1, 3},
    {1, 2, 1, 2, 2, 3, 2, 3, 0, 1, 1, 4, 1, 4, 1, 3, 0, 2, 1, 0},
    {1, 2, 1, 2, 2, 3, 2, 3, 0, 1, 2, 2, 0, 0, 1, 4, 0, 0, 1, 2},
    {1, 2, 1, 2, 2, 3, 2, 3, 0, 3, 2, 4, 2, 4, 2, 2, 0, 0, 2, 1},
    {1, 2, 1, 2, 2, 4, 2, 2, 0, 1, 2, 4, 1, 1, 1, 3, 0, 0, 1, 3},
    {1, 2, 1, 2, 2, 4, 2, 4, 0, 1, 2, 2, 2, 1, 2, 1, 0, 0, 2, 3},
    {1, 2, 1, 2, 2, 4, 2, 4, 0, 2, 2, 3, 0, 1, 1, 3, 0, 4, 1, 0},
    {1, 2, 1, 2, 2, 4, 2, 4, 2, 3, 2, 1, 0, 0, 2, 3, 0, 4, 2, 2},
    {1, 2, 1, 3, 0, 0, 1, 2, 0, 4, 2, 4, 0, 1, 1, 0, 2, 1, 2, 3},
    {1, 2, 1, 3, 0, 4, 2, 0, 0, 4, 2, 3, 0, 0, 2, 1, 2, 3, 1, 2},
    {1, 2, 1, 3, 0, 4, 2, 3, 0, 4, 2, 3, 0, 0, 2, 1, 2, 3, 1, 2},
    {1, 2, 1, 3, 1, 0, 1, 0, 0, 4, 2, 3, 0, 0, 1, 2, 2, 3, 1, 1},
    {1, 2, 1, 3, 1, 1, 2, 2, 0, 4, 2, 3, 0, 0, 1, 1, 2, 3, 1, 2},
    {1, 2, 1, 3, 1, 3, 2, 4, 0, 0, 2, 3, 2, 4, 2, 2, 0, 1, 2, 2},
    {1, 2, 1, 3, 1, 3, 2, 4, 2, 4, 2, 2, 0, 1, 1, 2, 0, 0, 2, 3},
    {1, 2, 1, 3, 1, 4, 1, 1, 0, 2, 1, 4, 2, 1, 1, 0, 0, 3, 1, 2},
    {1, 2, 1, 3, 2, 1, 2, 3, 0, 4, 2, 2, 0, 0, 1, 2, 2, 3, 2, 1},
    {1, 2, 1, 3, 2, 1, 2, 3, 0, 4, 2, 2, 0, 0, 2, 1, 2, 3, 1, 2},
    {1, 2, 1, 3, 2, 4, 2, 3, 0, 1, 1, 4, 0, 1, 1, 4, 0, 0, 2, 4},
    {1, 2, 1, 4, 0, 0, 1, 1, 0, 3, 2, 1, 2, 1, 2, 2, 1, 4, 1, 2},
    {1, 2, 1, 4, 0, 0, 1, 2, 0, 2, 2, 3, 2, 4, 2, 4, 0, 4, 1, 1},
    {1, 2, 1, 4, 0, 0, 2, 2, 0, 3, 2, 1, 2, 1, 1, 2, 1, 3, 1, 3},
    {1, 2, 1, 4, 0, 0, 2, 2, 0, 3, 2, 2, 2, 4, 2, 1, 0, 0, 1, 2},
    {1, 2, 1, 4, 0, 0, 2, 2, 0, 3, 2, 4, 2, 1, 1, 2, 0, 0, 2, 1},
    {1, 2, 1, 4, 0, 4, 1, 0, 0, 2, 1, 1, 0, 3, 1, 0, 1, 3, 1, 2},
    {1, 2, 1, 4, 1, 1, 2, 4, 0, 3, 2, 1, 2, 4, 2, 2, 0, 0, 1, 2},
    {1, 2, 1, 4, 1, 4, 2, 2, 0, 0, 2, 3, 0, 1, 1, 2, 2, 3, 2, 4},
    {1, 2, 1, 4, 2, 0, 2, 0, 0, 3, 2, 1, 2, 4, 2, 4, 0, 0, 1, 2},
    {1, 2, 1, 4, 2, 1, 1, 2, 0, 3, 1, 1, 2, 4, 2, 4, 0, 0, 2, 2},
    {1, 2, 1, 4, 2, 3, 2, 2, 0, 1, 2, 3, 0, 0, 1, 3, 1, 4, 1, 2},
    {1, 2, 1, 4, 2, 3, 2, 3, 0, 1, 2, 2, 0, 0, 1, 2, 0, 0, 1, 1},
    {1, 2, 1, 4, 2, 4, 1, 2, 0, 1, 2, 2, 1, 3, 2, 4, 0, 0, 1, 3},
    {1, 2, 1, 4, 2, 4, 1, 2, 0, 1, 2, 4, 2, 0, 2, 0, 0, 0, 2, 3},
    {1, 2, 1, 4, 2, 4, 2, 3, 0, 1, 1, 1, 0, 1, 1, 2, 0, 0, 2, 4},
    {1, 2, 1, 4, 2, 4, 2, 4, 0, 1, 2, 3, 0, 2, 2, 4, 0, 0, 1, 0},
    {1, 2, 1, 4, 2, 4, 2, 4, 0, 1, 2, 3, 2, 0, 2, 3, 0, 0, 1, 2},
    {1, 2, 2, 0, 2, 3, 2, 3, 0, 4, 2, 1, 0, 3, 1, 0, 2, 0, 1, 2},
    {1, 2, 2, 1, 0, 0, 1, 1, 0, 4, 1, 3, 1, 3, 1, 2, 2, 1, 2, 2},
    {1, 2, 2, 1, 0, 0, 1, 2, 0, 3, 1, 4, 2, 1, 2, 2, 0, 0, 1, 2},
    {1, 2, 2, 1, 0, 0, 1, 2, 0, 4, 1, 1, 0, 4, 2, 0, 2, 1, 2, 3},
    {1, 2, 2, 1, 0, 0, 1, 2, 0, 4, 1, 3, 1, 3, 1, 1, 2, 1, 2, 2},
    {1, 2, 2, 1, 0, 0, 1, 4, 0, 3, 1, 1, 2, 1, 2, 2, 0, 3, 1, 1},
    {1, 2, 2, 1, 0, 0, 2, 4, 2, 1, 1, 3, 1, 4, 1, 4, 0, 4, 2, 2},
    {1, 2, 2, 1, 0, 3, 2, 4, 2, 1, 2, 2, 0, 0, 1, 2, 2, 3, 2, 3},
    {1, 2, 2, 1, 2, 1, 1, 3, 0, 4, 2, 2, 0, 0, 1, 2, 2, 3, 2, 3},
    {1, 2, 2, 2, 0, 0, 1, 3, 0, 4, 2, 3, 0, 0, 1, 1, 2, 3, 1, 2},
    {1, 2, 2, 3, 0, 4, 1, 2, 0, 4, 1, 3, 0, 0, 1, 1, 2, 3, 2, 1},
    {1, 2, 2, 3, 1, 3, 1, 2, 2, 4, 2, 2, 0, 1, 2, 4, 0, 0, 1, 3},
    {1, 2, 2, 3, 2, 0, 1, 2, 0, 1, 1, 0, 2, 4, 2, 4, 0, 4, 2, 0},
    {1, 2, 2, 3, 2, 0, 2, 0, 0, 1, 1, 3, 0, 4, 1, 2, 2, 3, 1, 0},
    {1, 2, 2, 3, 2, 1, 1, 2, 0, 4, 2, 1, 0, 0, 1, 3, 2, 3, 2, 2},
    {1, 2, 2, 3, 2, 4, 1, 0, 2, 3, 2, 1, 0, 0, 2, 4, 0, 4, 2, 2},
    {1, 2, 2, 3, 2, 4, 2, 4, 0, 1, 2, 2, 2, 3, 1, 4, 0, 0, 1, 2},
    {1, 2, 2, 4, 0, 3, 2, 4, 2, 1, 1, 4, 1, 4, 1, 0, 0, 2, 2, 1},
    {1, 2, 2, 4, 2, 0, 2, 0, 0, 3, 1, 2, 2, 4, 2, 1, 0, 0, 1, 4},
    {1, 2, 2, 4, 2, 1, 1, 2, 0, 3, 2, 1, 2, 4, 2, 2, 0, 0, 1, 4},
    {1, 2, 2, 4, 2, 3, 1, 2, 0, 1, 2, 3, 0, 0, 1, 3, 2, 4, 2, 2},
    {1, 2, 2, 4, 2, 4, 2, 2, 0, 1, 2, 3, 2, 1, 2, 1, 0, 0, 1, 2},
    {1, 2, 2, 4, 2, 4, 2, 3, 0, 1, 1, 3, 0, 1, 1, 2, 0, 0, 1, 4},
    {1, 2, 2, 4, 2, 4, 2, 3, 0, 1, 1, 4, 0, 1, 1, 4, 0, 0, 1, 3},
    {1, 2, 2, 4, 2, 4, 2, 3, 0, 1, 1, 4, 0, 1, 2, 0, 0, 0, 1, 2},
    {1, 3, 1, 0, 0, 1, 1, 3, 2, 0, 1, 4, 0, 2, 2, 3, 1, 1, 1, 3},
    {1, 3, 1, 0, 0, 3, 2, 2, 0, 4, 1, 0, 2, 2, 2, 1, 1, 1, 1, 1},
    {1, 3, 1, 0, 2, 0, 2, 0, 0, 4, 1, 3, 0, 1, 2, 2, 2, 2, 1, 2},
    {1, 3, 1, 1, 0, 0, 1, 2, 1, 2, 2, 1, 0, 4, 2, 3, 2, 1, 1, 3},
    {1, 3, 1, 1, 0, 0, 1, 3, 1, 1, 2, 0, 0, 4, 1, 2, 2, 1, 2, 1},
    {1, 3, 1, 1, 0, 0, 1, 3, 2, 0, 2, 0, 0, 4, 2, 2, 2, 1, 2, 1},
    {1, 3, 1, 1, 0, 0, 1, 3, 2, 0, 2, 2, 0, 4, 2, 2, 2, 1, 2, 1},
    {1, 3, 1, 1, 0, 0, 1, 4, 0, 0, 1, 3, 0, 4, 2, 1, 2, 2, 2, 3},
    {1, 3, 1, 1, 0, 0, 1, 4, 2, 1, 2, 3, 0, 2, 2, 1, 0, 3, 1, 4},
    {1, 3, 1, 1, 0, 0, 2, 1, 0, 4, 2, 3, 0, 4, 2, 3, 2, 1, 1, 2},
    {1, 3, 1, 1, 0, 0, 2, 2, 2, 2, 2, 3, 0, 4, 2, 1, 2, 1, 1, 3},
    {1, 3, 1, 1, 0, 0, 2, 3, 0, 4, 2, 1, 0, 4, 2, 1, 2, 1, 1, 2},
    {1, 3, 1, 1, 0, 0, 2, 3, 1, 2, 1, 3, 0, 4, 2, 1, 2, 1, 1, 2},
    {1, 3, 1, 1, 0, 0, 2, 4, 2, 1, 1, 3, 0, 2, 2, 3, 0, 0, 2, 1},
    {1, 3, 1, 1, 1, 2, 1, 2, 2, 4, 2, 3, 0, 2, 2, 4, 0, 0, 1, 3},
    {1, 3, 1, 1, 1, 2, 1, 3, 2, 4, 2, 3, 0, 2, 2, 4, 0, 0, 1, 1},
    {1, 3, 1, 1, 1, 2, 2, 3, 2, 4, 2, 3, 0, 2, 2, 4, 0, 0, 2, 4},
    {1, 3, 1, 1, 1, 4, 1, 4, 2, 0, 1, 3, 0, 2, 2, 3, 0, 4, 1, 0},
    {1, 3, 1, 2, 0, 0, 1, 1, 0, 4, 1, 0, 0, 4, 2, 2, 2, 1, 2, 1},
    {1, 3, 1, 2, 0, 0, 1, 3, 1, 4, 1, 4, 0, 4, 2, 1, 2, 1, 2, 3},
    {1, 3, 1, 2, 0, 0, 2, 3, 0, 0, 2, 1, 0, 4, 2, 2, 2, 1, 1, 3},
    {1, 3, 1, 2, 0, 4, 2, 2, 0, 0, 1, 3, 0, 4, 2, 2, 2, 2, 2, 1},
    {1, 3, 1, 2, 0, 4, 2, 3, 0, 0, 1, 1, 0, 4, 2, 3, 2, 2, 2, 2},
    {1, 3, 1, 2, 1, 0, 1, 0, 0, 0, 1, 3, 0, 4, 1, 1, 2, 2, 2, 2},
    {1, 3, 1, 2, 1, 2, 1, 0, 0, 2, 1, 4, 0, 3, 1, 1, 0, 0, 1, 0},
    {1, 3, 1, 2, 1, 4, 1, 0, 0, 1, 1, 4, 2, 2, 2, 4, 0, 3, 2, 2},
    {1, 3, 1, 2, 2, 1, 2, 3, 0, 0, 2, 1, 0, 4, 2, 2, 2, 2, 1, 3},
    {1, 3, 1, 2, 2, 2, 1, 3, 0, 0, 2, 4, 0, 1, 2, 2, 0, 1, 2, 2},
    {1, 3, 1, 2, 2, 2, 1, 4, 0, 0, 2, 3, 0, 1, 2, 2, 0, 1, 2, 4},
    {1, 3, 1, 2, 2, 2, 2, 2, 0, 0, 1, 3, 0, 1, 2, 4, 1, 4, 2, 3},
    {1, 3, 1, 2, 2, 2, 2, 2, 0, 0, 1, 3, 0, 1, 2, 4, 2, 0, 2, 4},
    {1, 3, 1, 2, 2, 4, 1, 3, 1, 1, 2, 3, 0, 1, 2, 4, 0, 0, 2, 3},
    {1, 3, 1, 2, 2, 4, 1, 3, 1, 2, 2, 3, 0, 1, 2, 4, 0, 0, 1, 4},
    {1, 3, 1, 2, 2, 4, 2, 3, 0, 0, 2, 0, 0, 1, 1, 3, 0, 0, 2, 4},
    {1, 3, 1, 2, 2, 4, 2, 3, 1, 2, 1, 4, 0, 1, 2, 4, 0, 0, 1, 3},
    {1, 3, 1, 3, 0, 0, 1, 1, 2, 1, 2, 4, 0, 2, 2, 1, 0, 2, 2, 1},
    {1, 3, 1, 3, 0, 0, 2, 2, 0, 1, 2, 4, 2, 2, 2, 3, 2, 1, 2, 1},
    {1, 3, 1, 3, 0, 0, 2, 3, 0, 1, 2, 2, 2, 2, 2, 4, 2, 1, 2, 1},
    {1, 3, 1, 3, 0, 2, 1, 0, 1, 4, 1, 4, 2, 1, 2, 4, 0, 3, 2, 1},
    {1, 3, 1, 3, 0, 3, 1, 2, 0, 4, 1, 1, 1, 2, 2, 1, 2, 1, 1, 0},
    {1, 3, 1, 3, 0, 3, 2, 4, 1, 1, 1, 1, 2, 4, 2, 1, 0, 2, 1, 0},
    {1, 3, 1, 3, 0, 4, 1, 0, 0, 3, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2},
    {1, 3, 1, 3, 1, 0, 1, 0, 2, 4, 1, 1, 0, 2, 2, 4, 0, 0, 1, 4},
    {1, 3, 1, 3, 1, 0, 1, 0, 2, 4, 2, 4, 0, 2, 1, 1, 0, 0, 1, 4},
    {1, 3, 1, 3, 1, 2, 1, 0, 0, 3, 1, 2, 0, 4, 2, 1, 2, 1, 1, 1},
    {1, 3, 1, 3, 1, 4, 1, 0, 2, 1, 1, 4, 0, 3, 1, 1, 0, 2, 2, 4},
    {1, 3, 1, 3, 1, 4, 1, 4, 0, 0, 1, 1, 0, 4, 2, 2, 2, 2, 2, 3},
    {1, 3, 1, 3, 2, 0, 2, 2, 0, 0, 1, 2, 0, 4, 2, 2, 2, 2, 2, 1},
    {1, 3, 1, 3, 2, 2, 1, 4, 1, 4, 1, 0, 0, 3, 2, 2, 0, 1, 1, 2},
    {1, 3, 1, 3, 2, 2, 2, 2, 0, 2, 1, 0, 0, 3, 2, 4, 0, 1, 2, 1},
    {1, 3, 1, 3, 2, 2, 2, 3, 0, 0, 1, 2, 0, 1, 2, 4, 0, 0, 1, 4},
    {1, 3, 1, 3, 2, 2, 2, 3, 0, 0, 1, 4, 0, 1, 2, 2, 1, 1, 1, 1},
    {1, 3, 1, 3, 2, 4, 2, 1, 1, 1, 1, 0, 0, 2, 2, 4, 0, 3, 1, 4},
    {1, 3, 1, 3, 2, 4, 2, 3, 1, 1, 1, 4, 0, 1, 2, 4, 0, 0, 1, 2},
    {1, 3, 1, 4, 0, 0, 1, 1, 1, 4, 2, 4, 2, 1, 2, 3, 0, 2, 2, 1},
    {1, 3, 1, 4, 0, 0, 1, 3, 2, 1, 1, 1, 0, 2, 2, 3, 1, 4, 2, 1},
    {1, 3, 1, 4, 0, 0, 2, 3, 2, 1, 1, 3, 0, 2, 2, 1, 0, 0, 2, 3},
    {1, 3, 1, 4, 0, 0, 2, 3, 2, 1, 1, 3, 0, 2, 2, 4, 0, 0, 2, 1},
    {1, 3, 1, 4, 0, 1, 2, 3, 2, 4, 2, 3, 0, 2, 1, 3, 0, 0, 1, 1},
    {1, 3, 1, 4, 0, 2, 2, 1, 2, 4, 2, 3, 0, 2, 2, 4, 0, 0, 1, 1},
    {1, 3, 1, 4, 0, 2, 2, 4, 2, 4, 1, 1, 0, 2, 2, 4, 0, 0, 2, 1},
    {1, 3, 1, 4, 1, 4, 1, 0, 0, 1, 1, 4, 2, 2, 2, 4, 0, 3, 2, 2},
    {1, 3, 1, 4, 2, 0, 1, 0, 0, 1, 2, 0, 0, 2, 1, 3, 1, 2, 1, 2},
    {1, 3, 1, 4, 2, 2, 1, 3, 0, 0, 2, 3, 0, 1, 2, 4, 0, 0, 2, 2},
    {1, 3, 1, 4, 2, 4, 1, 2, 0, 1, 1, 2, 0, 3, 1, 4, 1, 2, 1, 0},
    {1, 3, 1, 4, 2, 4, 1, 3, 2, 2, 2, 3, 0, 1, 2, 4, 0, 0, 2, 2},
    {1, 3, 1, 4, 2, 4, 2, 2, 2, 0, 2, 0, 0, 1, 2, 4, 0, 0, 1, 3},
    {1, 3, 1, 4, 2, 4, 2, 3, 1, 2, 1, 3, 0, 1, 2, 4, 0, 0, 1, 2},
    {1, 3, 1, 4, 2, 4, 2, 4, 1, 0, 1, 0, 0, 1, 1, 2, 0, 0, 1, 3},
    {1, 3, 2, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 4, 1, 3, 2, 2, 2, 3},
    {1, 3, 2, 1, 0, 0, 1, 1, 2, 2, 1, 3, 0, 4, 2, 2, 2, 1, 2, 3},
    {1, 3, 2, 1, 0, 0, 1, 1, 2, 4, 2, 3, 0, 2, 1, 4, 0, 0, 1, 3},
    {1, 3, 2, 1, 0, 0, 1, 3, 0, 0, 1, 3, 0, 4, 1, 1, 2, 2, 2, 3},
    {1, 3, 2, 1, 0, 0, 1, 3, 2, 1, 2, 4, 0, 2, 1, 1, 0, 2, 1, 1},
    {1, 3, 2, 1, 0, 0, 1, 3, 2, 2, 1, 1, 0, 4, 2, 2, 2, 1, 2, 3},
    {1, 3, 2, 1, 0, 2, 1, 1, 1, 1, 1, 3, 2, 4, 2, 3, 0, 0, 2, 4},
    {1, 3, 2, 1, 2, 1, 1, 4, 2, 4, 2, 3, 0, 2, 2, 4, 0, 0, 1, 3},
    {1, 3, 2, 1, 2, 2, 2, 2, 0, 4, 1, 3, 0, 2, 2, 4, 2, 0, 1, 0},
    {1, 3, 2, 2, 0, 0, 1, 1, 2, 2, 1, 3, 0, 4, 2, 3, 2, 1, 2, 1},
    {1, 3, 2, 2, 0, 4, 2, 0, 0, 0, 1, 3, 0, 4, 1, 2, 2, 2, 2, 1},
    {1, 3, 2, 2, 1, 4, 1, 4, 0, 0, 2, 3, 2, 2, 1, 1, 0, 4, 2, 3},
    {1, 3, 2, 2, 2, 2, 2, 3, 0, 0, 1, 2, 0, 1, 1, 4, 1, 4, 1, 3},
    {1, 3, 2, 2, 2, 2, 2, 4, 0, 0, 1, 3, 0, 1, 1, 2, 0, 1, 1, 4},
    {1, 3, 2, 2, 2, 2, 2, 4, 0, 0, 1, 4, 0, 1, 1, 2, 0, 1, 1, 3},
    {1, 3, 2, 3, 1, 4, 1, 4, 0, 1, 1, 3, 0, 0, 2, 2, 2, 2, 2, 4},
    {1, 3, 2, 4, 2, 1, 1, 4, 2, 4, 2, 3, 0, 2, 2, 1, 0, 0, 1, 3},
    {1, 3, 2, 4, 2, 2, 1, 0, 0, 0, 2, 3, 2, 4, 2, 1, 0, 2, 2, 2},
    {1, 3, 2, 4, 2, 2, 2, 2, 0, 2, 1, 3, 2, 4, 2, 1, 0, 0, 2, 3},
    {1, 4, 1, 0, 0, 0, 2, 0, 0, 2, 1, 1, 1, 2, 1, 2, 0, 4, 1, 3},
    {1, 4, 1, 0, 0, 2, 1, 4, 2, 0, 2, 3, 2, 1, 2, 1, 0, 1, 2, 4},
    {1, 4, 1, 0, 0, 3, 1, 4, 2, 1, 2, 1, 2, 0, 2, 2, 0, 1, 2, 4},
    {1, 4, 1, 0, 1, 2, 1, 0, 0, 2, 1, 4, 2, 0, 1, 1, 0, 3, 1, 2},
    {1, 4, 1, 0, 1, 2, 1, 2, 0, 4, 2, 3, 0, 1, 1, 0, 2, 3, 2, 2},
    {1, 4, 1, 0, 1, 3, 1, 3, 0, 1, 1, 0, 0, 4, 2, 2, 2, 2, 2, 3},
    {1, 4, 1, 0, 2, 0, 1, 3, 0, 2, 1, 4, 1, 2, 1, 0, 0, 1, 1, 2},
    {1, 4, 1, 0, 2, 0, 2, 0, 0, 2, 1, 4, 1, 2, 1, 2, 0, 1, 1, 3},
    {1, 4, 1, 0, 2, 0, 2, 0, 1, 3, 1, 3, 0, 1, 1, 4, 0, 3, 1, 2},
    {1, 4, 1, 1, 0, 0, 1, 2, 1, 2, 2, 4, 2, 1, 1, 4, 0, 3, 2, 1},
    {1, 4, 1, 1, 0, 0, 1, 2, 2, 2, 1, 4, 2, 1, 2, 0, 0, 3, 2, 4},
    {1, 4, 1, 1, 0, 0, 1, 3, 2, 1, 1, 4, 1, 3, 2, 4, 0, 2, 2, 1},
    {1, 4, 1, 1, 0, 0, 1, 4, 0, 0, 1, 4, 2, 1, 2, 4, 0, 3, 2, 2},
    {1, 4, 1, 1, 0, 0, 1, 4, 0, 0, 1, 4, 2, 2, 2, 1, 0, 3, 2, 4},
    {1, 4, 1, 1, 0, 0, 1, 4, 2, 0, 2, 0, 2, 1, 2, 2, 0, 3, 2, 1},
    {1, 4, 1, 1, 0, 0, 2, 1, 2, 1, 1, 3, 1, 0, 2, 4, 0, 2, 2, 4},
    {1, 4, 1, 1, 0, 0, 2, 2, 0, 0, 2, 4, 2, 2, 1, 4, 0, 3, 2, 1},
    {1, 4, 1, 1, 0, 0, 2, 2, 2, 2, 2, 4, 2, 1, 1, 4, 0, 3, 2, 1},
    {1, 4, 1, 1, 0, 0, 2, 4, 0, 3, 1, 0, 2, 1, 1, 2, 0, 3, 2, 1},
    {1, 4, 1, 1, 0, 0, 2, 4, 1, 2, 1, 4, 2, 1, 1, 2, 0, 3, 2, 1},
    {1, 4, 1, 1, 0, 0, 2, 4, 2, 1, 1, 3, 0, 2, 2, 1, 0, 2, 2, 1},
    {1, 4, 1, 1, 0, 0, 2, 4, 2, 2, 1, 4, 2, 1, 2, 2, 0, 3, 2, 1},
    {1, 4, 1, 1, 0, 3, 1, 0, 0, 0, 1, 2, 2, 2, 2, 2, 0, 3, 2, 4},
    {1, 4, 1, 1, 0, 3, 1, 2, 0, 0, 1, 2, 2, 2, 2, 4, 0, 3, 2, 2},
    {1, 4, 1, 1, 1, 2, 1, 4, 2, 3, 2, 3, 0, 0, 1, 4, 0, 2, 2, 4},
    {1, 4, 1, 1, 2, 3, 2, 1, 1, 1, 2, 4, 0, 2, 1, 4, 0, 0, 2, 3},
    {1, 4, 1, 2, 0, 0, 1, 1, 0, 3, 2, 4, 2, 1, 2, 1, 0, 3, 2, 2},
    {1, 4, 1, 2, 0, 0, 2, 4, 0, 0, 1, 3, 2, 1, 1, 4, 0, 3, 2, 1},
    {1, 4, 1, 2, 0, 3, 2, 2, 0, 0, 1, 4, 2, 2, 2, 2, 0, 3, 2, 1},
    {1, 4, 1, 2, 0, 3, 2, 4, 0, 0, 1, 4, 2, 2, 2, 2, 0, 3, 2, 1},
    {1, 4, 1, 2, 1, 1, 2, 2, 0, 0, 1, 4, 2, 2, 2, 4, 0, 3, 1, 1},
    {1, 4, 1, 2, 1, 2, 1, 0, 0, 2, 1, 0, 0, 1, 1, 4, 0, 4, 1, 3},
    {1, 4, 1, 2, 1, 3, 1, 3, 0, 1, 1, 0, 0, 4, 2, 2, 2, 2, 2, 3},
    {1, 4, 1, 2, 2, 2, 1, 4, 0, 0, 2, 3, 2, 3, 2, 2, 0, 1, 2, 4},
    {1, 4, 1, 2, 2, 2, 2, 2, 0, 0, 1, 4, 2, 0, 2, 0, 0, 1, 2, 3},
    {1, 4, 1, 2, 2, 2, 2, 3, 0, 0, 2, 4, 0, 4, 2, 4, 0, 1, 2, 4},
    {1, 4, 1, 2, 2, 2, 2, 4, 0, 0, 1, 3, 0, 0, 2, 0, 0, 1, 2, 1},
    {1, 4, 1, 2, 2, 2, 2, 4, 0, 0, 1, 3, 2, 3, 1, 4, 0, 1, 2, 2},
    {1, 4, 1, 2, 2, 2, 2, 4, 0, 0, 2, 2, 2, 3, 1, 4, 0, 1, 1, 3},
    {1, 4, 1, 2, 2, 3, 2, 4, 0, 0, 1, 1, 0, 0, 1, 4, 0, 1, 2, 2},
    {1, 4, 1, 3, 0, 0, 1, 0, 1, 3, 1, 4, 0, 3, 1, 1, 0, 4, 1, 2},
    {1, 4, 1, 3, 0, 0, 1, 1, 2, 1, 2, 3, 0, 2, 2, 2, 0, 2, 2, 1},
    {1, 4, 1, 3, 0, 2, 1, 0, 2, 3, 2, 4, 0, 0, 1, 1, 0, 2, 2, 3},
    {1, 4, 1, 3, 0, 2, 1, 4, 2, 3, 2, 4, 0, 0, 1, 1, 0, 2, 2, 3},
    {1, 4, 1, 3, 0, 3, 1, 4, 1, 1, 1, 2, 2, 2, 1, 0, 0, 4, 1, 1},
    {1, 4, 1, 3, 0, 4, 2, 3, 1, 1, 1, 1, 0, 2, 1, 0, 2, 3, 2, 1},
    {1, 4, 1, 3, 1, 0, 1, 0, 2, 3, 1, 1, 0, 0, 2, 3, 0, 2, 1, 4},
    {1, 4, 1, 3, 2, 0, 2, 0, 0, 1, 1, 0, 1, 2, 1, 2, 0, 2, 1, 4},
    {1, 4, 1, 3, 2, 1, 1, 4, 2, 3, 2, 1, 0, 0, 2, 4, 0, 2, 2, 3},
    {1, 4, 1, 3, 2, 3, 1, 2, 0, 1, 2, 4, 0, 0, 2, 2, 0, 1, 2, 3},
    {1, 4, 1, 3, 2, 3, 1, 4, 1, 2, 2, 4, 0, 0, 1, 2, 0, 1, 2, 3},
    {1, 4, 1, 3, 2, 3, 2, 3, 2, 0, 2, 0, 0, 0, 1, 4, 0, 1, 2, 2},
    {1, 4, 1, 4, 0, 0, 1, 1, 0, 0, 1, 2, 2, 1, 2, 4, 0, 3, 2, 2},
    {1, 4, 1, 4, 0, 0, 1, 1, 2, 2, 2, 1, 2, 1, 2, 4, 0, 3, 1, 2},
    {1, 4, 1, 4, 0, 0, 1, 1, 2, 3, 2, 4, 0, 0, 1, 3, 0, 2, 2, 1},
    {1, 4, 1, 4, 0, 0, 1, 2, 1, 3, 1, 2, 2, 1, 2, 4, 0, 3, 2, 1},
    {1, 4, 1, 4, 0, 0, 1, 3, 2, 1, 2, 4, 1, 2, 1, 1, 0, 2, 2, 1},
    {1, 4, 1, 4, 0, 0, 2, 4, 1, 1, 1, 1, 0, 1, 2, 3, 2, 3, 1, 2},
    {1, 4, 1, 4, 0, 2, 1, 0, 2, 3, 2, 3, 0, 4, 1, 1, 1, 1, 1, 3},
    {1, 4, 1, 4, 0, 2, 1, 3, 2, 3, 1, 1, 1, 1, 1, 0, 0, 4, 2, 3},
    {1, 4, 1, 4, 0, 3, 2, 2, 2, 1, 1, 0, 1, 2, 2, 1, 0, 4, 1, 2},
    {1, 4, 1, 4, 1, 2, 1, 0, 0, 4, 2, 3, 0, 1, 1, 2, 2, 3, 2, 2},
    {1, 4, 1, 4, 1, 2, 1, 2, 2, 3, 2, 4, 0, 0, 1, 1, 0, 2, 2, 3},
    {1, 4, 1, 4, 1, 3, 1, 0, 0, 1, 2, 3, 0, 4, 2, 2, 2, 2, 1, 3},
    {1, 4, 1, 4, 1, 3, 1, 0, 2, 1, 2, 1, 0, 2, 1, 3, 0, 4, 1, 1},
    {1, 4, 1, 4, 1, 3, 1, 3, 0, 1, 1, 0, 0, 4, 2, 2, 2, 2, 2, 3},
    {1, 4, 1, 4, 2, 1, 2, 3, 2, 3, 2, 1, 0, 0, 1, 3, 0, 2, 2, 4},
    {1, 4, 1, 4, 2, 2, 2, 2, 0, 4, 1, 2, 0, 1, 1, 0, 1, 3, 1, 3},
    {1, 4, 1, 4, 2, 3, 1, 2, 1, 2, 2, 4, 0, 0, 1, 3, 0, 1, 2, 3},
    {1, 4, 1, 4, 2, 3, 2, 3, 0, 1, 1, 0, 0, 4, 1, 2, 1, 2, 1, 3},
    {1, 4, 1, 4, 2, 3, 2, 4, 1, 1, 1, 1, 0, 0, 1, 2, 0, 1, 2, 3},
    {1, 4, 1, 4, 2, 3, 2, 4, 2, 1, 2, 1, 0, 0, 2, 2, 0, 1, 2, 3},
    {1, 4, 2, 0, 0, 2, 2, 1, 1, 3, 1, 0, 2, 1, 2, 3, 0, 4, 2, 1},
    {1, 4, 2, 1, 0, 0, 1, 4, 2, 0, 2, 0, 2, 1, 2, 2, 0, 3, 1, 1},
    {1, 4, 2, 1, 0, 0, 1, 4, 2, 1, 2, 4, 1, 3, 1, 1, 0, 2, 1, 3},
    {1, 4, 2, 1, 0, 0, 2, 1, 0, 2, 2, 4, 2, 2, 2, 2, 2, 1, 2, 3},
    {1, 4, 2, 1, 0, 0, 2, 1, 1, 3, 2, 3, 0, 3, 2, 4, 2, 1, 1, 2},
    {1, 4, 2, 1, 0, 2, 2, 4, 0, 0, 1, 4, 2, 2, 2, 2, 2, 1, 2, 3},
    {1, 4, 2, 1, 2, 1, 1, 3, 2, 3, 1, 4, 0, 0, 2, 4, 0, 2, 2, 3},
    {1, 4, 2, 1, 2, 1, 1, 4, 0, 0, 1, 0, 2, 2, 2, 4, 0, 3, 2, 2},
    {1, 4, 2, 2, 0, 0, 1, 4, 0, 0, 1, 1, 2, 1, 2, 4, 0, 3, 1, 2},
    {1, 4, 2, 2, 0, 0, 1, 4, 0, 0, 1, 4, 2, 1, 2, 4, 0, 3, 1, 2},
    {1, 4, 2, 2, 0, 1, 1, 0, 2, 1, 2, 1, 2, 0, 1, 4, 0, 3, 2, 4},
    {1, 4, 2, 2, 1, 1, 2, 4, 0, 0, 1, 4, 2, 2, 1, 1, 0, 3, 1, 2},
    {1, 4, 2, 2, 2, 1, 1, 4, 0, 0, 1, 2, 2, 2, 2, 4, 0, 3, 2, 1},
    {1, 4, 2, 2, 2, 2, 2, 3, 0, 0, 1, 2, 0, 1, 1, 4, 0, 1, 1, 4},
    {1, 4, 2, 2, 2, 2, 2, 3, 0, 0, 1, 4, 0, 1, 2, 0, 0, 1, 1, 2},
    {1, 4, 2, 2, 2, 3, 2, 0, 2, 2, 1, 3, 0, 0, 1, 4, 0, 1, 2, 4},
    {1, 4, 2, 2, 2, 3, 2, 4, 0, 0, 1, 3, 0, 0, 1, 4, 0, 1, 1, 2},
    {1, 4, 2, 3, 0, 0, 1, 2, 2, 3, 2, 4, 0, 0, 1, 4, 0, 2, 1, 1},
    {1, 4, 2, 3, 0, 0, 1, 4, 2, 1, 2, 1, 2, 2, 2, 2, 0, 2, 2, 4},
    {1, 4, 2, 3, 0, 0, 2, 0, 0, 2, 1, 1, 2, 2, 2, 2, 0, 4, 2, 3},
    {1, 4, 2, 3, 0, 2, 1, 1, 2, 3, 2, 1, 0, 0, 1, 4, 0, 2, 1, 3},
    {1, 4, 2, 3, 1, 2, 1, 4, 2, 3, 2, 4, 0, 0, 1, 4, 0, 2, 1, 1},
    {1, 4, 2, 3, 2, 1, 1, 4, 2, 3, 2, 4, 0, 0, 1, 3, 0, 2, 2, 1},
    {1, 4, 2, 3, 2, 3, 2, 4, 1, 2, 1, 4, 0, 0, 1, 3, 0, 1, 1, 2},
    {1, 4, 2, 4, 2, 2, 2, 1, 0, 3, 1, 2, 1, 1, 1, 4, 0, 0, 2, 2},
    {2, 0, 1, 1, 0, 2, 1, 3, 1, 3, 2, 0, 0, 4, 2, 3, 2, 1, 2, 1},
    {2, 0, 1, 1, 0, 2, 1, 4, 1, 4, 2, 0, 2, 1, 2, 1, 0, 3, 2, 4},
    {2, 0, 1, 1, 0, 2, 2, 3, 1, 3, 2, 0, 0, 4, 2, 1, 2, 1, 1, 3},
    {2, 0, 1, 1, 0, 2, 2, 4, 1, 4, 2, 0, 2, 1, 1, 4, 0, 3, 2, 1},
    {2, 0, 1, 1, 0, 2, 2, 4, 2, 4, 2, 1, 1, 1, 1, 4, 0, 3, 2, 0},
    {2, 0, 1, 1, 0, 4, 1, 3, 2, 1, 2, 3, 0, 2, 2, 0, 1, 3, 2, 1},
    {2, 0, 1, 2, 0, 4, 2, 1, 0, 3, 1, 1, 1, 1, 2, 2, 2, 2, 1, 0},
    {2, 0, 1, 2, 1, 3, 2, 2, 0, 1, 1, 3, 0, 4, 2, 0, 2, 2, 2, 3},
    {2, 0, 1, 2, 1, 4, 2, 2, 0, 1, 1, 4, 2, 2, 2, 4, 0, 3, 2, 0},
    {2, 0, 1, 3, 1, 4, 1, 4, 2, 3, 2, 4, 0, 1, 2, 3, 0, 2, 2, 0},
    {2, 0, 1, 3, 1, 4, 2, 3, 2, 3, 2, 4, 0, 1, 1, 0, 0, 2, 1, 4},
    {2, 0, 1, 3, 1, 4, 2, 3, 2, 3, 2, 4, 0, 1, 1, 4, 0, 2, 2, 0},
    {2, 0, 1, 3, 2, 3, 1, 4, 1, 4, 2, 0, 0, 2, 2, 3, 0, 1, 2, 4},
    {2, 0, 1, 3, 2, 4, 2, 3, 1, 3, 2, 4, 0, 1, 2, 0, 0, 2, 1, 4},
    {2, 0, 1, 4, 0, 2, 2, 4, 2, 4, 1, 1, 1, 1, 2, 0, 0, 3, 2, 1},
    {2, 0, 1, 4, 1, 3, 2, 4, 2, 4, 2, 3, 0, 2, 1, 3, 0, 1, 2, 0},
    {2, 0, 1, 4, 2, 3, 2, 4, 1, 4, 1, 3, 0, 2, 2, 0, 0, 1, 2, 3},
    {2, 0, 1, 4, 2, 3, 2, 4, 1, 4, 2, 0, 0, 2, 1, 3, 0, 1, 2, 3},
    {2, 0, 2, 1, 0, 2, 2, 4, 2, 4, 1, 1, 1, 1, 1, 4, 0, 3, 2, 0},
    {2, 0, 2, 1, 0, 3, 1, 4, 2, 1, 2, 4, 1, 4, 1, 1, 0, 2, 2, 0},
    {2, 0, 2, 1, 0, 4, 2, 3, 0, 2, 2, 0, 2, 2, 2, 2, 2, 1, 1, 1},
    {2, 0, 2, 1, 0, 4, 2, 3, 1, 1, 1, 1, 0, 2, 1, 3, 2, 3, 2, 0},
    {2, 0, 2, 1, 0, 4, 2, 3, 1, 1, 1, 3, 0, 2, 2, 0, 2, 3, 1, 1},
    {2, 0, 2, 2, 0, 3, 1, 2, 0, 4, 1, 1, 1, 2, 2, 1, 2, 1, 2, 0},
    {2, 0, 2, 2, 1, 2, 1, 2, 0, 4, 2, 3, 0, 1, 1, 3, 2, 3, 2, 0},
    {2, 0, 2, 2, 1, 2, 1, 3, 0, 4, 2, 3, 0, 1, 2, 0, 2, 3, 1, 2},
    {2, 0, 2, 2, 1, 3, 1, 2, 0, 1, 2, 3, 0, 4, 2, 0, 2, 2, 2, 3},
    {2, 0, 2, 2, 1, 4, 1, 0, 0, 1, 1, 4, 2, 2, 2, 4, 0, 3, 1, 2},
    {2, 0, 2, 3, 0, 2, 2, 0, 1, 3, 1, 1, 0, 4, 2, 1, 2, 1, 1, 3},
    {2, 0, 2, 3, 0, 4, 1, 3, 2, 1, 2, 0, 0, 2, 2, 1, 1, 3, 1, 1},
    {2, 0, 2, 3, 1, 4, 1, 3, 2, 3, 1, 4, 0, 1, 2, 0, 0, 2, 2, 4},
    {2, 0, 2, 3, 2, 3, 2, 2, 0, 1, 1, 2, 0, 4, 1, 3, 1, 2, 2, 0},
    {2, 0, 2, 4, 0, 2, 1, 0, 1, 4, 1, 1, 2, 1, 2, 4, 0, 3, 2, 1},
    {2, 0, 2, 4, 0, 2, 1, 4, 1, 4, 1, 1, 2, 1, 2, 0, 0, 3, 2, 1},
    {2, 0, 2, 4, 0, 2, 2, 1, 2, 4, 1, 1, 1, 1, 1, 4, 0, 3, 2, 0},
    {2, 0, 2, 4, 0, 3, 1, 4, 2, 1, 2, 0, 1, 4, 1, 1, 0, 2, 2, 1},
    {2, 0, 2, 4, 2, 3, 1, 4, 1, 4, 1, 3, 0, 2, 2, 0, 0, 1, 2, 3},
    {2, 0, 2, 4, 2, 4, 1, 3, 1, 3, 2, 0, 0, 1, 2, 3, 0, 2, 1, 4},
    {2, 1, 1, 0, 0, 2, 1, 3, 0, 4, 2, 1, 1, 2, 1, 2, 1, 0, 2, 0},
    {2, 1, 1, 1, 0, 0, 1, 3, 0, 2, 2, 4, 1, 2, 1, 2, 0, 0, 1, 3},
    {2, 1, 1, 1, 0, 0, 1, 3, 1, 3, 1, 2, 0, 4, 1, 4, 2, 2, 2, 1},
    {2, 1, 1, 1, 0, 1, 1, 3, 1, 3, 2, 4, 2, 4, 2, 0, 0, 2, 2, 3},
    {2, 1, 1, 1, 0, 1, 2, 4, 1, 4, 2, 3, 0, 2, 2, 4, 2, 3, 2, 0},
    {2, 1, 1, 2, 0, 1, 1, 2, 1, 4, 1, 4, 0, 0, 2, 4, 0, 4, 2, 3},
    {2, 1, 1, 2, 0, 3, 1, 4, 0, 0, 2, 2, 1, 2, 1, 1, 1, 4, 2, 1},
    {2, 1, 1, 2, 0, 3, 1, 4, 1, 3, 1, 3, 1, 4, 2, 1, 0, 0, 1, 1},
    {2, 1, 1, 2, 0, 3, 2, 2, 0, 0, 2, 4, 1, 4, 1, 1, 0, 0, 2, 1},
    {2, 1, 1, 2, 0, 4, 1, 3, 0, 0, 2, 1, 0, 4, 1, 0, 1, 2, 2, 2},
    {2, 1, 1, 2, 0, 4, 1, 3, 1, 2, 2, 3, 0, 0, 2, 1, 1, 3, 1, 1},
    {2, 1, 1, 2, 0, 4, 2, 2, 0, 0, 1, 3, 0, 4, 1, 2, 1, 2, 2, 1},
    {2, 1, 1, 2, 0, 4, 2, 2, 0, 0, 2, 1, 1, 3, 1, 1, 1, 2, 1, 3},
    {2, 1, 1, 2, 1, 2, 1, 3, 0, 0, 2, 2, 0, 4, 1, 1, 2, 3, 2, 3},
    {2, 1, 1, 2, 1, 4, 1, 1, 0, 3, 1, 4, 2, 2, 2, 1, 0, 0, 2, 2},
    {2, 1, 1, 2, 1, 4, 1, 1, 1, 3, 1, 3, 0, 0, 1, 4, 0, 3, 2, 4},
    {2, 1, 1, 3, 0, 2, 1, 2, 1, 4, 1, 1, 1, 2, 1, 3, 0, 0, 2, 1},
    {2, 1, 1, 3, 0, 2, 2, 1, 1, 4, 1, 1, 0, 0, 2, 3, 0, 0, 2, 3},
    {2, 1, 1, 3, 0, 2, 2, 3, 1, 3, 1, 4, 0, 0, 2, 4, 0, 2, 2, 1},
    {2, 1, 1, 3, 0, 2, 2, 4, 1, 3, 1, 1, 0, 0, 2, 1, 0, 0, 2, 2},
    {2, 1, 1, 3, 0, 2, 2, 4, 1, 3, 1, 1, 0, 0, 2, 3, 2, 4, 2, 1},
    {2, 1, 1, 3, 0, 4, 2, 2, 2, 4, 2, 1, 0, 0, 2, 1, 1, 3, 1, 1},
    {2, 1, 1, 4, 0, 2, 1, 3, 1, 4, 1, 1, 1, 3, 2, 4, 0, 0, 2, 1},
    {2, 1, 1, 4, 0, 2, 2, 4, 1, 4, 1, 3, 1, 3, 1, 1, 0, 0, 2, 1},
    {2, 1, 1, 4, 0, 3, 1, 2, 1, 2, 2, 4, 1, 4, 1, 1, 0, 0, 2, 1},
    {2, 1, 1, 4, 0, 3, 2, 4, 1, 0, 2, 4, 1, 4, 1, 2, 0, 0, 2, 1},
    {2, 1, 1, 4, 1, 4, 1, 2, 1, 3, 2, 1, 0, 0, 1, 1, 0, 3, 1, 3},
    {2, 1, 1, 4, 1, 4, 2, 3, 0, 2, 2, 1, 2, 2, 2, 2, 0, 0, 1, 1},
    {2, 1, 2, 0, 0, 2, 1, 3, 1, 0, 1, 0, 0, 4, 2, 1, 1, 3, 2, 3},
    {2, 1, 2, 0, 0, 2, 2, 1, 1, 0, 1, 3, 0, 4, 1, 0, 1, 3, 2, 3},
    {2, 1, 2, 0, 0, 2, 2, 2, 0, 3, 2, 1, 1, 0, 2, 4, 2, 2, 2, 0},
    {2, 1, 2, 0, 0, 2, 2, 3, 1, 0, 2, 4, 0, 3, 2, 1, 2, 3, 1, 0},
    {2, 1, 2, 1, 0, 1, 1, 2, 2, 3, 2, 0, 0, 4, 2, 2, 1, 2, 2, 3},
    {2, 1, 2, 1, 0, 1, 1, 3, 0, 2, 2, 0, 0, 4, 2, 3, 1, 2, 2, 0},
    {2, 1, 2, 1, 0, 1, 1, 4, 1, 4, 2, 3, 0, 2, 2, 4, 2, 3, 2, 0},
    {2, 1, 2, 1, 0, 1, 2, 2, 1, 4, 2, 0, 2, 2, 1, 4, 0, 3, 1, 2},
    {2, 1, 2, 1, 0, 1, 2, 4, 2, 3, 2, 0, 0, 3, 2, 0, 0, 2, 1, 2},
    {2, 1, 2, 1, 0, 2, 1, 1, 1, 4, 1, 3, 0, 0, 2, 4, 0, 0, 2, 3},
    {2, 1, 2, 1, 0, 2, 1, 3, 1, 3, 1, 4, 0, 0, 2, 3, 1, 0, 1, 0},
    {2, 1, 2, 1, 0, 2, 1, 3, 1, 4, 1, 1, 1, 3, 1, 4, 0, 0, 2, 4},
    {2, 1, 2, 1, 0, 2, 1, 4, 1, 4, 1, 1, 0, 0, 2, 2, 0, 0, 2, 3},
    {2, 1, 2, 1, 0, 2, 2, 3, 1, 4, 1, 1, 2, 3, 1, 4, 0, 0, 2, 4},
    {2, 1, 2, 1, 0, 2, 2, 3, 1, 4, 1, 4, 0, 1, 2, 0, 2, 3, 2, 4},
    {2, 1, 2, 1, 0, 3, 1, 2, 0, 0, 1, 3, 1, 4, 1, 1, 0, 0, 2, 2},
    {2, 1, 2, 1, 0, 3, 1, 4, 0, 1, 1, 2, 2, 4, 2, 4, 1, 2, 2, 0},
    {2, 1, 2, 1, 0, 3, 1, 4, 1, 4, 1, 2, 2, 2, 2, 0, 0, 1, 2, 4},
    {2, 1, 2, 1, 0, 3, 1, 4, 2, 3, 2, 2, 1, 4, 1, 1, 0, 0, 2, 2},
    {2, 1, 2, 1, 0, 3, 2, 2, 2, 4, 2, 0, 1, 2, 1, 2, 0, 1, 2, 4},
    {2, 1, 2, 1, 0, 3, 2, 4, 0, 0, 2, 2, 1, 2, 1, 1, 2, 4, 1, 2},
    {2, 1, 2, 1, 0, 4, 1, 2, 0, 4, 1, 2, 0, 0, 2, 3, 1, 3, 1, 3},
    {2, 1, 2, 1, 0, 4, 1, 3, 0, 1, 2, 0, 1, 2, 2, 3, 2, 3, 1, 2},
    {2, 1, 2, 1, 0, 4, 1, 3, 1, 4, 1, 4, 0, 0, 1, 2, 1, 3, 1, 1},
    {2, 1, 2, 1, 0, 4, 1, 3, 2, 2, 2, 3, 0, 0, 2, 2, 1, 3, 1, 1},
    {2, 1, 2, 1, 0, 4, 2, 3, 0, 0, 2, 3, 0, 0, 1, 3, 1, 2, 1, 1},
    {2, 1, 2, 1, 1, 2, 1, 3, 0, 4, 2, 0, 0, 1, 1, 2, 2, 3, 2, 3},
    {2, 1, 2, 1, 1, 2, 1, 4, 0, 3, 2, 0, 2, 4, 2, 4, 0, 1, 1, 2},
    {2, 1, 2, 1, 1, 3, 1, 2, 0, 1, 1, 3, 0, 4, 2, 0, 2, 2, 2, 2},
    {2, 1, 2, 1, 1, 4, 1, 1, 1, 3, 1, 3, 0, 3, 1, 4, 0, 0, 1, 2},
    {2, 1, 2, 1, 2, 4, 2, 2, 0, 1, 2, 4, 1, 2, 1, 2, 0, 3, 2, 0},
    {2, 1, 2, 1, 2, 4, 2, 2, 0, 1, 2, 4, 1, 2, 2, 0, 0, 3, 1, 2},
    {2, 1, 2, 2, 0, 3, 1, 2, 0, 0, 1, 4, 1, 2, 2, 4, 0, 3, 1, 1},
    {2, 1, 2, 2, 0, 3, 1, 2, 0, 0, 2, 3, 1, 4, 1, 1, 0, 0, 2, 1},
    {2, 1, 2, 2, 0, 3, 1, 2, 0, 0, 2, 4, 1, 2, 1, 1, 2, 4, 2, 1},
    {2, 1, 2, 2, 0, 3, 1, 2, 0, 3, 2, 0, 1, 4, 1, 4, 0, 0, 2, 4},
    {2, 1, 2, 2, 0, 3, 2, 1, 2, 3, 2, 2, 1, 4, 1, 1, 0, 0, 1, 4},
    {2, 1, 2, 2, 0, 3, 2, 4, 0, 0, 2, 1, 1, 2, 1, 1, 0, 2, 2, 3},
    {2, 1, 2, 2, 0, 4, 1, 1, 0, 0, 2, 1, 0, 0, 1, 1, 1, 2, 1, 3},
    {2, 1, 2, 2, 0, 4, 1, 2, 0, 0, 1, 3, 1, 3, 2, 1, 1, 2, 1, 1},
    {2, 1, 2, 2, 0, 4, 1, 2, 0, 0, 2, 3, 0, 4, 2, 1, 1, 2, 1, 1},
    {2, 1, 2, 2, 0, 4, 1, 3, 0, 0, 1, 1, 0, 0, 1, 1, 1, 2, 2, 1},
    {2, 1, 2, 2, 0, 4, 1, 3, 0, 4, 2, 3, 0, 0, 2, 3, 1, 3, 1, 1},
    {2, 1, 2, 2, 1, 3, 1, 3, 0, 1, 1, 2, 0, 4, 2, 2, 2, 2, 2, 0},
    {2, 1, 2, 2, 1, 4, 1, 1, 0, 3, 1, 4, 2, 2, 1, 2, 0, 0, 2, 4},
    {2, 1, 2, 3, 0, 2, 1, 1, 1, 3, 2, 1, 0, 0, 1, 4, 1, 4, 1, 3},
    {2, 1, 2, 3, 0, 2, 1, 3, 1, 0, 2, 1, 0, 4, 1, 0, 2, 3, 2, 0},
    {2, 1, 2, 3, 0, 2, 1, 3, 1, 3, 2, 1, 0, 0, 1, 4, 1, 4, 1, 1},
    {2, 1, 2, 3, 0, 2, 1, 4, 1, 3, 1, 3, 0, 0, 2, 1, 1, 0, 1, 4},
    {2, 1, 2, 3, 0, 2, 1, 4, 1, 3, 1, 3, 0, 0, 2, 1, 1, 4, 1, 1},
    {2, 1, 2, 3, 0, 2, 1, 4, 1, 3, 2, 1, 0, 0, 1, 1, 0, 0, 1, 1},
    {2, 1, 2, 3, 0, 2, 1, 4, 1, 3, 2, 4, 0, 0, 1, 3, 0, 2, 2, 0},
    {2, 1, 2, 3, 0, 2, 1, 4, 1, 4, 1, 1, 0, 0, 2, 2, 0, 0, 2, 1},
    {2, 1, 2, 3, 0, 2, 2, 1, 1, 3, 1, 1, 0, 0, 1, 4, 0, 0, 1, 1},
    {2, 1, 2, 3, 0, 4, 1, 2, 0, 0, 2, 2, 0, 4, 1, 2, 1, 2, 1, 1},
    {2, 1, 2, 3, 0, 4, 1, 2, 0, 0, 2, 2, 0, 4, 2, 2, 1, 2, 1, 1},
    {2, 1, 2, 3, 0, 4, 1, 2, 0, 4, 1, 1, 0, 0, 1, 3, 1, 3, 2, 1},
    {2, 1, 2, 3, 0, 4, 1, 3, 0, 4, 1, 0, 0, 0, 2, 2, 1, 3, 1, 2},
    {2, 1, 2, 3, 0, 4, 1, 3, 2, 2, 1, 1, 0, 0, 2, 2, 1, 3, 2, 1},
    {2, 1, 2, 3, 0, 4, 1, 3, 2, 2, 2, 1, 0, 0, 2, 2, 1, 3, 1, 1},
    {2, 1, 2, 3, 0, 4, 2, 1, 0, 0, 2, 1, 0, 2, 2, 3, 1, 2, 1, 4},
    {2, 1, 2, 3, 0, 4, 2, 2, 2, 2, 1, 1, 0, 0, 2, 1, 1, 3, 1, 3},
    {2, 1, 2, 4, 0, 1, 2, 2, 0, 4, 2, 2, 0, 3, 2, 0, 2, 3, 2, 1},
    {2, 1, 2, 4, 0, 1, 2, 3, 1, 4, 2, 0, 0, 2, 2, 1, 2, 3, 2, 4},
    {2, 1, 2, 4, 0, 2, 1, 1, 1, 4, 1, 3, 0, 0, 1, 0, 0, 0, 2, 1},
    {2, 1, 2, 4, 0, 2, 1, 1, 1, 4, 1, 4, 0, 2, 1, 3, 0, 0, 2, 3},
    {2, 1, 2, 4, 0, 2, 1, 1, 1, 4, 2, 1, 0, 0, 1, 3, 0, 0, 1, 3},
    {2, 1, 2, 4, 0, 2, 2, 1, 1, 3, 1, 1, 0, 0, 2, 1, 0, 0, 2, 3},
    {2, 1, 2, 4, 0, 3, 1, 1, 0, 1, 2, 1, 1, 4, 1, 2, 0, 0, 1, 4},
    {2, 1, 2, 4, 0, 3, 1, 1, 0, 3, 1, 1, 1, 4, 1, 4, 0, 0, 2, 2},
    {2, 1, 2, 4, 0, 3, 1, 1, 2, 2, 1, 4, 1, 4, 2, 1, 0, 0, 1, 2},
    {2, 1, 2, 4, 0, 3, 1, 2, 1, 0, 1, 0, 1, 4, 1, 4, 0, 0, 2, 1},
    {2, 1, 2, 4, 0, 3, 1, 2, 2, 2, 1, 1, 1, 4, 1, 4, 0, 0, 2, 1},
    {2, 1, 2, 4, 0, 3, 1, 4, 0, 3, 1, 0, 1, 4, 1, 1, 0, 0, 2, 2},
    {2, 1, 2, 4, 0, 3, 1, 4, 0, 3, 1, 1, 1, 4, 2, 2, 0, 0, 1, 2},
    {2, 1, 2, 4, 0, 3, 1, 4, 1, 0, 1, 4, 1, 4, 2, 1, 0, 0, 1, 2},
    {2, 2, 1, 0, 1, 3, 1, 3, 0, 4, 1, 1, 0, 3, 2, 0, 1, 0, 2, 2},
    {2, 2, 1, 1, 0, 0, 1, 4, 1, 1, 2, 3, 2, 4, 2, 4, 0, 4, 1, 2},
    {2, 2, 1, 1, 0, 0, 2, 1, 0, 4, 2, 3, 2, 3, 2, 2, 1, 1, 1, 2},
    {2, 2, 1, 1, 0, 0, 2, 2, 0, 3, 2, 4, 1, 1, 1, 2, 0, 0, 2, 2},
    {2, 2, 1, 1, 0, 0, 2, 2, 0, 4, 2, 1, 0, 4, 1, 0, 1, 1, 1, 3},
    {2, 2, 1, 1, 0, 0, 2, 2, 0, 4, 2, 3, 2, 3, 2, 1, 1, 1, 1, 2},
    {2, 2, 1, 1, 0, 0, 2, 4, 0, 3, 2, 1, 1, 1, 1, 2, 0, 3, 2, 1},
    {2, 2, 1, 1, 0, 3, 1, 4, 1, 1, 1, 2, 0, 0, 2, 2, 1, 3, 1, 3},
    {2, 2, 1, 1, 1, 1, 2, 3, 0, 4, 1, 2, 0, 0, 2, 2, 1, 3, 1, 3},
    {2, 2, 1, 2, 0, 0, 2, 3, 0, 4, 1, 3, 0, 0, 2, 1, 1, 3, 2, 2},
    {2, 2, 1, 3, 0, 4, 2, 2, 0, 4, 2, 3, 0, 0, 2, 1, 1, 3, 1, 1},
    {2, 2, 1, 3, 1, 0, 2, 2, 0, 1, 2, 0, 1, 4, 1, 4, 0, 4, 1, 0},
    {2, 2, 1, 3, 1, 1, 2, 2, 0, 4, 1, 1, 0, 0, 2, 3, 1, 3, 1, 2},
    {2, 2, 1, 3, 1, 4, 1, 4, 0, 1, 1, 2, 1, 3, 2, 4, 0, 0, 2, 2},
    {2, 2, 1, 3, 1, 4, 2, 0, 1, 3, 1, 1, 0, 0, 1, 4, 0, 4, 1, 2},
    {2, 2, 1, 3, 2, 3, 2, 2, 1, 4, 1, 2, 0, 1, 1, 4, 0, 0, 2, 3},
    {2, 2, 1, 4, 0, 3, 1, 4, 1, 1, 2, 4, 2, 4, 2, 0, 0, 2, 1, 1},
    {2, 2, 1, 4, 1, 0, 1, 0, 0, 3, 2, 2, 1, 4, 1, 1, 0, 0, 2, 4},
    {2, 2, 1, 4, 1, 1, 2, 2, 0, 3, 1, 1, 1, 4, 1, 2, 0, 0, 2, 4},
    {2, 2, 1, 4, 1, 3, 2, 2, 0, 1, 1, 3, 0, 0, 2, 3, 1, 4, 1, 2},
    {2, 2, 1, 4, 1, 4, 1, 2, 0, 1, 1, 3, 1, 1, 1, 1, 0, 0, 2, 2},
    {2, 2, 1, 4, 1, 4, 1, 3, 0, 1, 2, 3, 0, 1, 2, 2, 0, 0, 2, 4},
    {2, 2, 1, 4, 1, 4, 1, 3, 0, 1, 2, 4, 0, 1, 1, 0, 0, 0, 2, 2},
    {2, 2, 1, 4, 1, 4, 1, 3, 0, 1, 2, 4, 0, 1, 2, 4, 0, 0, 2, 3},
    {2, 2, 2, 0, 0, 2, 1, 3, 1, 3, 1, 1, 0, 4, 2, 0, 2, 1, 2, 1},
    {2, 2, 2, 0, 0, 3, 2, 0, 1, 1, 1, 4, 2, 4, 2, 4, 0, 2, 1, 1},
    {2, 2, 2, 0, 0, 3, 2, 2, 0, 1, 2, 1, 1, 0, 2, 4, 2, 1, 2, 3},
    {2, 2, 2, 0, 0, 4, 1, 0, 0, 2, 1, 1, 0, 3, 2, 0, 1, 3, 1, 3},
    {2, 2, 2, 0, 1, 0, 2, 2, 0, 4, 2, 3, 2, 4, 2, 4, 0, 1, 1, 0},
    {2, 2, 2, 0, 2, 3, 2, 3, 0, 3, 1, 2, 0, 4, 2, 2, 1, 0, 2, 1},
    {2, 2, 2, 1, 0, 0, 1, 1, 0, 3, 1, 4, 1, 4, 2, 2, 0, 0, 1, 2},
    {2, 2, 2, 1, 0, 0, 1, 3, 0, 4, 1, 1, 0, 0, 2, 2, 1, 3, 1, 2},
    {2, 2, 2, 1, 0, 0, 1, 4, 0, 3, 1, 1, 1, 1, 2, 4, 0, 3, 1, 1},
    {2, 2, 2, 1, 0, 0, 1, 4, 0, 3, 1, 1, 1, 1, 2, 4, 0, 3, 1, 2},
    {2, 2, 2, 1, 0, 0, 2, 2, 0, 3, 1, 2, 1, 1, 1, 4, 0, 0, 1, 2},
    {2, 2, 2, 1, 0, 0, 2, 2, 0, 3, 1, 4, 1, 1, 1, 1, 1, 0, 1, 4},
    {2, 2, 2, 1, 0, 0, 2, 2, 0, 4, 2, 3, 2, 0, 2, 0, 1, 1, 1, 1},
    {2, 2, 2, 1, 0, 0, 2, 2, 0, 4, 2, 3, 2, 3, 1, 1, 1, 1, 1, 2},
    {2, 2, 2, 1, 0, 0, 2, 3, 0, 4, 1, 1, 2, 3, 1, 2, 1, 1, 2, 2},
    {2, 2, 2, 1, 0, 0, 2, 3, 0, 4, 1, 2, 0, 4, 2, 0, 1, 1, 1, 1},
    {2, 2, 2, 1, 0, 0, 2, 3, 0, 4, 1, 3, 0, 2, 2, 0, 1, 1, 1, 1},
    {2, 2, 2, 1, 0, 0, 2, 4, 0, 3, 1, 2, 1, 1, 2, 2, 2, 4, 1, 1},
    {2, 2, 2, 1, 0, 0, 2, 4, 0, 4, 1, 3, 0, 0, 1, 2, 1, 3, 2, 2},
    {2, 2, 2, 1, 1, 3, 2, 0, 0, 2, 2, 4, 2, 4, 2, 3, 0, 1, 2, 2},
    {2, 2, 2, 1, 2, 1, 2, 2, 0, 4, 1, 3, 0, 0, 2, 3, 1, 3, 1, 2},
    {2, 2, 2, 1, 2, 1, 2, 3, 0, 4, 1, 3, 0, 0, 1, 2, 1, 3, 2, 2},
    {2, 2, 2, 1, 2, 3, 2, 2, 0, 3, 1, 2, 1, 4, 1, 4, 0, 0, 2, 2},
    {2, 2, 2, 1, 2, 3, 2, 2, 0, 4, 2, 3, 0, 3, 2, 0, 1, 0, 2, 2},
    {2, 2, 2, 1, 2, 4, 1, 4, 0, 3, 2, 0, 1, 0, 2, 2, 0, 4, 1, 0},
    {2, 2, 2, 1, 2, 4, 2, 4, 0, 4, 1, 2, 0, 0, 2, 2, 1, 3, 1, 3},
    {2, 2, 2, 2, 0, 0, 1, 1, 0, 4, 2, 1, 1, 0, 1, 1, 1, 1, 1, 3},
    {2, 2, 2, 2, 0, 0, 1, 4, 0, 3, 1, 1, 1, 1, 1, 2, 1, 3, 1, 3},
    {2, 2, 2, 2, 0, 0, 2, 3, 0, 4, 1, 1, 1, 3, 2, 1, 1, 1, 1, 2},
    {2, 2, 2, 2, 0, 0, 2, 3, 0, 4, 1, 1, 2, 4, 2, 3, 1, 1, 1, 2},
    {2, 2, 2, 2, 0, 0, 2, 3, 0, 4, 1, 2, 2, 4, 2, 4, 1, 1, 1, 1},
    {2, 2, 2, 2, 0, 0, 2, 4, 0, 3, 1, 1, 1, 1, 1, 2, 2, 3, 2, 3},
    {2, 2, 2, 2, 0, 2, 1, 3, 1, 3, 1, 1, 0, 4, 2, 1, 2, 1, 2, 0},
    {2, 2, 2, 2, 0, 2, 2, 0, 2, 4, 2, 1, 1, 1, 2, 4, 0, 3, 1, 1},
    {2, 2, 2, 2, 0, 2, 2, 4, 2, 4, 2, 1, 1, 1, 2, 0, 0, 3, 1, 1},
    {2, 2, 2, 2, 0, 4, 2, 0, 2, 1, 2, 3, 0, 2, 2, 1, 1, 3, 1, 3},
    {2, 2, 2, 2, 0, 4, 2, 3, 0, 2, 1, 1, 0, 3, 2, 0, 1, 3, 2, 1},
    {2, 2, 2, 2, 1, 0, 1, 0, 0, 4, 1, 3, 0, 0, 2, 3, 1, 3, 1, 1},
    {2, 2, 2, 2, 1, 3, 1, 2, 0, 1, 1, 3, 0, 0, 2, 4, 0, 3, 2, 3},
    {2, 2, 2, 2, 1, 3, 1, 2, 0, 1, 1, 4, 0, 0, 2, 3, 0, 0, 2, 3},
    {2, 2, 2, 2, 1, 3, 1, 2, 0, 1, 2, 3, 0, 0, 1, 4, 0, 0, 2, 0},
    {2, 2, 2, 2, 1, 3, 1, 3, 0, 1, 1, 2, 0, 0, 2, 4, 0, 0, 2, 2},
    {2, 2, 2, 2, 1, 3, 1, 3, 0, 1, 2, 4, 2, 4, 2, 3, 0, 2, 2, 0},
    {2, 2, 2, 2, 1, 3, 1, 3, 0, 3, 1, 4, 1, 4, 1, 2, 0, 0, 1, 1},
    {2, 2, 2, 2, 1, 3, 2, 4, 0, 2, 1, 3, 2, 4, 2, 0, 0, 1, 2, 3},
    {2, 2, 2, 2, 1, 4, 1, 2, 0, 1, 1, 4, 2, 1, 2, 3, 0, 0, 2, 3},
    {2, 2, 2, 2, 1, 4, 1, 4, 0, 1, 1, 2, 1, 1, 1, 1, 0, 0, 1, 3},
    {2, 2, 2, 2, 1, 4, 1, 4, 0, 2, 1, 3, 0, 1, 2, 3, 0, 4, 2, 0},
    {2, 2, 2, 2, 1, 4, 1, 4, 1, 3, 1, 1, 0, 0, 1, 3, 0, 4, 1, 2},
    {2, 2, 2, 2, 2, 3, 1, 4, 0, 2, 2, 3, 1, 4, 2, 0, 0, 1, 1, 3},
    {2, 2, 2, 2, 2, 3, 2, 0, 0, 4, 2, 1, 0, 2, 2, 3, 1, 1, 1, 1},
    {2, 2, 2, 2, 2, 3, 2, 1, 0, 2, 2, 3, 0, 4, 2, 0, 1, 1, 1, 1},
    {2, 2, 2, 2, 2, 4, 2, 1, 0, 4, 1, 3, 0, 0, 2, 1, 1, 3, 1, 2},
    {2, 2, 2, 3, 0, 0, 2, 2, 0, 4, 1, 4, 0, 1, 2, 0, 1, 1, 1, 3},
    {2, 2, 2, 3, 0, 4, 1, 0, 0, 4, 1, 3, 0, 0, 1, 1, 1, 3, 2, 2},
    {2, 2, 2, 3, 0, 4, 1, 3, 0, 4, 1, 3, 0, 0, 1, 1, 1, 3, 2, 2},
    {2, 2, 2, 3, 1, 1, 1, 3, 0, 4, 1, 2, 0, 0, 1, 1, 1, 3, 2, 2},
    {2, 2, 2, 3, 1, 1, 1, 3, 0, 4, 1, 2, 0, 0, 2, 2, 1, 3, 1, 1},
    {2, 2, 2, 3, 1, 3, 1, 2, 0, 1, 1, 4, 0, 0, 2, 2, 0, 0, 2, 4},
    {2, 2, 2, 3, 1, 4, 1, 3, 0, 1, 2, 4, 0, 1, 2, 4, 0, 0, 1, 4},
    {2, 2, 2, 3, 2, 0, 2, 0, 0, 4, 1, 3, 0, 0, 2, 2, 1, 3, 2, 1},
    {2, 2, 2, 3, 2, 1, 1, 2, 0, 4, 1, 3, 0, 0, 2, 1, 1, 3, 2, 2},
    {2, 2, 2, 3, 2, 3, 1, 4, 0, 0, 1, 3, 1, 4, 1, 2, 0, 1, 1, 2},
    {2, 2, 2, 3, 2, 3, 1, 4, 1, 4, 1, 2, 0, 1, 2, 2, 0, 0, 1, 3},
    {2, 2, 2, 3, 2, 4, 2, 1, 0, 2, 2, 4, 1, 1, 2, 0, 0, 3, 2, 2},
    {2, 2, 2, 4, 0, 0, 1, 2, 0, 3, 1, 1, 1, 1, 2, 2, 2, 3, 2, 3},
    {2, 2, 2, 4, 0, 0, 1, 2, 0, 3, 1, 2, 1, 4, 1, 1, 0, 0, 2, 2},
    {2, 2, 2, 4, 0, 0, 1, 2, 0, 3, 1, 4, 1, 1, 2, 2, 0, 0, 1, 1},
    {2, 2, 2, 4, 0, 0, 2, 1, 0, 3, 1, 1, 1, 1, 1, 2, 2, 4, 2, 2},
    {2, 2, 2, 4, 0, 0, 2, 2, 0, 2, 1, 3, 1, 4, 1, 4, 0, 4, 2, 1},
    {2, 2, 2, 4, 0, 3, 2, 1, 1, 1, 1, 2, 0, 0, 1, 1, 2, 3, 2, 3},
    {2, 2, 2, 4, 0, 4, 2, 0, 0, 2, 2, 1, 0, 3, 2, 0, 2, 3, 2, 2},
    {2, 2, 2, 4, 1, 0, 1, 0, 0, 3, 1, 1, 1, 4, 1, 4, 0, 0, 2, 2},
    {2, 2, 2, 4, 1, 3, 1, 2, 0, 1, 1, 3, 0, 0, 2, 3, 2, 4, 2, 2},
    {2, 2, 2, 4, 1, 4, 1, 3, 0, 1, 2, 1, 0, 1, 2, 2, 0, 0, 1, 4},
    {2, 2, 2, 4, 1, 4, 1, 4, 0, 1, 1, 3, 0, 2, 1, 4, 0, 0, 2, 0},
    {2, 2, 2, 4, 1, 4, 1, 4, 0, 1, 1, 3, 1, 0, 1, 3, 0, 0, 2, 2},
    {2, 2, 2, 4, 1, 4, 2, 2, 0, 1, 1, 2, 2, 3, 1, 4, 0, 0, 2, 3},
    {2, 2, 2, 4, 1, 4, 2, 2, 0, 1, 1, 4, 1, 0, 1, 0, 0, 0, 1, 3},
    {2, 2, 2, 4, 2, 1, 1, 4, 0, 3, 1, 1, 1, 4, 1, 2, 0, 0, 2, 2},
    {2, 2, 2, 4, 2, 4, 1, 2, 0, 0, 1, 3, 0, 1, 2, 2, 1, 3, 1, 4},
    {2, 3, 1, 1, 0, 0, 2, 1, 0, 0, 2, 1, 0, 4, 2, 3, 1, 2, 1, 3},
    {2, 3, 1, 1, 0, 0, 2, 1, 1, 2, 2, 3, 0, 4, 1, 2, 1, 1, 1, 3},
    {2, 3, 1, 1, 0, 0, 2, 1, 1, 4, 1, 3, 0, 2, 2, 4, 0, 0, 2, 3},
    {2, 3, 1, 1, 0, 0, 2, 3, 0, 0, 2, 3, 0, 4, 2, 1, 1, 2, 1, 3},
    {2, 3, 1, 1, 0, 0, 2, 3, 1, 1, 1, 4, 0, 2, 2, 1, 0, 2, 2, 1},
    {2, 3, 1, 1, 0, 0, 2, 3, 1, 2, 2, 1, 0, 4, 1, 2, 1, 1, 1, 3},
    {2, 3, 1, 1, 0, 2, 2, 1, 2, 1, 2, 3, 1, 4, 1, 3, 0, 0, 1, 4},
    {2, 3, 1, 1, 1, 1, 2, 4, 1, 4, 1, 3, 0, 2, 1, 4, 0, 0, 2, 3},
    {2, 3, 1, 1, 1, 2, 1, 2, 0, 4, 2, 3, 0, 2, 1, 4, 1, 0, 2, 0},
    {2, 3, 1, 2, 0, 0, 2, 1, 1, 2, 2, 3, 0, 4, 1, 3, 1, 1, 1, 1},
    {2, 3, 1, 2, 0, 4, 1, 0, 0, 0, 2, 3, 0, 4, 2, 2, 1, 2, 1, 1},
    {2, 3, 1, 2, 1, 2, 1, 3, 0, 0, 2, 2, 0, 1, 2, 4, 2, 4, 2, 3},
    {2, 3, 1, 2, 1, 2, 1, 4, 0, 0, 2, 3, 0, 1, 2, 2, 0, 1, 2, 4},
    {2, 3, 1, 2, 1, 2, 1, 4, 0, 0, 2, 4, 0, 1, 2, 2, 0, 1, 2, 3},
    {2, 3, 1, 2, 2, 4, 2, 4, 0, 0, 1, 3, 1, 2, 2, 1, 0, 4, 1, 3},
    {2, 3, 1, 3, 2, 4, 2, 4, 0, 1, 2, 3, 0, 0, 1, 2, 1, 2, 1, 4},
    {2, 3, 1, 4, 0, 0, 2, 3, 1, 1, 1, 1, 0, 2, 1, 3, 1, 4, 2, 1},
    {2, 3, 1, 4, 1, 1, 2, 4, 1, 4, 1, 3, 0, 2, 1, 1, 0, 0, 2, 3},
    {2, 3, 1, 4, 1, 2, 2, 0, 0, 0, 1, 3, 1, 4, 1, 1, 0, 2, 1, 2},
    {2, 3, 2, 0, 0, 1, 2, 3, 1, 0, 2, 4, 0, 2, 1, 3, 2, 1, 2, 3},
    {2, 3, 2, 0, 0, 3, 1, 2, 0, 4, 2, 0, 1, 2, 1, 1, 2, 1, 2, 1},
    {2, 3, 2, 0, 1, 0, 1, 0, 0, 4, 2, 3, 0, 1, 1, 2, 1, 2, 2, 2},
    {2, 3, 2, 1, 0, 0, 1, 1, 0, 4, 1, 3, 0, 4, 1, 3, 1, 1, 2, 2},
    {2, 3, 2, 1, 0, 0, 1, 2, 1, 2, 1, 3, 0, 4, 1, 1, 1, 1, 2, 3},
    {2, 3, 2, 1, 0, 0, 1, 3, 0, 4, 1, 1, 0, 4, 1, 1, 1, 1, 2, 2},
    {2, 3, 2, 1, 0, 0, 1, 3, 2, 2, 2, 3, 0, 4, 1, 1, 1, 1, 2, 2},
    {2, 3, 2, 1, 0, 0, 1, 4, 1, 1, 2, 3, 0, 2, 1, 3, 0, 0, 1, 1},
    {2, 3, 2, 1, 0, 0, 2, 3, 1, 0, 1, 0, 0, 4, 1, 2, 1, 1, 1, 1},
    {2, 3, 2, 1, 0, 0, 2, 3, 1, 0, 1, 2, 0, 4, 1, 2, 1, 1, 1, 1},
    {2, 3, 2, 1, 0, 0, 2, 3, 2, 1, 1, 0, 0, 4, 2, 2, 1, 1, 1, 1},
    {2, 3, 2, 1, 0, 0, 2, 4, 0, 0, 2, 3, 0, 4, 1, 1, 1, 2, 1, 3},
    {2, 3, 2, 1, 0, 0, 2, 4, 1, 1, 1, 3, 0, 2, 1, 1, 0, 3, 2, 4},
    {2, 3, 2, 1, 2, 2, 1, 3, 1, 4, 1, 3, 0, 2, 1, 4, 0, 0, 1, 4},
    {2, 3, 2, 1, 2, 2, 2, 2, 1, 4, 1, 3, 0, 2, 1, 4, 0, 0, 2, 3},
    {2, 3, 2, 1, 2, 2, 2, 3, 1, 4, 1, 3, 0, 2, 1, 4, 0, 0, 2, 1},
    {2, 3, 2, 1, 2, 4, 2, 4, 1, 0, 2, 3, 0, 2, 1, 3, 0, 4, 2, 0},
    {2, 3, 2, 2, 0, 0, 1, 3, 0, 0, 1, 1, 0, 4, 1, 2, 1, 1, 2, 3},
    {2, 3, 2, 2, 0, 0, 2, 1, 0, 4, 2, 0, 0, 4, 1, 2, 1, 1, 1, 1},
    {2, 3, 2, 2, 0, 0, 2, 3, 2, 4, 2, 4, 0, 4, 1, 1, 1, 1, 1, 3},
    {2, 3, 2, 2, 0, 4, 1, 2, 0, 0, 2, 3, 0, 4, 1, 2, 1, 2, 1, 1},
    {2, 3, 2, 2, 0, 4, 1, 3, 0, 0, 2, 1, 0, 4, 1, 3, 1, 2, 1, 2},
    {2, 3, 2, 2, 1, 1, 1, 3, 0, 0, 1, 1, 0, 4, 1, 2, 1, 2, 2, 3},
    {2, 3, 2, 2, 1, 2, 1, 2, 0, 0, 2, 3, 0, 1, 1, 4, 1, 0, 1, 4},
    {2, 3, 2, 2, 1, 2, 1, 2, 0, 0, 2, 3, 0, 1, 1, 4, 2, 4, 1, 3},
    {2, 3, 2, 2, 1, 2, 2, 3, 0, 0, 1, 4, 0, 1, 1, 2, 0, 1, 1, 2},
    {2, 3, 2, 2, 1, 2, 2, 4, 0, 0, 1, 3, 0, 1, 1, 2, 0, 1, 1, 4},
    {2, 3, 2, 2, 1, 4, 1, 3, 2, 2, 2, 4, 0, 1, 1, 4, 0, 0, 2, 3},
    {2, 3, 2, 2, 1, 4, 2, 3, 2, 1, 1, 3, 0, 1, 1, 4, 0, 0, 1, 3},
    {2, 3, 2, 2, 1, 4, 2, 3, 2, 2, 1, 3, 0, 1, 1, 4, 0, 0, 2, 4},
    {2, 3, 2, 2, 2, 0, 2, 0, 0, 0, 2, 3, 0, 4, 2, 1, 1, 2, 1, 2},
    {2, 3, 2, 2, 2, 2, 2, 0, 0, 2, 2, 4, 0, 3, 2, 1, 0, 0, 2, 0},
    {2, 3, 2, 2, 2, 4, 2, 0, 0, 1, 2, 4, 1, 2, 1, 4, 0, 3, 1, 2},
    {2, 3, 2, 3, 0, 0, 1, 2, 0, 1, 1, 4, 1, 2, 1, 3, 1, 1, 1, 1},
    {2, 3, 2, 3, 0, 0, 1, 3, 0, 1, 1, 2, 1, 2, 1, 4, 1, 1, 1, 1},
    {2, 3, 2, 3, 0, 0, 2, 1, 1, 1, 1, 4, 0, 2, 1, 1, 0, 2, 1, 1},
    {2, 3, 2, 3, 0, 2, 2, 0, 2, 4, 2, 4, 1, 1, 1, 4, 0, 3, 1, 1},
    {2, 3, 2, 3, 0, 3, 1, 4, 2, 1, 2, 1, 1, 4, 1, 1, 0, 2, 2, 0},
    {2, 3, 2, 3, 0, 3, 2, 2, 0, 4, 2, 1, 2, 2, 1, 1, 1, 1, 2, 0},
    {2, 3, 2, 3, 0, 4, 1, 2, 0, 0, 2, 2, 0, 4, 1, 2, 1, 2, 1, 1},
    {2, 3, 2, 3, 0, 4, 2, 0, 0, 3, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2},
    {2, 3, 2, 3, 1, 0, 1, 2, 0, 0, 2, 2, 0, 4, 1, 2, 1, 2, 1, 1},
    {2, 3, 2, 3, 1, 2, 1, 2, 0, 2, 2, 0, 0, 3, 1, 4, 0, 1, 1, 1},
    {2, 3, 2, 3, 1, 2, 1, 3, 0, 0, 1, 4, 0, 1, 1, 2, 1, 1, 1, 1},
    {2, 3, 2, 3, 1, 2, 1, 3, 0, 0, 2, 2, 0, 1, 1, 4, 0, 0, 2, 4},
    {2, 3, 2, 3, 1, 2, 1, 3, 0, 0, 2, 4, 0, 1, 1, 2, 2, 1, 2, 1},
    {2, 3, 2, 3, 1, 4, 1, 1, 2, 1, 2, 0, 0, 2, 1, 4, 0, 3, 2, 4},
    {2, 3, 2, 3, 1, 4, 1, 3, 2, 1, 2, 4, 0, 1, 1, 4, 0, 0, 2, 2},
    {2, 3, 2, 3, 2, 0, 2, 0, 1, 4, 1, 4, 0, 2, 2, 1, 0, 0, 2, 4},
    {2, 3, 2, 3, 2, 0, 2, 0, 1, 4, 2, 1, 0, 2, 1, 4, 0, 0, 2, 4},
    {2, 3, 2, 3, 2, 2, 2, 0, 0, 3, 2, 2, 0, 4, 1, 1, 1, 1, 2, 1},
    {2, 3, 2, 3, 2, 4, 2, 0, 1, 1, 2, 4, 0, 3, 2, 1, 0, 2, 1, 4},
    {2, 3, 2, 3, 2, 4, 2, 4, 0, 0, 2, 1, 0, 4, 1, 2, 1, 2, 1, 3},
    {2, 3, 2, 4, 0, 0, 1, 3, 1, 1, 2, 3, 0, 2, 1, 4, 0, 0, 1, 1},
    {2, 3, 2, 4, 0, 0, 2, 1, 2, 4, 1, 4, 1, 1, 1, 3, 0, 2, 1, 1},
    {2, 3, 2, 4, 0, 0, 2, 3, 1, 1, 2, 1, 0, 2, 1, 3, 2, 4, 1, 1},
    {2, 3, 2, 4, 0, 1, 1, 3, 1, 4, 1, 3, 0, 2, 2, 3, 0, 0, 2, 1},
    {2, 3, 2, 4, 0, 2, 1, 1, 1, 4, 1, 3, 0, 2, 1, 4, 0, 0, 2, 1},
    {2, 3, 2, 4, 1, 0, 2, 0, 0, 1, 1, 0, 0, 2, 2, 3, 2, 2, 2, 2},
    {2, 3, 2, 4, 1, 2, 2, 3, 0, 0, 1, 3, 0, 1, 1, 4, 0, 0, 1, 2},
    {2, 3, 2, 4, 1, 4, 1, 2, 1, 0, 1, 0, 0, 1, 1, 4, 0, 0, 2, 3},
    {2, 3, 2, 4, 1, 4, 1, 3, 2, 2, 2, 3, 0, 1, 1, 4, 0, 0, 2, 2},
    {2, 3, 2, 4, 1, 4, 1, 4, 2, 0, 2, 0, 0, 1, 2, 2, 0, 0, 2, 3},
    {2, 3, 2, 4, 1, 4, 2, 2, 0, 1, 2, 2, 0, 3, 2, 4, 2, 2, 2, 0},
    {2, 3, 2, 4, 1, 4, 2, 3, 1, 2, 1, 3, 0, 1, 1, 4, 0, 0, 1, 2},
    {2, 3, 2, 4, 2, 4, 2, 0, 0, 1, 2, 4, 1, 2, 1, 4, 0, 3, 1, 2},
    {2, 4, 1, 0, 0, 2, 1, 1, 2, 3, 2, 0, 1, 1, 1, 3, 0, 4, 1, 1},
    {2, 4, 1, 1, 0, 0, 1, 1, 0, 2, 1, 4, 1, 2, 1, 2, 1, 1, 1, 3},
    {2, 4, 1, 1, 0, 0, 1, 1, 2, 3, 1, 3, 0, 3, 1, 4, 1, 1, 2, 2},
    {2, 4, 1, 1, 0, 0, 2, 4, 1, 0, 1, 0, 1, 1, 1, 2, 0, 3, 2, 1},
    {2, 4, 1, 1, 0, 0, 2, 4, 1, 1, 1, 4, 2, 3, 2, 1, 0, 2, 2, 3},
    {2, 4, 1, 1, 0, 2, 1, 4, 0, 0, 2, 4, 1, 2, 1, 2, 1, 1, 1, 3},
    {2, 4, 1, 1, 1, 1, 2, 3, 1, 3, 2, 4, 0, 0, 1, 4, 0, 2, 1, 3},
    {2, 4, 1, 1, 1, 1, 2, 4, 0, 0, 2, 0, 1, 2, 1, 4, 0, 3, 1, 2},
    {2, 4, 1, 2, 0, 0, 2, 4, 0, 0, 2, 1, 1, 1, 1, 4, 0, 3, 2, 2},
    {2, 4, 1, 2, 0, 0, 2, 4, 0, 0, 2, 4, 1, 1, 1, 4, 0, 3, 2, 2},
    {2, 4, 1, 2, 0, 1, 2, 0, 1, 1, 1, 1, 1, 0, 2, 4, 0, 3, 1, 4},
    {2, 4, 1, 2, 1, 1, 2, 4, 0, 0, 2, 2, 1, 2, 1, 4, 0, 3, 1, 1},
    {2, 4, 1, 2, 1, 2, 1, 3, 0, 0, 2, 2, 0, 1, 2, 4, 0, 1, 2, 4},
    {2, 4, 1, 2, 1, 2, 1, 4, 0, 0, 2, 2, 2, 3, 2, 4, 0, 1, 2, 3},
    {2, 4, 1, 2, 1, 3, 1, 0, 1, 2, 2, 3, 0, 0, 2, 4, 0, 1, 1, 4},
    {2, 4, 1, 2, 1, 3, 1, 4, 0, 0, 2, 3, 0, 0, 2, 4, 0, 1, 2, 2},
    {2, 4, 1, 2, 2, 1, 1, 4, 0, 0, 2, 4, 1, 2, 2, 1, 0, 3, 2, 2},
    {2, 4, 1, 3, 0, 0, 1, 0, 0, 2, 2, 1, 1, 2, 1, 2, 0, 4, 1, 3},
    {2, 4, 1, 3, 0, 0, 2, 4, 1, 1, 1, 1, 1, 2, 1, 2, 0, 2, 1, 4},
    {2, 4, 1, 3, 0, 2, 2, 1, 1, 3, 1, 1, 0, 0, 2, 4, 0, 2, 2, 3},
    {2, 4, 1, 3, 1, 1, 2, 4, 1, 3, 1, 4, 0, 0, 2, 3, 0, 2, 1, 1},
    {2, 4, 1, 3, 1, 3, 1, 4, 2, 2, 2, 4, 0, 0, 2, 3, 0, 1, 2, 2},
    {2, 4, 1, 3, 2, 2, 2, 4, 1, 3, 1, 4, 0, 0, 2, 4, 0, 2, 2, 1},
    {2, 4, 1, 4, 1, 2, 1, 1, 0, 3, 2, 2, 2, 1, 2, 4, 0, 0, 1, 2},
    {2, 4, 2, 0, 0, 0, 1, 0, 0, 2, 2, 1, 2, 2, 2, 2, 0, 4, 2, 3},
    {2, 4, 2, 0, 0, 2, 2, 4, 1, 0, 1, 3, 1, 1, 1, 1, 0, 1, 1, 4},
    {2, 4, 2, 0, 1, 0, 1, 0, 0, 2, 2, 4, 2, 2, 2, 2, 0, 1, 2, 3},
    {2, 4, 2, 0, 1, 0, 1, 0, 2, 3, 2, 3, 0, 1, 2, 4, 0, 3, 2, 2},
    {2, 4, 2, 0, 1, 0, 2, 3, 0, 2, 2, 4, 2, 2, 2, 0, 0, 1, 2, 2},
    {2, 4, 2, 0, 2, 2, 2, 0, 0, 2, 2, 4, 1, 0, 2, 1, 0, 3, 2, 2},
    {2, 4, 2, 0, 2, 2, 2, 2, 0, 4, 1, 3, 0, 1, 2, 0, 1, 3, 1, 2},
    {2, 4, 2, 0, 2, 3, 2, 3, 0, 1, 2, 0, 0, 4, 1, 2, 1, 2, 1, 3},
    {2, 4, 2, 1, 0, 0, 1, 1, 1, 1, 2, 3, 2, 0, 1, 4, 0, 2, 1, 4},
    {2, 4, 2, 1, 0, 0, 1, 2, 1, 2, 1, 4, 1, 1, 2, 4, 0, 3, 1, 1},
    {2, 4, 2, 1, 0, 0, 1, 4, 0, 3, 2, 0, 1, 1, 2, 2, 0, 3, 1, 1},
    {2, 4, 2, 1, 0, 0, 1, 4, 1, 1, 2, 3, 0, 2, 1, 1, 0, 2, 1, 1},
    {2, 4, 2, 1, 0, 0, 1, 4, 1, 2, 2, 4, 1, 1, 1, 2, 0, 3, 1, 1},
    {2, 4, 2, 1, 0, 0, 1, 4, 2, 2, 2, 4, 1, 1, 2, 2, 0, 3, 1, 1},
    {2, 4, 2, 1, 0, 0, 2, 2, 1, 2, 2, 4, 1, 1, 1, 0, 0, 3, 1, 4},
    {2, 4, 2, 1, 0, 0, 2, 2, 2, 2, 1, 4, 1, 1, 2, 4, 0, 3, 1, 1},
    {2, 4, 2, 1, 0, 0, 2, 3, 1, 1, 2, 4, 2, 3, 1, 4, 0, 2, 1, 1},
    {2, 4, 2, 1, 0, 0, 2, 4, 0, 0, 2, 4, 1, 1, 1, 4, 0, 3, 1, 2},
    {2, 4, 2, 1, 0, 0, 2, 4, 0, 0, 2, 4, 1, 2, 1, 1, 0, 3, 1, 4},
    {2, 4, 2, 1, 0, 0, 2, 4, 1, 0, 1, 0, 1, 1, 1, 2, 0, 3, 1, 1},
    {2, 4, 2, 1, 0, 3, 2, 0, 0, 0, 2, 2, 1, 2, 1, 2, 0, 3, 1, 4},
    {2, 4, 2, 1, 0, 3, 2, 2, 0, 0, 2, 2, 1, 2, 1, 4, 0, 3, 1, 2},
    {2, 4, 2, 1, 1, 3, 1, 1, 2, 1, 1, 4, 0, 2, 2, 4, 0, 0, 1, 3},
    {2, 4, 2, 1, 2, 2, 2, 4, 1, 3, 1, 3, 0, 0, 2, 4, 0, 2, 1, 4},
    {2, 4, 2, 2, 0, 0, 1, 4, 0, 0, 2, 3, 1, 1, 2, 4, 0, 3, 1, 1},
    {2, 4, 2, 2, 0, 0, 2, 1, 0, 3, 1, 4, 1, 1, 1, 1, 0, 3, 1, 2},
    {2, 4, 2, 2, 0, 3, 1, 2, 0, 0, 2, 4, 1, 2, 1, 2, 0, 3, 1, 1},
    {2, 4, 2, 2, 0, 3, 1, 4, 0, 0, 2, 4, 1, 2, 1, 2, 0, 3, 1, 1},
    {2, 4, 2, 2, 1, 2, 1, 2, 0, 0, 2, 3, 0, 1, 1, 3, 0, 1, 1, 4},
    {2, 4, 2, 2, 1, 2, 1, 2, 0, 0, 2, 4, 1, 0, 1, 0, 0, 1, 1, 3},
    {2, 4, 2, 2, 1, 2, 1, 4, 0, 0, 1, 2, 1, 3, 2, 4, 0, 1, 2, 3},
    {2, 4, 2, 2, 1, 2, 1, 4, 0, 0, 2, 3, 0, 0, 1, 0, 0, 1, 1, 1},
    {2, 4, 2, 2, 1, 2, 1, 4, 0, 0, 2, 3, 1, 3, 2, 4, 0, 1, 1, 2},
    {2, 4, 2, 2, 1, 2, 2, 4, 0, 0, 1, 3, 1, 3, 1, 2, 0, 1, 1, 4},
    {2, 4, 2, 2, 1, 3, 1, 4, 0, 0, 2, 1, 0, 0, 2, 4, 0, 1, 1, 2},
    {2, 4, 2, 2, 1, 3, 1, 4, 0, 0, 2, 4, 0, 0, 2, 4, 0, 1, 1, 3},
    {2, 4, 2, 2, 2, 1, 1, 2, 0, 0, 2, 4, 1, 2, 1, 4, 0, 3, 2, 1},
    {2, 4, 2, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 1, 2, 4, 0, 4, 2, 3},
    {2, 4, 2, 2, 2, 3, 2, 3, 0, 1, 2, 0, 0, 4, 1, 2, 1, 2, 1, 3},
    {2, 4, 2, 3, 0, 0, 2, 0, 2, 3, 2, 4, 0, 3, 2, 1, 0, 4, 2, 2},
    {2, 4, 2, 3, 0, 0, 2, 1, 1, 1, 1, 3, 0, 2, 1, 2, 0, 2, 1, 1},
    {2, 4, 2, 3, 0, 2, 2, 0, 1, 3, 1, 4, 0, 0, 2, 1, 0, 2, 1, 3},
    {2, 4, 2, 3, 0, 2, 2, 4, 1, 3, 1, 4, 0, 0, 2, 1, 0, 2, 1, 3},
    {2, 4, 2, 3, 0, 3, 2, 4, 2, 1, 2, 2, 1, 2, 2, 0, 0, 4, 2, 1},
    {2, 4, 2, 3, 0, 4, 1, 3, 2, 1, 2, 1, 0, 2, 2, 0, 1, 3, 1, 1},
    {2, 4, 2, 3, 1, 0, 1, 0, 0, 1, 2, 0, 2, 2, 2, 2, 0, 2, 2, 4},
    {2, 4, 2, 3, 1, 1, 2, 4, 1, 3, 1, 1, 0, 0, 1, 4, 0, 2, 1, 3},
    {2, 4, 2, 3, 1, 3, 1, 3, 1, 0, 1, 0, 0, 0, 2, 4, 0, 1, 1, 2},
    {2, 4, 2, 3, 1, 3, 2, 2, 0, 1, 1, 4, 0, 0, 1, 2, 0, 1, 1, 3},
    {2, 4, 2, 3, 1, 3, 2, 4, 2, 2, 1, 4, 0, 0, 2, 2, 0, 1, 1, 3},
    {2, 4, 2, 3, 2, 0, 2, 0, 1, 3, 1, 3, 0, 0, 2, 4, 0, 2, 2, 1},
    {2, 4, 2, 3, 2, 0, 2, 0, 1, 3, 2, 1, 0, 0, 1, 3, 0, 2, 2, 4},
    {2, 4, 2, 4, 0, 0, 1, 4, 2, 1, 2, 1, 0, 1, 1, 3, 1, 3, 2, 2},
    {2, 4, 2, 4, 0, 0, 2, 1, 1, 2, 1, 1, 1, 1, 1, 4, 0, 3, 2, 2},
    {2, 4, 2, 4, 0, 0, 2, 2, 2, 3, 2, 2, 1, 1, 1, 4, 0, 3, 1, 1},
    {2, 4, 2, 4, 0, 2, 2, 0, 1, 3, 1, 3, 0, 4, 2, 1, 2, 1, 2, 3},
    {2, 4, 2, 4, 0, 2, 2, 3, 1, 3, 2, 1, 2, 1, 2, 0, 0, 4, 1, 3},
    {2, 4, 2, 4, 0, 3, 1, 2, 1, 1, 2, 0, 2, 2, 1, 1, 0, 4, 2, 2},
    {2, 4, 2, 4, 1, 1, 1, 3, 1, 3, 1, 1, 0, 0, 2, 3, 0, 2, 1, 4},
    {2, 4, 2, 4, 1, 2, 1, 2, 0, 4, 2, 2, 0, 1, 2, 0, 2, 3, 2, 3},
    {2, 4, 2, 4, 1, 3, 1, 3, 0, 1, 2, 0, 0, 4, 2, 2, 2, 2, 2, 3},
    {2, 4, 2, 4, 1, 3, 1, 4, 1, 1, 1, 1, 0, 0, 1, 2, 0, 1, 1, 3},
    {2, 4, 2, 4, 1, 3, 1, 4, 2, 1, 2, 1, 0, 0, 2, 2, 0, 1, 1, 3},
    {2, 4, 2, 4, 1, 3, 2, 2, 2, 2, 1, 4, 0, 0, 2, 3, 0, 1, 1, 3},
    {2, 4, 2, 4, 2, 2, 2, 0, 0, 4, 1, 3, 0, 1, 2, 2, 1, 3, 1, 2},
    {2, 4, 2, 4, 2, 2, 2, 2, 0, 2, 2, 3, 0, 0, 2, 0, 0, 4, 2, 1},
    {2, 4, 2, 4, 2, 2, 2, 2, 1, 3, 1, 4, 0, 0, 2, 1, 0, 2, 1, 3},
    {2, 4, 2, 4, 2, 3, 2, 0, 0, 1, 1, 3, 0, 4, 1, 2, 1, 2, 2, 3},
    {2, 4, 2, 4, 2, 3, 2, 0, 1, 1, 1, 1, 0, 2, 2, 3, 0, 4, 2, 1},
};
// END AUTO M5 AUTOMATA

// BEGIN AUTO M6 AUTOMATA
static const vector<array<int, 24>> kSeedAutomataRawM6 = {
    {0, 0, 1, 1, 0, 2, 1, 3, 2, 1, 2, 1, 1, 4, 1, 2, 0, 4, 1, 5, 1, 0, 1, 0},
    {0, 0, 1, 1, 0, 2, 2, 5, 1, 1, 2, 3, 2, 4, 2, 4, 0, 4, 2, 1, 2, 0, 2, 3},
    {0, 0, 1, 1, 0, 3, 1, 3, 2, 5, 2, 5, 2, 4, 2, 0, 0, 4, 2, 2, 0, 5, 2, 1},
    {0, 0, 1, 1, 0, 3, 2, 4, 1, 3, 1, 3, 0, 5, 2, 1, 2, 0, 1, 4, 1, 1, 1, 2},
    {0, 0, 1, 1, 0, 4, 1, 5, 1, 1, 1, 3, 1, 4, 1, 0, 0, 2, 2, 1, 1, 0, 1, 4},
    {0, 0, 1, 1, 0, 5, 1, 4, 0, 2, 2, 4, 2, 0, 2, 0, 0, 3, 1, 0, 1, 2, 1, 0},
    {0, 0, 1, 1, 0, 5, 1, 5, 0, 2, 1, 3, 1, 0, 2, 4, 0, 2, 2, 1, 1, 2, 2, 0},
    {0, 0, 1, 1, 1, 3, 1, 3, 2, 0, 2, 3, 1, 4, 2, 5, 2, 5, 2, 2, 0, 3, 2, 2},
    {0, 0, 1, 1, 1, 5, 2, 4, 0, 4, 2, 5, 2, 0, 1, 5, 2, 0, 1, 3, 0, 5, 2, 2},
    {0, 0, 1, 2, 0, 3, 1, 4, 1, 5, 1, 5, 1, 1, 1, 1, 1, 0, 1, 0, 0, 5, 2, 1},
    {0, 0, 1, 2, 0, 3, 2, 2, 0, 4, 2, 1, 1, 2, 1, 1, 2, 1, 2, 5, 2, 0, 2, 0},
    {0, 0, 1, 2, 0, 5, 2, 1, 0, 3, 2, 4, 1, 1, 2, 2, 2, 0, 2, 0, 2, 2, 1, 1},
    {0, 0, 1, 2, 1, 0, 1, 0, 0, 4, 1, 3, 1, 5, 1, 3, 1, 2, 2, 2, 0, 5, 1, 1},
    {0, 0, 1, 2, 1, 4, 1, 4, 1, 5, 1, 5, 2, 0, 2, 1, 0, 1, 2, 3, 0, 5, 2, 4},
    {0, 0, 1, 2, 2, 0, 2, 1, 0, 3, 2, 3, 1, 4, 1, 4, 0, 4, 2, 5, 0, 1, 2, 0},
    {0, 0, 1, 2, 2, 0, 2, 4, 0, 4, 2, 3, 2, 4, 2, 0, 0, 5, 2, 1, 1, 2, 2, 2},
    {0, 0, 1, 2, 2, 5, 1, 4, 0, 1, 2, 3, 2, 1, 2, 0, 1, 0, 1, 1, 1, 2, 1, 5},
    {0, 0, 1, 3, 1, 0, 1, 0, 1, 3, 2, 4, 0, 5, 1, 1, 0, 2, 1, 4, 2, 4, 2, 3},
    {0, 0, 1, 3, 1, 0, 1, 1, 1, 3, 2, 5, 0, 4, 1, 5, 2, 5, 2, 3, 0, 2, 1, 1},
    {0, 0, 1, 3, 1, 1, 1, 5, 2, 3, 2, 3, 1, 5, 1, 4, 1, 0, 1, 0, 0, 2, 1, 1},
    {0, 0, 1, 3, 2, 0, 2, 0, 2, 3, 2, 3, 0, 5, 2, 1, 0, 2, 2, 4, 1, 4, 1, 4},
    {0, 0, 1, 3, 2, 3, 1, 3, 0, 2, 1, 5, 0, 1, 2, 4, 2, 2, 2, 3, 1, 0, 1, 0},
    {0, 0, 1, 3, 2, 3, 2, 5, 0, 1, 2, 3, 0, 2, 2, 4, 2, 2, 2, 2, 2, 0, 2, 0},
    {0, 0, 1, 4, 0, 1, 1, 5, 1, 1, 2, 3, 0, 2, 1, 1, 0, 2, 2, 4, 1, 0, 1, 0},
    {0, 0, 1, 4, 0, 2, 2, 0, 2, 0, 1, 5, 1, 5, 1, 1, 0, 3, 1, 0, 0, 5, 2, 1},
    {0, 0, 1, 4, 0, 3, 1, 0, 1, 5, 1, 5, 2, 4, 1, 1, 1, 1, 1, 2, 0, 0, 1, 1},
    {0, 0, 1, 4, 0, 5, 1, 3, 2, 1, 2, 4, 1, 0, 2, 4, 0, 2, 2, 1, 1, 4, 1, 1},
    {0, 0, 1, 4, 2, 4, 1, 3, 1, 3, 2, 4, 0, 1, 2, 3, 0, 2, 2, 5, 2, 0, 2, 0},
    {0, 0, 1, 5, 1, 3, 1, 3, 0, 2, 2, 3, 0, 1, 1, 4, 1, 0, 1, 2, 1, 2, 1, 0},
    {0, 0, 1, 5, 2, 5, 1, 4, 0, 1, 1, 2, 1, 0, 2, 2, 0, 1, 1, 3, 1, 2, 1, 3},
    {0, 0, 1, 5, 2, 5, 2, 2, 2, 0, 2, 0, 0, 3, 2, 5, 2, 3, 2, 3, 0, 1, 2, 4},
    {0, 0, 2, 1, 0, 2, 1, 5, 2, 1, 1, 3, 1, 4, 1, 4, 0, 4, 1, 1, 1, 0, 1, 3},
    {0, 0, 2, 1, 0, 2, 2, 3, 1, 1, 1, 1, 2, 4, 2, 2, 0, 4, 2, 5, 2, 0, 2, 0},
    {0, 0, 2, 1, 0, 3, 1, 4, 2, 3, 2, 3, 0, 5, 1, 1, 1, 0, 2, 4, 2, 1, 2, 2},
    {0, 0, 2, 1, 0, 3, 2, 3, 1, 5, 1, 5, 1, 4, 1, 0, 0, 4, 1, 2, 0, 5, 1, 1},
    {0, 0, 2, 1, 0, 4, 2, 5, 2, 1, 2, 3, 2, 4, 2, 0, 0, 2, 1, 1, 2, 0, 2, 4},
    {0, 0, 2, 1, 0, 5, 2, 4, 0, 2, 1, 4, 1, 0, 1, 0, 0, 3, 2, 0, 2, 2, 2, 0},
    {0, 0, 2, 1, 0, 5, 2, 5, 0, 2, 2, 3, 2, 0, 1, 4, 0, 2, 1, 1, 2, 2, 1, 0},
    {0, 0, 2, 1, 2, 3, 2, 3, 1, 0, 1, 3, 2, 4, 1, 5, 1, 5, 1, 2, 0, 3, 1, 2},
    {0, 0, 2, 1, 2, 5, 1, 4, 0, 4, 1, 5, 1, 0, 2, 5, 1, 0, 2, 3, 0, 5, 1, 2},
    {0, 0, 2, 2, 0, 3, 1, 2, 0, 4, 1, 1, 2, 2, 2, 1, 1, 1, 1, 5, 1, 0, 1, 0},
    {0, 0, 2, 2, 0, 3, 2, 4, 2, 5, 2, 5, 2, 1, 2, 1, 2, 0, 2, 0, 0, 5, 1, 1},
    {0, 0, 2, 2, 0, 5, 1, 1, 0, 3, 1, 4, 2, 1, 1, 2, 1, 0, 1, 0, 1, 2, 2, 1},
    {0, 0, 2, 2, 1, 0, 1, 1, 0, 3, 1, 3, 2, 4, 2, 4, 0, 4, 1, 5, 0, 1, 1, 0},
    {0, 0, 2, 2, 1, 0, 1, 4, 0, 4, 1, 3, 1, 4, 1, 0, 0, 5, 1, 1, 2, 2, 1, 2},
    {0, 0, 2, 2, 1, 5, 2, 4, 0, 1, 1, 3, 1, 1, 1, 0, 2, 0, 2, 1, 2, 2, 2, 5},
    {0, 0, 2, 2, 2, 0, 2, 0, 0, 4, 2, 3, 2, 5, 2, 3, 2, 2, 1, 2, 0, 5, 2, 1},
    {0, 0, 2, 2, 2, 4, 2, 4, 2, 5, 2, 5, 1, 0, 1, 1, 0, 1, 1, 3, 0, 5, 1, 4},
    {0, 0, 2, 3, 1, 0, 1, 0, 1, 3, 1, 3, 0, 5, 1, 1, 0, 2, 1, 4, 2, 4, 2, 4},
    {0, 0, 2, 3, 1, 3, 1, 5, 0, 1, 1, 3, 0, 2, 1, 4, 1, 2, 1, 2, 1, 0, 1, 0},
    {0, 0, 2, 3, 1, 3, 2, 3, 0, 2, 2, 5, 0, 1, 1, 4, 1, 2, 1, 3, 2, 0, 2, 0},
    {0, 0, 2, 3, 2, 0, 2, 0, 2, 3, 1, 4, 0, 5, 2, 1, 0, 2, 2, 4, 1, 4, 1, 3},
    {0, 0, 2, 3, 2, 0, 2, 1, 2, 3, 1, 5, 0, 4, 2, 5, 1, 5, 1, 3, 0, 2, 2, 1},
    {0, 0, 2, 3, 2, 1, 2, 5, 1, 3, 1, 3, 2, 5, 2, 4, 2, 0, 2, 0, 0, 2, 2, 1},
    {0, 0, 2, 4, 0, 1, 2, 5, 2, 1, 1, 3, 0, 2, 2, 1, 0, 2, 1, 4, 2, 0, 2, 0},
    {0, 0, 2, 4, 0, 2, 1, 0, 1, 0, 2, 5, 2, 5, 2, 1, 0, 3, 2, 0, 0, 5, 1, 1},
    {0, 0, 2, 4, 0, 3, 2, 0, 2, 5, 2, 5, 1, 4, 2, 1, 2, 1, 2, 2, 0, 0, 2, 1},
    {0, 0, 2, 4, 0, 5, 2, 3, 1, 1, 1, 4, 2, 0, 1, 4, 0, 2, 1, 1, 2, 4, 2, 1},
    {0, 0, 2, 4, 1, 4, 2, 3, 2, 3, 1, 4, 0, 1, 1, 3, 0, 2, 1, 5, 1, 0, 1, 0},
    {0, 0, 2, 5, 1, 5, 1, 2, 1, 0, 1, 0, 0, 3, 1, 5, 1, 3, 1, 3, 0, 1, 1, 4},
    {0, 0, 2, 5, 1, 5, 2, 4, 0, 1, 2, 2, 2, 0, 1, 2, 0, 1, 2, 3, 2, 2, 2, 3},
    {0, 0, 2, 5, 2, 3, 2, 3, 0, 2, 1, 3, 0, 1, 2, 4, 2, 0, 2, 2, 2, 2, 2, 0},
    {0, 1, 1, 0, 0, 2, 1, 3, 1, 3, 1, 5, 0, 4, 2, 4, 2, 1, 2, 3, 2, 0, 2, 0},
    {0, 1, 1, 0, 1, 2, 2, 3, 0, 5, 2, 2, 2, 4, 2, 4, 0, 4, 2, 0, 2, 0, 1, 2},
    {0, 1, 1, 0, 1, 3, 1, 4, 2, 0, 2, 3, 0, 2, 2, 4, 2, 5, 1, 0, 1, 0, 1, 3},
    {0, 1, 1, 0, 1, 4, 1, 4, 2, 5, 2, 4, 2, 0, 1, 0, 0, 2, 2, 5, 0, 1, 1, 3},
    {0, 1, 1, 0, 1, 5, 1, 2, 1, 3, 1, 3, 0, 3, 1, 5, 2, 0, 2, 0, 0, 4, 2, 5},
    {0, 1, 1, 0, 1, 5, 1, 4, 2, 0, 2, 3, 0, 2, 1, 5, 0, 3, 2, 5, 0, 2, 2, 0},
    {0, 1, 1, 0, 2, 2, 2, 0, 0, 5, 1, 2, 1, 4, 1, 1, 0, 4, 2, 2, 1, 0, 1, 3},
    {0, 1, 1, 0, 2, 3, 2, 4, 1, 0, 1, 3, 0, 5, 2, 3, 2, 5, 2, 5, 0, 2, 2, 0},
    {0, 1, 1, 2, 1, 4, 1, 5, 0, 3, 2, 4, 2, 0, 2, 4, 0, 3, 2, 0, 1, 3, 1, 3},
    {0, 1, 1, 2, 1, 5, 2, 3, 1, 4, 1, 5, 1, 2, 1, 0, 2, 0, 2, 0, 0, 4, 2, 5},
    {0, 1, 1, 3, 1, 2, 2, 3, 0, 4, 1, 0, 0, 1, 1, 5, 2, 3, 2, 2, 0, 4, 1, 2},
    {0, 1, 1, 4, 1, 3, 1, 2, 0, 1, 1, 4, 0, 5, 2, 2, 0, 5, 1, 3, 2, 0, 2, 3},
    {0, 1, 1, 4, 1, 4, 1, 0, 1, 0, 2, 1, 2, 5, 2, 2, 0, 3, 2, 5, 0, 1, 2, 4},
    {0, 1, 1, 4, 1, 4, 2, 0, 2, 5, 1, 2, 2, 0, 2, 2, 0, 3, 1, 0, 1, 4, 1, 4},
    {0, 1, 1, 4, 2, 2, 2, 0, 0, 3, 1, 0, 1, 5, 2, 4, 0, 3, 1, 2, 0, 1, 1, 4},
    {0, 1, 1, 4, 2, 3, 1, 0, 2, 4, 2, 4, 1, 0, 2, 2, 0, 4, 2, 5, 2, 1, 2, 0},
    {0, 1, 1, 5, 0, 3, 2, 0, 1, 3, 1, 1, 1, 4, 1, 2, 2, 0, 1, 4, 1, 1, 1, 0},
    {0, 1, 1, 5, 2, 0, 2, 3, 2, 3, 2, 0, 0, 4, 1, 0, 1, 5, 1, 3, 0, 2, 2, 5},
    {0, 1, 1, 5, 2, 4, 2, 2, 0, 1, 2, 4, 1, 2, 1, 0, 0, 3, 1, 5, 1, 1, 1, 0},
    {0, 1, 1, 5, 2, 5, 2, 0, 2, 0, 2, 5, 1, 2, 1, 2, 1, 0, 2, 3, 0, 4, 1, 0},
    {0, 1, 2, 0, 0, 2, 2, 3, 2, 3, 2, 5, 0, 4, 1, 4, 1, 1, 1, 3, 1, 0, 1, 0},
    {0, 1, 2, 0, 1, 2, 1, 0, 0, 5, 2, 2, 2, 4, 2, 1, 0, 4, 1, 2, 2, 0, 2, 3},
    {0, 1, 2, 0, 1, 3, 1, 4, 2, 0, 2, 3, 0, 5, 1, 3, 1, 5, 1, 5, 0, 2, 1, 0},
    {0, 1, 2, 0, 2, 2, 1, 3, 0, 5, 1, 2, 1, 4, 1, 4, 0, 4, 1, 0, 1, 0, 2, 2},
    {0, 1, 2, 0, 2, 3, 2, 4, 1, 0, 1, 3, 0, 2, 1, 4, 1, 5, 2, 0, 2, 0, 2, 3},
    {0, 1, 2, 0, 2, 4, 2, 4, 1, 5, 1, 4, 1, 0, 2, 0, 0, 2, 1, 5, 0, 1, 2, 3},
    {0, 1, 2, 0, 2, 5, 2, 2, 2, 3, 2, 3, 0, 3, 2, 5, 1, 0, 1, 0, 0, 4, 1, 5},
    {0, 1, 2, 0, 2, 5, 2, 4, 1, 0, 1, 3, 0, 2, 2, 5, 0, 3, 1, 5, 0, 2, 1, 0},
    {0, 1, 2, 2, 2, 4, 2, 5, 0, 3, 1, 4, 1, 0, 1, 4, 0, 3, 1, 0, 2, 3, 2, 3},
    {0, 1, 2, 2, 2, 5, 1, 3, 2, 4, 2, 5, 2, 2, 2, 0, 1, 0, 1, 0, 0, 4, 1, 5},
    {0, 1, 2, 3, 2, 2, 1, 3, 0, 4, 2, 0, 0, 1, 2, 5, 1, 3, 1, 2, 0, 4, 2, 2},
    {0, 1, 2, 4, 1, 2, 1, 0, 0, 3, 2, 0, 2, 5, 1, 4, 0, 3, 2, 2, 0, 1, 2, 4},
    {0, 1, 2, 4, 1, 3, 2, 0, 1, 4, 1, 4, 2, 0, 1, 2, 0, 4, 1, 5, 1, 1, 1, 0},
    {0, 1, 2, 4, 2, 3, 2, 2, 0, 1, 2, 4, 0, 5, 1, 2, 0, 5, 2, 3, 1, 0, 1, 3},
    {0, 1, 2, 4, 2, 4, 1, 0, 1, 5, 2, 2, 1, 0, 1, 2, 0, 3, 2, 0, 2, 4, 2, 4},
    {0, 1, 2, 4, 2, 4, 2, 0, 2, 0, 1, 1, 1, 5, 1, 2, 0, 3, 1, 5, 0, 1, 1, 4},
    {0, 1, 2, 5, 0, 3, 1, 0, 2, 3, 2, 1, 2, 4, 2, 2, 1, 0, 2, 4, 2, 1, 2, 0},
    {0, 1, 2, 5, 1, 0, 1, 3, 1, 3, 1, 0, 0, 4, 2, 0, 2, 5, 2, 3, 0, 2, 1, 5},
    {0, 1, 2, 5, 1, 4, 1, 2, 0, 1, 1, 4, 2, 2, 2, 0, 0, 3, 2, 5, 2, 1, 2, 0},
    {0, 1, 2, 5, 1, 5, 1, 0, 1, 0, 1, 5, 2, 2, 2, 2, 2, 0, 1, 3, 0, 4, 2, 0},
    {0, 2, 1, 0, 0, 0, 1, 1, 1, 3, 1, 1, 0, 4, 1, 3, 2, 0, 2, 5, 0, 4, 2, 3},
    {0, 2, 1, 0, 1, 3, 2, 5, 1, 1, 1, 1, 2, 5, 1, 5, 2, 0, 2, 0, 0, 4, 2, 1},
    {0, 2, 1, 1, 0, 3, 2, 0, 1, 1, 2, 5, 2, 0, 2, 1, 1, 0, 1, 0, 1, 4, 1, 4},
    {0, 2, 1, 1, 0, 5, 1, 0, 1, 1, 1, 3, 1, 4, 1, 4, 0, 4, 2, 0, 2, 0, 2, 1},
    {0, 2, 1, 1, 0, 5, 1, 0, 1, 4, 1, 0, 1, 2, 1, 4, 0, 5, 1, 3, 2, 0, 2, 1},
    {0, 2, 1, 2, 0, 5, 1, 2, 2, 3, 2, 4, 0, 5, 1, 1, 0, 2, 2, 3, 1, 4, 1, 0},
    {0, 2, 1, 3, 0, 2, 1, 1, 1, 5, 1, 5, 1, 4, 1, 1, 2, 1, 2, 0, 0, 4, 2, 5},
    {0, 2, 1, 3, 0, 5, 1, 3, 2, 1, 2, 0, 0, 0, 1, 4, 0, 2, 1, 1, 1, 4, 1, 5},
    {0, 2, 1, 3, 0, 5, 2, 0, 1, 1, 1, 1, 0, 4, 2, 1, 1, 3, 1, 0, 2, 0, 2, 3},
    {0, 2, 1, 3, 1, 3, 2, 1, 1, 4, 2, 4, 1, 0, 1, 0, 0, 5, 1, 1, 1, 1, 1, 4},
    {0, 2, 1, 3, 1, 5, 2, 3, 1, 3, 2, 0, 0, 4, 1, 0, 2, 0, 1, 5, 0, 1, 2, 5},
    {0, 2, 1, 3, 2, 0, 2, 0, 1, 3, 1, 0, 0, 1, 1, 5, 1, 4, 2, 3, 1, 2, 2, 4},
    {0, 2, 1, 3, 2, 2, 2, 3, 2, 3, 2, 0, 0, 4, 1, 0, 1, 0, 2, 5, 1, 1, 1, 0},
    {0, 2, 1, 3, 2, 4, 2, 1, 1, 1, 1, 0, 0, 5, 2, 0, 1, 3, 1, 4, 2, 0, 2, 4},
    {0, 2, 1, 3, 2, 5, 2, 3, 1, 3, 1, 5, 0, 1, 2, 5, 1, 0, 1, 0, 0, 0, 1, 4},
    {0, 2, 1, 4, 0, 3, 1, 1, 1, 5, 2, 0, 2, 4, 2, 5, 0, 2, 1, 1, 0, 3, 1, 0},
    {0, 2, 1, 4, 1, 0, 1, 3, 2, 3, 2, 0, 0, 1, 2, 4, 1, 5, 1, 5, 0, 2, 1, 5},
    {0, 2, 1, 4, 2, 0, 2, 5, 2, 5, 2, 0, 1, 0, 2, 4, 2, 1, 2, 1, 0, 3, 1, 5},
    {0, 2, 1, 4, 2, 5, 2, 2, 2, 4, 2, 0, 1, 0, 2, 1, 0, 3, 1, 0, 0, 5, 2, 4},
    {0, 2, 1, 5, 0, 3, 2, 5, 2, 5, 2, 0, 1, 0, 2, 4, 2, 1, 2, 1, 0, 1, 1, 0},
    {0, 2, 1, 5, 0, 4, 1, 0, 2, 1, 2, 0, 1, 3, 2, 1, 1, 0, 1, 1, 2, 3, 2, 3},
    {0, 2, 1, 5, 1, 3, 2, 3, 1, 0, 1, 4, 0, 5, 2, 4, 0, 1, 1, 0, 2, 4, 1, 3},
    {0, 2, 1, 5, 2, 0, 2, 3, 1, 3, 2, 0, 0, 1, 1, 4, 1, 1, 1, 3, 0, 1, 1, 4},
    {0, 2, 2, 0, 0, 0, 2, 1, 2, 3, 2, 1, 0, 4, 2, 3, 1, 0, 1, 5, 0, 4, 1, 3},
    {0, 2, 2, 0, 2, 3, 1, 5, 2, 1, 2, 1, 1, 5, 2, 5, 1, 0, 1, 0, 0, 4, 1, 1},
    {0, 2, 2, 1, 0, 3, 1, 0, 2, 1, 1, 5, 1, 0, 1, 1, 2, 0, 2, 0, 2, 4, 2, 4},
    {0, 2, 2, 1, 0, 5, 2, 0, 2, 1, 2, 3, 2, 4, 2, 4, 0, 4, 1, 0, 1, 0, 1, 1},
    {0, 2, 2, 1, 0, 5, 2, 0, 2, 4, 2, 0, 2, 2, 2, 4, 0, 5, 2, 3, 1, 0, 1, 1},
    {0, 2, 2, 2, 0, 5, 2, 2, 1, 3, 1, 4, 0, 5, 2, 1, 0, 2, 1, 3, 2, 4, 2, 0},
    {0, 2, 2, 3, 0, 2, 2, 1, 2, 5, 2, 5, 2, 4, 2, 1, 1, 1, 1, 0, 0, 4, 1, 5},
    {0, 2, 2, 3, 0, 5, 1, 0, 2, 1, 2, 1, 0, 4, 1, 1, 2, 3, 2, 0, 1, 0, 1, 3},
    {0, 2, 2, 3, 0, 5, 2, 3, 1, 1, 1, 0, 0, 0, 2, 4, 0, 2, 2, 1, 2, 4, 2, 5},
    {0, 2, 2, 3, 1, 0, 1, 0, 2, 3, 2, 0, 0, 1, 2, 5, 2, 4, 1, 3, 2, 2, 1, 4},
    {0, 2, 2, 3, 1, 2, 1, 3, 1, 3, 1, 0, 0, 4, 2, 0, 2, 0, 1, 5, 2, 1, 2, 0},
    {0, 2, 2, 3, 1, 4, 1, 1, 2, 1, 2, 0, 0, 5, 1, 0, 2, 3, 2, 4, 1, 0, 1, 4},
    {0, 2, 2, 3, 1, 5, 1, 3, 2, 3, 2, 5, 0, 1, 1, 5, 2, 0, 2, 0, 0, 0, 2, 4},
    {0, 2, 2, 3, 2, 3, 1, 1, 2, 4, 1, 4, 2, 0, 2, 0, 0, 5, 2, 1, 2, 1, 2, 4},
    {0, 2, 2, 3, 2, 5, 1, 3, 2, 3, 1, 0, 0, 4, 2, 0, 1, 0, 2, 5, 0, 1, 1, 5},
    {0, 2, 2, 4, 0, 3, 2, 1, 2, 5, 1, 0, 1, 4, 1, 5, 0, 2, 2, 1, 0, 3, 2, 0},
    {0, 2, 2, 4, 1, 0, 1, 5, 1, 5, 1, 0, 2, 0, 1, 4, 1, 1, 1, 1, 0, 3, 2, 5},
    {0, 2, 2, 4, 1, 5, 1, 2, 1, 4, 1, 0, 2, 0, 1, 1, 0, 3, 2, 0, 0, 5, 1, 4},
    {0, 2, 2, 4, 2, 0, 2, 3, 1, 3, 1, 0, 0, 1, 1, 4, 2, 5, 2, 5, 0, 2, 2, 5},
    {0, 2, 2, 5, 0, 3, 1, 5, 1, 5, 1, 0, 2, 0, 1, 4, 1, 1, 1, 1, 0, 1, 2, 0},
    {0, 2, 2, 5, 0, 4, 2, 0, 1, 1, 1, 0, 2, 3, 1, 1, 2, 0, 2, 1, 1, 3, 1, 3},
    {0, 2, 2, 5, 1, 0, 1, 3, 2, 3, 1, 0, 0, 1, 2, 4, 2, 1, 2, 3, 0, 1, 2, 4},
    {0, 2, 2, 5, 2, 3, 1, 3, 2, 0, 2, 4, 0, 5, 1, 4, 0, 1, 2, 0, 1, 4, 2, 3},
    {0, 3, 1, 0, 0, 2, 2, 0, 1, 4, 1, 1, 2, 0, 2, 1, 0, 5, 1, 4, 2, 1, 2, 4},
    {0, 3, 1, 0, 2, 0, 2, 0, 1, 5, 1, 5, 1, 4, 1, 4, 0, 1, 1, 2, 0, 5, 2, 4},
    {0, 3, 1, 0, 2, 5, 1, 1, 1, 1, 1, 1, 1, 5, 1, 2, 2, 0, 2, 5, 0, 4, 2, 0},
    {0, 3, 1, 1, 0, 2, 1, 0, 2, 4, 2, 0, 0, 2, 2, 1, 0, 5, 1, 4, 1, 3, 1, 2},
    {0, 3, 1, 1, 0, 4, 2, 3, 0, 3, 2, 1, 1, 5, 1, 0, 2, 0, 2, 2, 0, 4, 2, 5},
    {0, 3, 1, 1, 1, 4, 1, 4, 0, 5, 1, 0, 2, 2, 2, 2, 0, 4, 2, 0, 1, 0, 1, 2},
    {0, 3, 1, 1, 2, 1, 1, 2, 0, 3, 2, 4, 1, 4, 1, 4, 0, 5, 2, 0, 2, 0, 2, 4},
    {0, 3, 1, 1, 2, 5, 2, 5, 0, 4, 2, 0, 1, 2, 1, 2, 2, 0, 2, 2, 1, 4, 1, 0},
    {0, 3, 1, 2, 0, 2, 1, 0, 2, 4, 2, 1, 0, 5, 1, 0, 0, 5, 1, 1, 1, 1, 1, 3},
    {0, 3, 1, 2, 0, 3, 1, 5, 0, 4, 1, 0, 2, 2, 2, 1, 1, 0, 2, 2, 2, 2, 2, 0},
    {0, 3, 1, 2, 1, 0, 2, 0, 1, 3, 1, 4, 0, 1, 1, 5, 0, 4, 1, 0, 1, 4, 1, 3},
    {0, 3, 1, 2, 2, 0, 2, 0, 0, 0, 2, 5, 1, 5, 2, 1, 2, 2, 1, 5, 0, 4, 2, 2},
    {0, 3, 1, 2, 2, 0, 2, 4, 0, 3, 1, 2, 1, 4, 2, 2, 0, 1, 2, 5, 2, 5, 1, 4},
    {0, 3, 1, 2, 2, 0, 2, 5, 0, 4, 1, 1, 1, 1, 2, 0, 0, 4, 2, 1, 2, 2, 1, 5},
    {0, 3, 1, 2, 2, 4, 2, 1, 2, 2, 2, 1, 2, 5, 2, 5, 1, 0, 1, 5, 0, 4, 1, 0},
    {0, 3, 1, 3, 0, 3, 1, 0, 0, 5, 1, 4, 2, 2, 2, 0, 1, 4, 2, 2, 1, 1, 1, 2},
    {0, 3, 1, 4, 0, 2, 2, 0, 1, 5, 1, 1, 0, 4, 2, 5, 2, 1, 2, 5, 0, 4, 2, 1},
    {0, 3, 1, 4, 0, 2, 2, 5, 2, 0, 2, 0, 1, 1, 1, 0, 1, 1, 1, 2, 0, 2, 2, 3},
    {0, 3, 1, 4, 1, 0, 1, 0, 0, 0, 1, 2, 1, 4, 1, 1, 0, 5, 2, 4, 2, 2, 2, 2},
    {0, 3, 1, 4, 1, 2, 2, 4, 0, 3, 1, 5, 2, 4, 2, 0, 0, 1, 1, 0, 2, 0, 2, 1},
    {0, 3, 1, 4, 2, 0, 2, 4, 1, 5, 2, 0, 1, 4, 2, 5, 0, 1, 1, 5, 0, 2, 1, 0},
    {0, 3, 1, 4, 2, 1, 1, 0, 0, 5, 2, 4, 1, 2, 1, 2, 0, 0, 2, 1, 2, 0, 2, 2},
    {0, 3, 1, 4, 2, 2, 1, 5, 2, 4, 2, 5, 1, 5, 1, 0, 1, 0, 1, 1, 0, 1, 2, 2},
    {0, 3, 1, 4, 2, 2, 2, 5, 1, 2, 2, 0, 1, 4, 1, 0, 0, 5, 2, 1, 2, 0, 2, 4},
    {0, 3, 1, 4, 2, 4, 2, 2, 0, 5, 2, 0, 2, 2, 1, 0, 2, 1, 2, 1, 1, 0, 1, 2},
    {0, 3, 1, 5, 0, 2, 2, 2, 2, 0, 2, 1, 1, 1, 1, 4, 0, 0, 1, 0, 0, 2, 2, 4},
    {0, 3, 1, 5, 0, 4, 2, 0, 0, 4, 2, 5, 1, 2, 1, 2, 2, 0, 2, 1, 0, 3, 1, 5},
    {0, 3, 1, 5, 1, 0, 1, 0, 0, 1, 2, 2, 2, 2, 1, 2, 0, 4, 2, 0, 1, 4, 1, 4},
    {0, 3, 1, 5, 2, 0, 2, 4, 1, 4, 2, 0, 1, 5, 1, 4, 0, 3, 2, 4, 0, 1, 1, 2},
    {0, 3, 1, 5, 2, 2, 2, 2, 0, 4, 1, 4, 2, 5, 1, 0, 1, 1, 2, 5, 1, 0, 2, 1},
    {0, 3, 1, 5, 2, 4, 1, 2, 2, 1, 1, 0, 2, 5, 2, 1, 1, 0, 2, 5, 0, 4, 1, 0},
    {0, 3, 2, 0, 0, 2, 1, 0, 2, 4, 2, 1, 1, 0, 1, 1, 0, 5, 2, 4, 1, 1, 1, 4},
    {0, 3, 2, 0, 1, 0, 1, 0, 2, 5, 2, 5, 2, 4, 2, 4, 0, 1, 2, 2, 0, 5, 1, 4},
    {0, 3, 2, 0, 1, 5, 2, 1, 2, 1, 2, 1, 2, 5, 2, 2, 1, 0, 1, 5, 0, 4, 1, 0},
    {0, 3, 2, 1, 0, 2, 2, 0, 1, 4, 1, 0, 0, 2, 1, 1, 0, 5, 2, 4, 2, 3, 2, 2},
    {0, 3, 2, 1, 0, 4, 1, 3, 0, 3, 1, 1, 2, 5, 2, 0, 1, 0, 1, 2, 0, 4, 1, 5},
    {0, 3, 2, 1, 1, 1, 2, 2, 0, 3, 1, 4, 2, 4, 2, 4, 0, 5, 1, 0, 1, 0, 1, 4},
    {0, 3, 2, 1, 1, 5, 1, 5, 0, 4, 1, 0, 2, 2, 2, 2, 1, 0, 1, 2, 2, 4, 2, 0},
    {0, 3, 2, 1, 2, 4, 2, 4, 0, 5, 2, 0, 1, 2, 1, 2, 0, 4, 1, 0, 2, 0, 2, 2},
    {0, 3, 2, 2, 0, 2, 2, 0, 1, 4, 1, 1, 0, 5, 2, 0, 0, 5, 2, 1, 2, 1, 2, 3},
    {0, 3, 2, 2, 0, 3, 2, 5, 0, 4, 2, 0, 1, 2, 1, 1, 2, 0, 1, 2, 1, 2, 1, 0},
    {0, 3, 2, 2, 1, 0, 1, 0, 0, 0, 1, 5, 2, 5, 1, 1, 1, 2, 2, 5, 0, 4, 1, 2},
    {0, 3, 2, 2, 1, 0, 1, 4, 0, 3, 2, 2, 2, 4, 1, 2, 0, 1, 1, 5, 1, 5, 2, 4},
    {0, 3, 2, 2, 1, 0, 1, 5, 0, 4, 2, 1, 2, 1, 1, 0, 0, 4, 1, 1, 1, 2, 2, 5},
    {0, 3, 2, 2, 1, 4, 1, 1, 1, 2, 1, 1, 1, 5, 1, 5, 2, 0, 2, 5, 0, 4, 2, 0},
    {0, 3, 2, 2, 2, 0, 1, 0, 2, 3, 2, 4, 0, 1, 2, 5, 0, 4, 2, 0, 2, 4, 2, 3},
    {0, 3, 2, 3, 0, 3, 2, 0, 0, 5, 2, 4, 1, 2, 1, 0, 2, 4, 1, 2, 2, 1, 2, 2},
    {0, 3, 2, 4, 0, 2, 1, 0, 2, 5, 2, 1, 0, 4, 1, 5, 1, 1, 1, 5, 0, 4, 1, 1},
    {0, 3, 2, 4, 0, 2, 1, 5, 1, 0, 1, 0, 2, 1, 2, 0, 2, 1, 2, 2, 0, 2, 1, 3},
    {0, 3, 2, 4, 1, 0, 1, 4, 2, 5, 1, 0, 2, 4, 1, 5, 0, 1, 2, 5, 0, 2, 2, 0},
    {0, 3, 2, 4, 1, 1, 2, 0, 0, 5, 1, 4, 2, 2, 2, 2, 0, 0, 1, 1, 1, 0, 1, 2},
    {0, 3, 2, 4, 1, 2, 1, 5, 2, 2, 1, 0, 2, 4, 2, 0, 0, 5, 1, 1, 1, 0, 1, 4},
    {0, 3, 2, 4, 1, 2, 2, 5, 1, 4, 1, 5, 2, 5, 2, 0, 2, 0, 2, 1, 0, 1, 1, 2},
    {0, 3, 2, 4, 1, 4, 1, 2, 0, 5, 1, 0, 1, 2, 2, 0, 1, 1, 1, 1, 2, 0, 2, 2},
    {0, 3, 2, 4, 2, 0, 2, 0, 0, 0, 2, 2, 2, 4, 2, 1, 0, 5, 1, 4, 1, 2, 1, 2},
    {0, 3, 2, 4, 2, 2, 1, 4, 0, 3, 2, 5, 1, 4, 1, 0, 0, 1, 2, 0, 1, 0, 1, 1},
    {0, 3, 2, 5, 0, 2, 1, 2, 1, 0, 1, 1, 2, 1, 2, 4, 0, 0, 2, 0, 0, 2, 1, 4},
    {0, 3, 2, 5, 0, 4, 1, 0, 0, 4, 1, 5, 2, 2, 2, 2, 1, 0, 1, 1, 0, 3, 2, 5},
    {0, 3, 2, 5, 1, 0, 1, 4, 2, 4, 1, 0, 2, 5, 2, 4, 0, 3, 1, 4, 0, 1, 2, 2},
    {0, 3, 2, 5, 1, 2, 1, 2, 0, 4, 2, 4, 1, 5, 2, 0, 2, 1, 1, 5, 2, 0, 1, 1},
    {0, 3, 2, 5, 1, 4, 2, 2, 1, 1, 2, 0, 1, 5, 1, 1, 2, 0, 1, 5, 0, 4, 2, 0},
    {0, 3, 2, 5, 2, 0, 2, 0, 0, 1, 1, 2, 1, 2, 2, 2, 0, 4, 1, 0, 2, 4, 2, 4},
    {0, 4, 1, 0, 0, 1, 2, 3, 1, 0, 1, 3, 0, 2, 2, 0, 2, 3, 1, 5, 1, 1, 1, 1},
    {0, 4, 1, 0, 0, 3, 1, 5, 0, 3, 1, 1, 1, 0, 2, 5, 2, 2, 2, 0, 0, 3, 1, 5},
    {0, 4, 1, 0, 1, 0, 2, 3, 0, 1, 1, 1, 2, 4, 2, 2, 2, 2, 1, 5, 1, 1, 1, 1},
    {0, 4, 1, 0, 1, 5, 1, 5, 1, 0, 2, 0, 0, 2, 1, 1, 2, 3, 2, 3, 0, 5, 1, 3},
    {0, 4, 1, 0, 2, 0, 2, 0, 1, 5, 2, 3, 0, 1, 2, 3, 1, 2, 1, 2, 2, 3, 1, 5},
    {0, 4, 1, 1, 0, 5, 1, 5, 0, 5, 1, 3, 0, 4, 1, 0, 1, 2, 2, 0, 2, 0, 2, 2},
    {0, 4, 1, 1, 0, 5, 2, 1, 0, 3, 2, 0, 1, 2, 1, 0, 1, 1, 1, 2, 2, 0, 2, 2},
    {0, 4, 1, 1, 1, 5, 2, 2, 0, 3, 1, 2, 1, 0, 1, 5, 2, 2, 2, 0, 1, 1, 1, 0},
    {0, 4, 1, 2, 0, 1, 1, 3, 0, 2, 1, 5, 0, 4, 1, 1, 1, 2, 2, 0, 1, 1, 1, 2},
    {0, 4, 1, 2, 0, 3, 2, 1, 0, 3, 2, 1, 2, 0, 2, 0, 1, 2, 1, 5, 0, 4, 1, 2},
    {0, 4, 1, 2, 2, 0, 1, 0, 0, 1, 1, 5, 1, 5, 2, 5, 1, 2, 2, 2, 0, 3, 2, 0},
    {0, 4, 1, 3, 0, 1, 2, 0, 2, 1, 2, 1, 0, 5, 1, 0, 1, 3, 2, 2, 2, 0, 2, 3},
    {0, 4, 1, 3, 0, 2, 2, 0, 2, 0, 2, 3, 0, 2, 1, 5, 1, 1, 1, 0, 2, 1, 2, 1},
    {0, 4, 1, 3, 0, 4, 1, 3, 2, 0, 2, 0, 0, 2, 2, 5, 1, 3, 1, 1, 0, 2, 2, 4},
    {0, 4, 1, 3, 1, 4, 1, 4, 1, 0, 1, 1, 1, 5, 1, 5, 0, 2, 2, 0, 0, 5, 1, 0},
    {0, 4, 1, 3, 2, 3, 2, 2, 0, 1, 2, 0, 0, 5, 1, 4, 0, 5, 2, 3, 1, 2, 1, 2},
    {0, 4, 1, 3, 2, 3, 2, 5, 2, 0, 1, 1, 1, 2, 1, 5, 1, 5, 2, 0, 0, 1, 1, 0},
    {0, 4, 1, 5, 0, 1, 2, 2, 2, 3, 2, 3, 0, 3, 1, 0, 2, 0, 1, 1, 1, 1, 1, 3},
    {0, 4, 1, 5, 2, 0, 2, 0, 0, 1, 1, 3, 2, 2, 1, 4, 1, 5, 1, 0, 0, 1, 2, 2},
    {0, 4, 2, 0, 0, 1, 1, 3, 2, 0, 2, 3, 0, 2, 1, 0, 1, 3, 2, 5, 2, 1, 2, 1},
    {0, 4, 2, 0, 0, 3, 2, 5, 0, 3, 2, 1, 2, 0, 1, 5, 1, 2, 1, 0, 0, 3, 2, 5},
    {0, 4, 2, 0, 1, 0, 1, 0, 2, 5, 1, 3, 0, 1, 1, 3, 2, 2, 2, 2, 1, 3, 2, 5},
    {0, 4, 2, 0, 2, 0, 1, 3, 0, 1, 2, 1, 1, 4, 1, 2, 1, 2, 2, 5, 2, 1, 2, 1},
    {0, 4, 2, 0, 2, 5, 2, 5, 2, 0, 1, 0, 0, 2, 2, 1, 1, 3, 1, 3, 0, 5, 2, 3},
    {0, 4, 2, 1, 0, 5, 1, 1, 0, 3, 1, 0, 2, 2, 2, 0, 2, 1, 2, 2, 1, 0, 1, 2},
    {0, 4, 2, 1, 0, 5, 2, 5, 0, 5, 2, 3, 0, 4, 2, 0, 2, 2, 1, 0, 1, 0, 1, 2},
    {0, 4, 2, 1, 2, 5, 1, 2, 0, 3, 2, 2, 2, 0, 2, 5, 1, 2, 1, 0, 2, 1, 2, 0},
    {0, 4, 2, 2, 0, 1, 2, 3, 0, 2, 2, 5, 0, 4, 2, 1, 2, 2, 1, 0, 2, 1, 2, 2},
    {0, 4, 2, 2, 0, 3, 1, 1, 0, 3, 1, 1, 1, 0, 1, 0, 2, 2, 2, 5, 0, 4, 2, 2},
    {0, 4, 2, 2, 1, 0, 2, 0, 0, 1, 2, 5, 2, 5, 1, 5, 2, 2, 1, 2, 0, 3, 1, 0},
    {0, 4, 2, 3, 0, 1, 1, 0, 1, 1, 1, 1, 0, 5, 2, 0, 2, 3, 1, 2, 1, 0, 1, 3},
    {0, 4, 2, 3, 0, 2, 1, 0, 1, 0, 1, 3, 0, 2, 2, 5, 2, 1, 2, 0, 1, 1, 1, 1},
    {0, 4, 2, 3, 0, 4, 2, 3, 1, 0, 1, 0, 0, 2, 1, 5, 2, 3, 2, 1, 0, 2, 1, 4},
    {0, 4, 2, 3, 1, 3, 1, 2, 0, 1, 1, 0, 0, 5, 2, 4, 0, 5, 1, 3, 2, 2, 2, 2},
    {0, 4, 2, 3, 1, 3, 1, 5, 1, 0, 2, 1, 2, 2, 2, 5, 2, 5, 1, 0, 0, 1, 2, 0},
    {0, 4, 2, 3, 2, 4, 2, 4, 2, 0, 2, 1, 2, 5, 2, 5, 0, 2, 1, 0, 0, 5, 2, 0},
    {0, 4, 2, 5, 0, 1, 1, 2, 1, 3, 1, 3, 0, 3, 2, 0, 1, 0, 2, 1, 2, 1, 2, 3},
    {0, 4, 2, 5, 1, 0, 1, 0, 0, 1, 2, 3, 1, 2, 2, 4, 2, 5, 2, 0, 0, 1, 1, 2},
    {0, 5, 1, 0, 0, 4, 2, 2, 2, 3, 2, 3, 0, 3, 2, 1, 2, 0, 1, 1, 1, 1, 2, 0},
    {0, 5, 1, 0, 0, 5, 1, 4, 0, 3, 1, 2, 1, 1, 2, 2, 1, 4, 1, 1, 2, 2, 2, 0},
    {0, 5, 1, 1, 0, 2, 1, 3, 1, 4, 1, 0, 1, 0, 1, 3, 2, 1, 2, 4, 2, 3, 2, 1},
    {0, 5, 1, 1, 0, 2, 1, 3, 2, 0, 2, 1, 0, 4, 1, 1, 1, 1, 1, 0, 1, 1, 2, 0},
    {0, 5, 1, 1, 0, 2, 2, 2, 2, 0, 1, 3, 1, 2, 1, 4, 0, 4, 1, 1, 1, 1, 2, 0},
    {0, 5, 1, 1, 1, 2, 1, 2, 0, 4, 1, 3, 0, 2, 2, 0, 1, 0, 2, 3, 2, 3, 1, 0},
    {0, 5, 1, 1, 1, 3, 1, 3, 1, 0, 1, 4, 1, 0, 1, 0, 0, 2, 2, 1, 2, 4, 2, 4},
    {0, 5, 1, 1, 1, 5, 1, 5, 1, 0, 1, 3, 1, 4, 1, 4, 0, 4, 2, 2, 2, 2, 1, 0},
    {0, 5, 1, 2, 0, 3, 1, 0, 0, 3, 1, 4, 2, 0, 2, 4, 0, 3, 1, 1, 1, 1, 2, 0},
    {0, 5, 1, 2, 0, 3, 1, 1, 2, 4, 1, 0, 1, 0, 2, 4, 1, 1, 2, 1, 2, 2, 2, 0},
    {0, 5, 1, 2, 0, 5, 2, 2, 0, 3, 1, 4, 1, 0, 2, 4, 0, 3, 1, 1, 2, 4, 2, 0},
    {0, 5, 1, 2, 0, 5, 2, 4, 1, 1, 1, 3, 0, 2, 1, 0, 2, 2, 2, 1, 2, 3, 2, 3},
    {0, 5, 1, 2, 2, 0, 2, 4, 0, 1, 2, 2, 2, 4, 2, 0, 0, 3, 1, 4, 1, 2, 1, 0},
    {0, 5, 1, 2, 2, 2, 1, 4, 1, 3, 2, 2, 2, 0, 2, 4, 0, 1, 2, 0, 1, 4, 1, 3},
    {0, 5, 1, 2, 2, 3, 1, 0, 0, 4, 1, 0, 1, 2, 2, 4, 2, 0, 2, 1, 1, 1, 2, 0},
    {0, 5, 1, 2, 2, 3, 1, 0, 1, 1, 1, 1, 0, 4, 2, 3, 2, 0, 2, 0, 1, 3, 1, 0},
    {0, 5, 1, 3, 0, 1, 2, 2, 2, 0, 2, 0, 0, 0, 2, 3, 2, 1, 2, 1, 2, 3, 2, 4},
    {0, 5, 1, 3, 0, 2, 2, 1, 1, 0, 1, 4, 2, 1, 1, 1, 2, 3, 1, 3, 2, 1, 2, 0},
    {0, 5, 1, 3, 0, 4, 2, 2, 2, 0, 1, 1, 2, 2, 2, 0, 1, 3, 2, 1, 1, 1, 2, 3},
    {0, 5, 1, 3, 1, 3, 1, 0, 1, 0, 1, 2, 0, 3, 1, 0, 1, 4, 1, 1, 2, 2, 1, 4},
    {0, 5, 1, 3, 1, 3, 2, 2, 0, 1, 1, 0, 1, 4, 1, 2, 2, 0, 1, 0, 2, 2, 2, 0},
    {0, 5, 1, 3, 2, 0, 2, 0, 0, 1, 2, 2, 0, 1, 2, 4, 2, 5, 1, 2, 1, 3, 1, 0},
    {0, 5, 1, 4, 0, 1, 1, 0, 1, 1, 1, 1, 0, 3, 1, 2, 1, 3, 2, 4, 2, 0, 1, 3},
    {0, 5, 1, 4, 0, 3, 1, 0, 2, 1, 1, 4, 2, 0, 2, 0, 0, 3, 2, 4, 1, 4, 1, 2},
    {0, 5, 1, 4, 0, 5, 2, 3, 0, 4, 1, 0, 2, 4, 2, 3, 1, 1, 1, 2, 2, 2, 2, 2},
    {0, 5, 1, 4, 1, 5, 1, 0, 2, 0, 2, 4, 0, 5, 1, 1, 0, 2, 1, 0, 1, 4, 2, 3},
    {0, 5, 1, 5, 0, 3, 2, 5, 0, 2, 2, 4, 0, 3, 2, 0, 2, 3, 1, 3, 2, 2, 2, 1},
    {0, 5, 1, 5, 1, 2, 2, 0, 2, 0, 2, 2, 2, 1, 2, 4, 0, 3, 1, 4, 1, 4, 1, 1},
    {0, 5, 2, 0, 0, 4, 1, 2, 1, 3, 1, 3, 0, 3, 1, 1, 1, 0, 2, 1, 2, 1, 1, 0},
    {0, 5, 2, 0, 0, 5, 2, 4, 0, 3, 2, 2, 2, 1, 1, 2, 2, 4, 2, 1, 1, 2, 1, 0},
    {0, 5, 2, 1, 0, 2, 1, 2, 1, 0, 2, 3, 2, 2, 2, 4, 0, 4, 2, 1, 2, 1, 1, 0},
    {0, 5, 2, 1, 0, 2, 2, 3, 1, 0, 1, 1, 0, 4, 2, 1, 2, 1, 2, 0, 2, 1, 1, 0},
    {0, 5, 2, 1, 0, 2, 2, 3, 2, 4, 2, 0, 2, 0, 2, 3, 1, 1, 1, 4, 1, 3, 1, 1},
    {0, 5, 2, 1, 2, 2, 2, 2, 0, 4, 2, 3, 0, 2, 1, 0, 2, 0, 1, 3, 1, 3, 2, 0},
    {0, 5, 2, 1, 2, 3, 2, 3, 2, 0, 2, 4, 2, 0, 2, 0, 0, 2, 1, 1, 1, 4, 1, 4},
    {0, 5, 2, 1, 2, 5, 2, 5, 2, 0, 2, 3, 2, 4, 2, 4, 0, 4, 1, 2, 1, 2, 2, 0},
    {0, 5, 2, 2, 0, 3, 2, 0, 0, 3, 2, 4, 1, 0, 1, 4, 0, 3, 2, 1, 2, 1, 1, 0},
    {0, 5, 2, 2, 0, 3, 2, 1, 1, 4, 2, 0, 2, 0, 1, 4, 2, 1, 1, 1, 1, 2, 1, 0},
    {0, 5, 2, 2, 0, 5, 1, 2, 0, 3, 2, 4, 2, 0, 1, 4, 0, 3, 2, 1, 1, 4, 1, 0},
    {0, 5, 2, 2, 0, 5, 1, 4, 2, 1, 2, 3, 0, 2, 2, 0, 1, 2, 1, 1, 1, 3, 1, 3},
    {0, 5, 2, 2, 1, 0, 1, 4, 0, 1, 1, 2, 1, 4, 1, 0, 0, 3, 2, 4, 2, 2, 2, 0},
    {0, 5, 2, 2, 1, 2, 2, 4, 2, 3, 1, 2, 1, 0, 1, 4, 0, 1, 1, 0, 2, 4, 2, 3},
    {0, 5, 2, 2, 1, 3, 2, 0, 0, 4, 2, 0, 2, 2, 1, 4, 1, 0, 1, 1, 2, 1, 1, 0},
    {0, 5, 2, 2, 1, 3, 2, 0, 2, 1, 2, 1, 0, 4, 1, 3, 1, 0, 1, 0, 2, 3, 2, 0},
    {0, 5, 2, 3, 0, 1, 1, 2, 1, 0, 1, 0, 0, 0, 1, 3, 1, 1, 1, 1, 1, 3, 1, 4},
    {0, 5, 2, 3, 0, 2, 1, 1, 2, 0, 2, 4, 1, 1, 2, 1, 1, 3, 2, 3, 1, 1, 1, 0},
    {0, 5, 2, 3, 0, 4, 1, 2, 1, 0, 2, 1, 1, 2, 1, 0, 2, 3, 1, 1, 2, 1, 1, 3},
    {0, 5, 2, 3, 1, 0, 1, 0, 0, 1, 1, 2, 0, 1, 1, 4, 1, 5, 2, 2, 2, 3, 2, 0},
    {0, 5, 2, 3, 2, 3, 1, 2, 0, 1, 2, 0, 2, 4, 2, 2, 1, 0, 2, 0, 1, 2, 1, 0},
    {0, 5, 2, 3, 2, 3, 2, 0, 2, 0, 2, 2, 0, 3, 2, 0, 2, 4, 2, 1, 1, 2, 2, 4},
    {0, 5, 2, 4, 0, 1, 2, 0, 2, 1, 2, 1, 0, 3, 2, 2, 2, 3, 1, 4, 1, 0, 2, 3},
    {0, 5, 2, 4, 0, 3, 2, 0, 1, 1, 2, 4, 1, 0, 1, 0, 0, 3, 1, 4, 2, 4, 2, 2},
    {0, 5, 2, 4, 0, 5, 1, 3, 0, 4, 2, 0, 1, 4, 1, 3, 2, 1, 2, 2, 1, 2, 1, 2},
    {0, 5, 2, 4, 2, 5, 2, 0, 1, 0, 1, 4, 0, 5, 2, 1, 0, 2, 2, 0, 2, 4, 1, 3},
    {0, 5, 2, 5, 0, 3, 1, 5, 0, 2, 1, 4, 0, 3, 1, 0, 1, 3, 2, 3, 1, 2, 1, 1},
    {0, 5, 2, 5, 2, 2, 1, 0, 1, 0, 1, 2, 1, 1, 1, 4, 0, 3, 2, 4, 2, 4, 2, 1},
    {1, 0, 1, 1, 0, 4, 1, 0, 1, 1, 2, 5, 0, 4, 1, 0, 2, 5, 2, 3, 0, 2, 1, 5},
    {1, 0, 1, 3, 0, 5, 1, 3, 2, 4, 1, 0, 0, 4, 2, 4, 2, 1, 2, 3, 1, 3, 2, 2},
    {1, 0, 1, 5, 0, 3, 2, 5, 0, 4, 1, 0, 1, 2, 1, 2, 2, 1, 2, 2, 0, 3, 2, 1},
    {1, 0, 2, 1, 0, 3, 1, 0, 0, 5, 2, 2, 2, 2, 1, 1, 1, 3, 1, 3, 1, 1, 1, 4},
    {1, 0, 2, 2, 2, 2, 1, 5, 0, 3, 2, 5, 1, 5, 1, 2, 2, 0, 1, 0, 0, 1, 2, 4},
    {1, 0, 2, 4, 2, 3, 1, 4, 1, 2, 1, 3, 0, 5, 1, 0, 0, 1, 2, 3, 1, 4, 1, 2},
    {1, 0, 2, 4, 2, 3, 2, 5, 1, 4, 1, 3, 0, 2, 1, 4, 0, 1, 2, 4, 0, 2, 2, 0},
    {1, 1, 1, 1, 0, 1, 1, 2, 0, 3, 1, 0, 2, 5, 2, 2, 1, 2, 2, 5, 0, 4, 1, 5},
    {1, 1, 1, 1, 0, 1, 2, 4, 1, 3, 1, 3, 0, 5, 2, 3, 0, 2, 1, 0, 2, 4, 1, 4},
    {1, 1, 1, 1, 0, 1, 2, 5, 0, 2, 1, 0, 1, 5, 2, 2, 2, 2, 1, 3, 0, 3, 2, 4},
    {1, 1, 1, 1, 0, 4, 2, 2, 0, 0, 1, 5, 0, 0, 2, 5, 2, 3, 2, 1, 2, 4, 1, 2},
    {1, 1, 1, 1, 0, 4, 2, 2, 2, 4, 2, 4, 1, 5, 1, 0, 2, 3, 1, 5, 0, 1, 2, 3},
    {1, 1, 1, 1, 0, 4, 2, 2, 2, 5, 2, 5, 0, 1, 1, 0, 2, 3, 1, 3, 0, 5, 2, 3},
    {1, 1, 1, 1, 0, 4, 2, 5, 0, 1, 1, 2, 0, 3, 2, 2, 2, 2, 1, 0, 2, 3, 2, 3},
    {1, 1, 1, 1, 0, 5, 2, 1, 0, 0, 2, 3, 1, 4, 1, 2, 2, 2, 2, 4, 2, 3, 2, 2},
    {1, 1, 1, 1, 0, 5, 2, 2, 0, 3, 1, 2, 1, 4, 1, 0, 0, 1, 2, 4, 2, 2, 1, 4},
    {1, 1, 1, 1, 0, 5, 2, 4, 0, 0, 1, 1, 1, 3, 1, 2, 0, 0, 1, 3, 2, 4, 2, 1},
    {1, 1, 1, 2, 0, 0, 2, 3, 0, 0, 2, 3, 2, 4, 2, 1, 0, 5, 2, 4, 1, 3, 1, 3},
    {1, 1, 1, 2, 0, 1, 1, 5, 0, 2, 1, 1, 1, 5, 1, 3, 2, 3, 1, 0, 0, 4, 1, 0},
    {1, 1, 1, 2, 0, 2, 2, 3, 2, 3, 2, 1, 0, 0, 1, 5, 1, 1, 2, 2, 1, 2, 2, 4},
    {1, 1, 1, 2, 0, 2, 2, 3, 2, 4, 2, 5, 2, 0, 2, 2, 0, 0, 1, 4, 0, 0, 2, 5},
    {1, 1, 1, 2, 0, 3, 2, 2, 0, 0, 2, 1, 2, 4, 1, 1, 2, 5, 2, 1, 1, 2, 2, 0},
    {1, 1, 1, 2, 0, 3, 2, 2, 0, 0, 2, 5, 0, 4, 2, 1, 2, 2, 1, 1, 2, 3, 2, 3},
    {1, 1, 1, 2, 0, 4, 2, 3, 1, 4, 1, 1, 0, 0, 2, 5, 2, 3, 2, 1, 1, 2, 2, 4},
    {1, 1, 1, 3, 0, 2, 2, 1, 2, 4, 2, 4, 0, 5, 2, 3, 0, 0, 1, 4, 1, 3, 1, 1},
    {1, 1, 1, 4, 0, 1, 1, 5, 0, 4, 1, 0, 0, 3, 2, 2, 1, 2, 1, 2, 1, 3, 1, 3},
    {1, 1, 1, 4, 0, 3, 1, 5, 0, 3, 1, 5, 2, 5, 2, 1, 1, 4, 2, 5, 0, 0, 1, 2},
    {1, 1, 1, 4, 1, 3, 1, 5, 1, 5, 2, 0, 2, 4, 2, 5, 0, 2, 1, 1, 0, 3, 2, 4},
    {1, 1, 1, 4, 2, 4, 2, 2, 0, 1, 2, 4, 2, 3, 1, 2, 0, 5, 1, 0, 1, 2, 2, 3},
    {1, 1, 1, 5, 0, 3, 1, 2, 1, 3, 1, 3, 2, 0, 1, 1, 0, 4, 2, 0, 1, 4, 1, 0},
    {1, 1, 1, 5, 2, 2, 2, 2, 1, 4, 2, 0, 2, 5, 1, 4, 0, 3, 2, 5, 0, 0, 2, 4},
    {1, 1, 2, 0, 2, 3, 2, 5, 0, 1, 1, 2, 0, 4, 2, 3, 1, 2, 1, 0, 2, 4, 2, 0},
    {1, 1, 2, 1, 0, 0, 2, 4, 0, 0, 1, 3, 1, 5, 1, 1, 0, 3, 1, 2, 2, 4, 2, 5},
    {1, 1, 2, 1, 0, 1, 1, 3, 2, 4, 1, 5, 1, 2, 1, 2, 1, 5, 1, 0, 0, 2, 2, 4},
    {1, 1, 2, 1, 0, 5, 2, 3, 2, 3, 1, 4, 0, 0, 1, 1, 0, 2, 2, 4, 2, 4, 1, 3},
    {1, 1, 2, 2, 0, 4, 2, 1, 2, 4, 2, 4, 0, 0, 1, 5, 2, 3, 1, 1, 1, 5, 2, 3},
    {1, 1, 2, 2, 2, 3, 2, 1, 0, 0, 1, 2, 0, 5, 2, 3, 2, 2, 1, 0, 1, 4, 2, 4},
    {1, 1, 2, 3, 0, 2, 1, 3, 2, 3, 1, 5, 0, 0, 1, 1, 1, 1, 2, 0, 1, 4, 1, 0},
    {1, 1, 2, 3, 2, 4, 1, 3, 1, 5, 1, 5, 0, 1, 2, 0, 1, 3, 1, 2, 0, 5, 1, 4},
    {1, 1, 2, 4, 0, 0, 1, 1, 1, 3, 1, 4, 0, 5, 2, 3, 0, 2, 1, 3, 2, 4, 2, 0},
    {1, 1, 2, 4, 0, 1, 2, 3, 0, 2, 1, 0, 0, 5, 2, 3, 0, 5, 1, 4, 2, 2, 2, 2},
    {1, 1, 2, 4, 0, 3, 1, 0, 0, 3, 2, 4, 1, 4, 1, 2, 0, 5, 2, 2, 2, 1, 1, 4},
    {1, 1, 2, 4, 2, 4, 1, 3, 1, 3, 2, 3, 1, 5, 2, 5, 0, 0, 1, 2, 0, 5, 2, 1},
    {1, 1, 2, 5, 0, 2, 1, 3, 2, 3, 2, 4, 0, 0, 1, 1, 0, 2, 1, 4, 2, 5, 2, 3},
    {1, 2, 1, 0, 0, 1, 1, 2, 0, 5, 1, 3, 1, 1, 1, 1, 1, 4, 2, 0, 2, 0, 1, 4},
    {1, 2, 1, 1, 0, 0, 1, 2, 0, 4, 2, 3, 0, 5, 2, 1, 2, 1, 2, 2, 1, 3, 2, 5},
    {1, 2, 1, 1, 0, 0, 1, 3, 0, 5, 2, 3, 0, 5, 1, 5, 0, 0, 2, 3, 2, 1, 2, 4},
    {1, 2, 1, 1, 0, 2, 2, 3, 2, 3, 2, 1, 0, 5, 1, 0, 2, 0, 1, 3, 1, 1, 1, 4},
    {1, 2, 1, 1, 0, 5, 2, 4, 0, 3, 2, 2, 2, 1, 1, 2, 2, 5, 2, 5, 0, 0, 2, 1},
    {1, 2, 1, 2, 0, 1, 1, 4, 0, 3, 2, 2, 2, 4, 2, 4, 0, 0, 1, 5, 1, 1, 1, 1},
    {1, 2, 1, 2, 0, 3, 1, 4, 0, 2, 2, 5, 1, 5, 1, 4, 0, 0, 2, 4, 2, 1, 2, 1},
    {1, 2, 1, 2, 1, 4, 1, 2, 0, 3, 1, 5, 2, 4, 2, 2, 0, 0, 1, 4, 1, 1, 1, 1},
    {1, 2, 1, 2, 2, 0, 2, 3, 1, 5, 1, 2, 0, 1, 1, 3, 2, 3, 2, 5, 0, 4, 1, 5},
    {1, 2, 1, 2, 2, 2, 1, 3, 0, 5, 2, 3, 0, 0, 1, 4, 2, 1, 1, 4, 2, 3, 2, 2},
    {1, 2, 1, 2, 2, 3, 1, 4, 0, 1, 1, 0, 0, 5, 1, 2, 1, 0, 1, 3, 2, 4, 2, 3},
    {1, 2, 1, 2, 2, 3, 2, 3, 0, 0, 2, 1, 0, 3, 1, 5, 0, 4, 2, 2, 1, 4, 1, 4},
    {1, 2, 1, 2, 2, 4, 2, 2, 0, 0, 2, 5, 1, 5, 1, 5, 0, 3, 1, 4, 0, 1, 2, 4},
    {1, 2, 1, 2, 2, 5, 1, 4, 0, 0, 2, 1, 0, 3, 2, 2, 2, 3, 2, 3, 0, 5, 2, 4},
    {1, 2, 1, 3, 0, 0, 1, 4, 0, 5, 2, 3, 0, 0, 1, 4, 0, 5, 2, 2, 2, 1, 2, 2},
    {1, 2, 1, 3, 1, 3, 2, 1, 0, 5, 2, 4, 2, 1, 1, 2, 0, 0, 1, 4, 2, 4, 2, 2},
    {1, 2, 1, 3, 2, 4, 2, 2, 0, 1, 2, 4, 2, 5, 2, 5, 0, 0, 1, 2, 0, 0, 1, 4},
    {1, 2, 1, 4, 0, 0, 1, 2, 0, 5, 2, 3, 2, 0, 1, 1, 2, 3, 1, 0, 2, 1, 2, 1},
    {1, 2, 1, 4, 0, 5, 2, 4, 0, 1, 1, 3, 1, 1, 1, 1, 0, 0, 1, 2, 2, 4, 2, 2},
    {1, 2, 1, 4, 2, 4, 1, 5, 2, 3, 2, 4, 1, 5, 1, 5, 0, 0, 2, 2, 0, 1, 1, 0},
    {1, 2, 1, 4, 2, 4, 2, 4, 0, 1, 2, 3, 2, 0, 1, 5, 0, 0, 1, 2, 1, 5, 2, 2},
    {1, 2, 1, 4, 2, 5, 2, 2, 0, 1, 1, 5, 0, 2, 2, 5, 2, 3, 2, 3, 0, 0, 1, 2},
    {1, 2, 1, 5, 0, 0, 1, 1, 0, 4, 2, 3, 2, 0, 1, 2, 2, 1, 2, 1, 0, 4, 1, 0},
    {1, 2, 1, 5, 0, 2, 2, 5, 0, 3, 2, 4, 2, 5, 2, 2, 0, 0, 2, 1, 0, 0, 2, 1},
    {1, 2, 1, 5, 1, 4, 1, 4, 0, 3, 2, 1, 2, 5, 2, 2, 2, 2, 2, 5, 0, 0, 1, 1},
    {1, 2, 1, 5, 2, 0, 1, 0, 0, 4, 2, 1, 0, 4, 1, 1, 2, 5, 2, 0, 0, 0, 1, 3},
    {1, 2, 1, 5, 2, 5, 1, 2, 0, 1, 2, 2, 1, 4, 2, 3, 1, 3, 2, 5, 0, 0, 1, 3},
    {1, 2, 2, 0, 1, 3, 1, 0, 0, 5, 1, 2, 0, 3, 1, 0, 0, 1, 1, 2, 0, 5, 1, 4},
    {1, 2, 2, 1, 0, 3, 1, 4, 0, 2, 2, 1, 1, 4, 1, 1, 0, 5, 1, 0, 2, 1, 2, 4},
    {1, 2, 2, 1, 0, 3, 1, 5, 2, 1, 2, 1, 1, 5, 1, 0, 0, 2, 2, 2, 0, 2, 2, 4},
    {1, 2, 2, 3, 0, 5, 2, 1, 2, 1, 1, 0, 0, 4, 2, 0, 1, 0, 1, 3, 2, 3, 1, 2},
    {1, 2, 2, 4, 0, 0, 2, 3, 2, 4, 2, 5, 2, 4, 1, 5, 0, 1, 2, 1, 2, 1, 1, 1},
    {1, 2, 2, 4, 0, 3, 1, 4, 2, 1, 2, 5, 1, 4, 1, 0, 0, 2, 2, 1, 1, 0, 2, 0},
    {1, 2, 2, 4, 2, 2, 1, 4, 0, 5, 1, 3, 1, 1, 2, 5, 0, 0, 2, 3, 2, 4, 2, 2},
    {1, 2, 2, 5, 1, 0, 1, 5, 2, 4, 2, 4, 2, 5, 1, 4, 0, 3, 2, 5, 0, 1, 2, 4},
    {1, 2, 2, 5, 2, 4, 1, 5, 0, 1, 1, 2, 1, 5, 1, 4, 0, 3, 2, 0, 2, 0, 2, 4},
    {1, 2, 2, 5, 2, 4, 2, 2, 0, 3, 1, 5, 2, 5, 2, 4, 0, 3, 1, 2, 0, 0, 1, 1},
    {1, 3, 1, 0, 1, 2, 1, 2, 0, 5, 2, 4, 2, 4, 2, 1, 0, 1, 1, 0, 2, 0, 2, 2},
    {1, 3, 1, 1, 0, 0, 1, 2, 1, 2, 2, 1, 0, 4, 2, 3, 2, 1, 1, 5, 0, 4, 1, 0},
    {1, 3, 1, 1, 0, 0, 2, 5, 2, 1, 1, 3, 0, 2, 2, 1, 2, 5, 2, 3, 0, 2, 1, 4},
    {1, 3, 1, 1, 0, 1, 1, 5, 1, 1, 2, 1, 0, 3, 1, 2, 1, 5, 2, 5, 0, 4, 1, 0},
    {1, 3, 1, 1, 0, 2, 1, 4, 2, 4, 2, 1, 1, 1, 2, 4, 0, 3, 1, 5, 0, 2, 2, 0},
    {1, 3, 1, 1, 0, 2, 1, 5, 1, 5, 2, 1, 0, 1, 2, 5, 2, 1, 2, 0, 0, 4, 1, 1},
    {1, 3, 1, 1, 2, 2, 2, 5, 1, 5, 1, 5, 2, 4, 2, 5, 0, 2, 2, 4, 0, 3, 1, 0},
    {1, 3, 1, 2, 0, 0, 2, 1, 0, 0, 2, 5, 0, 4, 2, 1, 2, 2, 1, 3, 0, 4, 2, 3},
    {1, 3, 1, 2, 1, 1, 2, 3, 0, 0, 1, 1, 0, 4, 2, 5, 2, 2, 1, 3, 0, 0, 2, 0},
    {1, 3, 1, 2, 1, 4, 2, 2, 0, 1, 2, 3, 0, 0, 2, 5, 2, 2, 2, 3, 2, 1, 1, 4},
    {1, 3, 1, 2, 1, 5, 2, 2, 0, 1, 2, 5, 0, 0, 1, 5, 2, 0, 2, 3, 2, 2, 2, 4},
    {1, 3, 1, 2, 2, 4, 2, 3, 0, 4, 2, 5, 0, 1, 1, 2, 0, 0, 1, 3, 2, 2, 2, 1},
    {1, 3, 1, 3, 0, 0, 1, 2, 1, 3, 2, 1, 0, 3, 1, 4, 1, 5, 1, 5, 0, 5, 1, 1},
    {1, 3, 1, 3, 0, 0, 1, 4, 2, 0, 1, 1, 0, 5, 2, 1, 1, 5, 2, 2, 2, 1, 2, 3},
    {1, 3, 1, 3, 0, 0, 1, 5, 0, 4, 2, 1, 0, 2, 2, 3, 2, 1, 1, 1, 1, 2, 1, 2},
    {1, 3, 1, 3, 0, 5, 2, 3, 1, 2, 2, 1, 0, 5, 2, 2, 0, 0, 1, 4, 2, 4, 2, 4},
    {1, 3, 1, 3, 1, 0, 2, 1, 2, 5, 1, 4, 0, 3, 1, 5, 0, 2, 2, 1, 1, 4, 1, 0},
    {1, 3, 1, 3, 1, 4, 2, 4, 2, 2, 1, 4, 0, 1, 2, 5, 2, 5, 2, 2, 0, 3, 1, 0},
    {1, 3, 1, 3, 1, 5, 1, 5, 2, 4, 2, 4, 0, 3, 1, 4, 0, 1, 1, 0, 0, 2, 2, 5},
    {1, 3, 1, 4, 2, 0, 1, 1, 0, 0, 2, 1, 0, 5, 2, 1, 0, 0, 1, 3, 2, 4, 2, 2},
    {1, 3, 1, 5, 0, 1, 1, 3, 0, 0, 2, 3, 0, 2, 2, 4, 2, 1, 2, 1, 1, 2, 1, 2},
    {1, 3, 1, 5, 0, 1, 2, 4, 2, 0, 1, 3, 0, 2, 2, 3, 2, 2, 2, 2, 1, 1, 2, 3},
    {1, 3, 1, 5, 2, 2, 1, 3, 2, 0, 2, 2, 0, 4, 1, 5, 1, 5, 1, 2, 0, 1, 2, 5},
    {1, 3, 1, 5, 2, 2, 2, 2, 0, 4, 2, 3, 0, 2, 2, 5, 2, 5, 1, 3, 0, 0, 2, 1},
    {1, 3, 2, 1, 0, 0, 1, 1, 1, 4, 1, 4, 0, 5, 1, 2, 0, 4, 2, 3, 2, 1, 1, 3},
    {1, 3, 2, 1, 0, 0, 1, 3, 1, 4, 2, 1, 0, 4, 1, 2, 2, 1, 2, 5, 2, 0, 1, 1},
    {1, 3, 2, 2, 1, 0, 1, 2, 0, 1, 2, 0, 1, 4, 1, 4, 0, 5, 1, 3, 1, 2, 1, 0},
    {1, 3, 2, 2, 2, 4, 1, 3, 0, 1, 1, 4, 0, 5, 2, 3, 0, 0, 1, 2, 2, 2, 2, 4},
    {1, 3, 2, 2, 2, 5, 2, 4, 2, 1, 2, 0, 0, 1, 2, 5, 0, 1, 2, 1, 0, 0, 1, 4},
    {1, 3, 2, 3, 1, 5, 1, 1, 0, 0, 2, 4, 2, 4, 2, 3, 0, 5, 1, 1, 0, 4, 2, 2},
    {1, 3, 2, 4, 0, 1, 1, 3, 0, 0, 1, 2, 0, 5, 2, 3, 2, 1, 2, 1, 2, 2, 2, 2},
    {1, 3, 2, 4, 1, 0, 1, 3, 0, 5, 1, 2, 1, 2, 1, 5, 0, 1, 2, 2, 1, 4, 1, 4},
    {1, 3, 2, 4, 2, 4, 2, 2, 0, 1, 1, 2, 0, 5, 1, 4, 0, 0, 1, 3, 2, 2, 2, 3},
    {1, 3, 2, 5, 0, 1, 1, 5, 2, 1, 2, 1, 0, 4, 2, 3, 2, 5, 1, 3, 0, 0, 2, 2},
    {1, 3, 2, 5, 0, 1, 2, 3, 2, 1, 1, 1, 2, 4, 2, 2, 0, 0, 2, 4, 1, 5, 2, 4},
    {1, 3, 2, 5, 0, 4, 1, 0, 2, 1, 2, 5, 0, 2, 1, 1, 1, 3, 2, 1, 0, 3, 2, 0},
    {1, 3, 2, 5, 0, 4, 1, 1, 1, 1, 1, 0, 0, 3, 1, 2, 2, 2, 1, 5, 0, 4, 2, 2},
    {1, 3, 2, 5, 1, 1, 2, 3, 2, 4, 1, 3, 0, 2, 2, 4, 0, 0, 1, 1, 2, 2, 2, 2},
    {1, 3, 2, 5, 2, 2, 2, 2, 0, 4, 2, 0, 1, 1, 1, 5, 1, 5, 1, 3, 0, 1, 2, 5},
    {1, 4, 1, 0, 0, 1, 1, 4, 2, 0, 2, 3, 2, 1, 2, 5, 0, 2, 2, 5, 2, 2, 2, 1},
    {1, 4, 1, 1, 0, 0, 2, 1, 2, 3, 1, 4, 0, 0, 2, 1, 0, 2, 2, 5, 2, 0, 2, 5},
    {1, 4, 1, 2, 0, 1, 2, 3, 1, 1, 1, 1, 0, 5, 2, 4, 0, 0, 1, 2, 1, 3, 1, 4},
    {1, 4, 1, 2, 1, 2, 2, 2, 0, 0, 1, 5, 1, 5, 1, 4, 0, 3, 2, 4, 1, 1, 1, 1},
    {1, 4, 1, 2, 2, 2, 2, 2, 0, 0, 2, 3, 2, 5, 1, 4, 0, 1, 2, 4, 2, 3, 1, 5},
    {1, 4, 1, 2, 2, 5, 2, 4, 2, 3, 1, 5, 1, 2, 1, 4, 0, 1, 2, 5, 0, 0, 1, 5},
    {1, 4, 1, 3, 0, 5, 2, 1, 1, 0, 1, 5, 2, 1, 1, 4, 0, 3, 1, 2, 1, 4, 1, 1},
    {1, 4, 1, 3, 2, 0, 2, 5, 0, 0, 2, 1, 0, 0, 1, 4, 0, 5, 2, 1, 2, 3, 2, 2},
    {1, 4, 1, 3, 2, 1, 2, 4, 0, 0, 1, 4, 1, 3, 1, 2, 0, 5, 2, 2, 2, 2, 2, 1},
    {1, 4, 1, 3, 2, 2, 1, 4, 0, 0, 1, 5, 0, 0, 1, 5, 0, 1, 2, 4, 1, 5, 2, 3},
    {1, 4, 1, 3, 2, 3, 2, 3, 2, 0, 1, 2, 0, 0, 2, 5, 0, 1, 2, 4, 0, 4, 2, 2},
    {1, 4, 1, 4, 0, 0, 1, 3, 2, 1, 2, 5, 2, 3, 1, 1, 0, 2, 2, 1, 2, 5, 2, 4},
    {1, 4, 1, 4, 0, 2, 1, 0, 0, 5, 2, 1, 2, 2, 2, 2, 0, 4, 1, 1, 1, 1, 2, 3},
    {1, 4, 1, 4, 0, 2, 1, 1, 2, 3, 2, 1, 0, 5, 1, 3, 0, 4, 2, 3, 1, 1, 1, 0},
    {1, 4, 1, 4, 1, 2, 1, 2, 0, 4, 2, 5, 0, 1, 1, 0, 2, 3, 2, 2, 0, 1, 1, 3},
    {1, 4, 1, 4, 1, 3, 1, 0, 2, 1, 1, 5, 0, 4, 1, 0, 0, 2, 1, 3, 1, 2, 2, 1},
    {1, 4, 1, 4, 1, 3, 1, 2, 0, 1, 2, 2, 0, 5, 2, 3, 0, 4, 1, 3, 2, 2, 1, 0},
    {1, 4, 1, 4, 2, 2, 1, 1, 0, 1, 2, 3, 2, 5, 2, 5, 0, 4, 1, 2, 0, 5, 1, 0},
    {1, 4, 1, 4, 2, 5, 1, 0, 0, 1, 2, 5, 1, 1, 1, 1, 1, 2, 1, 2, 0, 4, 1, 3},
    {1, 4, 1, 4, 2, 5, 1, 2, 0, 0, 1, 2, 2, 1, 2, 4, 0, 3, 2, 2, 1, 2, 1, 2},
    {1, 4, 1, 5, 1, 2, 1, 2, 0, 2, 2, 3, 0, 0, 1, 0, 2, 3, 2, 4, 0, 1, 1, 1},
    {1, 4, 1, 5, 2, 2, 2, 4, 0, 0, 2, 5, 2, 5, 2, 2, 0, 1, 1, 4, 0, 3, 1, 2},
    {1, 4, 1, 5, 2, 5, 2, 3, 2, 0, 1, 1, 0, 0, 2, 2, 0, 1, 2, 2, 0, 0, 1, 4},
    {1, 4, 2, 1, 0, 0, 1, 2, 0, 2, 2, 5, 2, 2, 1, 4, 2, 1, 2, 3, 2, 0, 1, 1},
    {1, 4, 2, 1, 1, 2, 2, 4, 0, 3, 1, 1, 2, 1, 1, 2, 2, 5, 2, 5, 0, 0, 2, 2},
    {1, 4, 2, 1, 2, 3, 2, 3, 0, 0, 1, 5, 2, 2, 2, 2, 0, 3, 2, 5, 0, 3, 2, 5},
    {1, 4, 2, 1, 2, 5, 2, 5, 2, 3, 1, 3, 0, 0, 2, 4, 0, 2, 1, 4, 0, 5, 2, 3},
    {1, 4, 2, 3, 1, 2, 2, 4, 1, 3, 2, 1, 0, 0, 1, 2, 0, 5, 1, 3, 1, 1, 1, 4},
    {1, 4, 2, 3, 2, 3, 1, 2, 1, 5, 1, 5, 0, 0, 2, 4, 0, 1, 1, 3, 0, 5, 1, 4},
    {1, 4, 2, 3, 2, 3, 2, 3, 0, 5, 1, 0, 0, 3, 2, 2, 0, 4, 2, 1, 1, 2, 2, 4},
    {1, 4, 2, 4, 0, 1, 1, 2, 0, 0, 2, 2, 1, 1, 1, 1, 0, 5, 1, 3, 2, 2, 1, 4},
    {1, 4, 2, 4, 1, 3, 1, 2, 0, 2, 1, 4, 0, 3, 1, 5, 0, 0, 1, 1, 1, 2, 1, 3},
    {1, 4, 2, 5, 0, 1, 1, 0, 1, 1, 1, 4, 0, 2, 1, 2, 0, 4, 1, 3, 1, 1, 2, 1},
    {1, 4, 2, 5, 2, 2, 2, 2, 0, 3, 2, 5, 0, 3, 1, 4, 2, 5, 2, 1, 0, 0, 2, 4},
    {1, 5, 1, 0, 1, 3, 2, 2, 2, 3, 2, 5, 0, 4, 1, 5, 2, 0, 1, 1, 0, 3, 2, 1},
    {1, 5, 1, 0, 2, 4, 2, 4, 1, 3, 1, 3, 0, 3, 1, 4, 0, 1, 1, 0, 0, 5, 1, 2},
    {1, 5, 1, 1, 0, 0, 2, 5, 0, 0, 1, 3, 2, 1, 2, 0, 2, 2, 1, 5, 0, 4, 2, 1},
    {1, 5, 1, 1, 0, 4, 1, 5, 0, 3, 2, 2, 1, 1, 1, 2, 2, 2, 2, 5, 0, 0, 2, 1},
    {1, 5, 1, 1, 1, 2, 1, 1, 0, 2, 1, 0, 1, 4, 1, 1, 0, 5, 1, 0, 2, 3, 1, 4},
    {1, 5, 1, 1, 2, 4, 2, 3, 1, 1, 2, 4, 0, 0, 1, 5, 2, 3, 2, 1, 0, 2, 2, 5},
    {1, 5, 1, 2, 2, 2, 2, 4, 0, 0, 2, 5, 2, 4, 1, 5, 0, 3, 2, 2, 0, 1, 1, 4},
    {1, 5, 1, 2, 2, 2, 2, 4, 0, 3, 1, 0, 1, 4, 1, 5, 0, 1, 2, 2, 1, 0, 1, 4},
    {1, 5, 1, 2, 2, 3, 2, 3, 0, 0, 2, 2, 0, 4, 2, 5, 2, 2, 2, 1, 0, 3, 1, 5},
    {1, 5, 1, 3, 0, 1, 1, 5, 0, 0, 1, 2, 1, 1, 1, 1, 2, 2, 2, 2, 0, 4, 2, 5},
    {1, 5, 1, 3, 0, 1, 2, 2, 0, 0, 1, 2, 1, 1, 1, 1, 2, 2, 1, 5, 0, 4, 2, 5},
    {1, 5, 1, 3, 0, 2, 1, 3, 2, 3, 2, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 2, 2, 4},
    {1, 5, 1, 3, 1, 1, 1, 3, 0, 0, 1, 2, 0, 4, 1, 1, 2, 2, 2, 5, 0, 4, 2, 5},
    {1, 5, 1, 3, 2, 4, 2, 5, 0, 4, 2, 4, 1, 1, 2, 4, 0, 0, 2, 4, 0, 1, 2, 2},
    {1, 5, 1, 4, 1, 2, 2, 3, 2, 5, 2, 5, 2, 4, 2, 5, 0, 0, 1, 1, 0, 3, 2, 4},
    {1, 5, 1, 4, 2, 4, 2, 2, 2, 3, 2, 4, 2, 5, 2, 4, 0, 0, 2, 5, 0, 1, 1, 2},
    {1, 5, 1, 5, 0, 1, 1, 2, 0, 0, 1, 2, 0, 4, 1, 3, 2, 1, 2, 1, 0, 5, 2, 3},
    {1, 5, 1, 5, 0, 1, 1, 3, 0, 2, 2, 5, 1, 2, 1, 2, 2, 1, 2, 1, 0, 0, 2, 4},
    {1, 5, 1, 5, 0, 1, 2, 3, 1, 3, 1, 3, 0, 2, 1, 0, 1, 1, 1, 1, 0, 5, 1, 4},
    {1, 5, 1, 5, 0, 2, 1, 3, 2, 1, 2, 3, 0, 4, 1, 0, 2, 3, 1, 1, 0, 5, 2, 1},
    {1, 5, 1, 5, 0, 2, 2, 1, 2, 3, 1, 1, 0, 5, 1, 0, 1, 1, 1, 3, 0, 4, 2, 3},
    {1, 5, 1, 5, 0, 4, 1, 0, 0, 3, 2, 2, 2, 1, 1, 2, 1, 2, 1, 1, 0, 5, 2, 1},
    {1, 5, 1, 5, 1, 2, 1, 2, 0, 2, 1, 0, 1, 4, 1, 1, 0, 5, 2, 4, 0, 3, 1, 4},
    {1, 5, 2, 1, 0, 2, 1, 5, 1, 5, 1, 1, 2, 0, 2, 5, 2, 1, 2, 1, 0, 4, 2, 3},
    {1, 5, 2, 2, 0, 2, 1, 0, 1, 4, 1, 3, 0, 5, 1, 5, 0, 5, 2, 1, 2, 1, 2, 4},
    {1, 5, 2, 2, 1, 0, 1, 0, 0, 1, 1, 5, 0, 4, 1, 2, 1, 2, 1, 3, 1, 3, 1, 4},
    {1, 5, 2, 2, 2, 0, 2, 4, 2, 4, 2, 1, 0, 0, 1, 2, 0, 4, 2, 3, 2, 3, 2, 1},
    {1, 5, 2, 3, 0, 4, 2, 3, 1, 1, 1, 3, 0, 2, 2, 5, 2, 3, 2, 0, 0, 4, 1, 1},
    {1, 5, 2, 3, 2, 2, 1, 2, 0, 4, 1, 2, 0, 0, 1, 3, 2, 3, 2, 2, 1, 1, 1, 5},
    {1, 5, 2, 3, 2, 3, 1, 4, 0, 1, 2, 0, 0, 0, 1, 5, 0, 0, 1, 2, 0, 1, 2, 2},
    {1, 5, 2, 4, 0, 1, 2, 5, 2, 3, 1, 0, 2, 1, 1, 4, 0, 0, 2, 2, 2, 4, 2, 3},
    {1, 5, 2, 4, 0, 3, 2, 3, 0, 5, 1, 3, 2, 4, 2, 1, 0, 0, 1, 2, 0, 3, 1, 4},
    {1, 5, 2, 4, 1, 0, 1, 4, 1, 3, 1, 3, 0, 3, 1, 1, 0, 0, 1, 4, 2, 4, 1, 2},
    {1, 5, 2, 5, 0, 0, 2, 0, 2, 3, 1, 1, 0, 0, 1, 5, 0, 3, 2, 2, 0, 2, 2, 4},
    {1, 5, 2, 5, 0, 1, 1, 5, 2, 3, 2, 3, 0, 3, 2, 4, 2, 1, 2, 1, 0, 0, 2, 2},
    {1, 5, 2, 5, 1, 4, 1, 4, 0, 4, 1, 1, 1, 2, 1, 2, 0, 2, 1, 5, 0, 0, 1, 3},
    {2, 0, 1, 1, 0, 3, 2, 0, 0, 5, 1, 2, 1, 2, 2, 1, 2, 3, 2, 3, 2, 1, 2, 4},
    {2, 0, 1, 2, 1, 2, 2, 5, 0, 3, 1, 5, 2, 5, 2, 2, 1, 0, 2, 0, 0, 1, 1, 4},
    {2, 0, 1, 4, 1, 3, 1, 5, 2, 4, 2, 3, 0, 2, 2, 4, 0, 1, 1, 4, 0, 2, 1, 0},
    {2, 0, 1, 4, 1, 3, 2, 4, 2, 2, 2, 3, 0, 5, 2, 0, 0, 1, 1, 3, 2, 4, 2, 2},
    {2, 0, 2, 1, 0, 4, 2, 0, 2, 1, 1, 5, 0, 4, 2, 0, 1, 5, 1, 3, 0, 2, 2, 5},
    {2, 0, 2, 3, 0, 5, 2, 3, 1, 4, 2, 0, 0, 4, 1, 4, 1, 1, 1, 3, 2, 3, 1, 2},
    {2, 0, 2, 5, 0, 3, 1, 5, 0, 4, 2, 0, 2, 2, 2, 2, 1, 1, 1, 2, 0, 3, 1, 1},
    {2, 1, 1, 0, 1, 3, 1, 5, 0, 1, 2, 2, 0, 4, 1, 3, 2, 2, 2, 0, 1, 4, 1, 0},
    {2, 1, 1, 1, 0, 0, 1, 4, 0, 0, 2, 3, 2, 5, 2, 1, 0, 3, 2, 2, 1, 4, 1, 5},
    {2, 1, 1, 1, 0, 1, 2, 3, 1, 4, 2, 5, 2, 2, 2, 2, 2, 5, 2, 0, 0, 2, 1, 4},
    {2, 1, 1, 1, 0, 5, 1, 3, 1, 3, 2, 4, 0, 0, 2, 1, 0, 2, 1, 4, 1, 4, 2, 3},
    {2, 1, 1, 2, 0, 4, 1, 1, 1, 4, 1, 4, 0, 0, 2, 5, 1, 3, 2, 1, 2, 5, 1, 3},
    {2, 1, 1, 2, 1, 3, 1, 1, 0, 0, 2, 2, 0, 5, 1, 3, 1, 2, 2, 0, 2, 4, 1, 4},
    {2, 1, 1, 3, 0, 2, 2, 3, 1, 3, 2, 5, 0, 0, 2, 1, 2, 1, 1, 0, 2, 4, 2, 0},
    {2, 1, 1, 3, 1, 4, 2, 3, 2, 5, 2, 5, 0, 1, 1, 0, 2, 3, 2, 2, 0, 5, 2, 4},
    {2, 1, 1, 4, 0, 0, 2, 1, 2, 3, 2, 4, 0, 5, 1, 3, 0, 2, 2, 3, 1, 4, 1, 0},
    {2, 1, 1, 4, 0, 1, 1, 3, 0, 2, 2, 0, 0, 5, 1, 3, 0, 5, 2, 4, 1, 2, 1, 2},
    {2, 1, 1, 4, 0, 3, 2, 0, 0, 3, 1, 4, 2, 4, 2, 2, 0, 5, 1, 2, 1, 1, 2, 4},
    {2, 1, 1, 4, 1, 4, 2, 3, 2, 3, 1, 3, 2, 5, 1, 5, 0, 0, 2, 2, 0, 5, 1, 1},
    {2, 1, 1, 5, 0, 2, 2, 3, 1, 3, 1, 4, 0, 0, 2, 1, 0, 2, 2, 4, 1, 5, 1, 3},
    {2, 1, 2, 1, 0, 1, 1, 4, 2, 3, 2, 3, 0, 5, 1, 3, 0, 2, 2, 0, 1, 4, 2, 4},
    {2, 1, 2, 1, 0, 1, 1, 5, 0, 2, 2, 0, 2, 5, 1, 2, 1, 2, 2, 3, 0, 3, 1, 4},
    {2, 1, 2, 1, 0, 1, 2, 2, 0, 3, 2, 0, 1, 5, 1, 2, 2, 2, 1, 5, 0, 4, 2, 5},
    {2, 1, 2, 1, 0, 4, 1, 2, 0, 0, 2, 5, 0, 0, 1, 5, 1, 3, 1, 1, 1, 4, 2, 2},
    {2, 1, 2, 1, 0, 4, 1, 2, 1, 4, 1, 4, 2, 5, 2, 0, 1, 3, 2, 5, 0, 1, 1, 3},
    {2, 1, 2, 1, 0, 4, 1, 2, 1, 5, 1, 5, 0, 1, 2, 0, 1, 3, 2, 3, 0, 5, 1, 3},
    {2, 1, 2, 1, 0, 4, 1, 5, 0, 1, 2, 2, 0, 3, 1, 2, 1, 2, 2, 0, 1, 3, 1, 3},
    {2, 1, 2, 1, 0, 5, 1, 1, 0, 0, 1, 3, 2, 4, 2, 2, 1, 2, 1, 4, 1, 3, 1, 2},
    {2, 1, 2, 1, 0, 5, 1, 2, 0, 3, 2, 2, 2, 4, 2, 0, 0, 1, 1, 4, 1, 2, 2, 4},
    {2, 1, 2, 1, 0, 5, 1, 4, 0, 0, 2, 1, 2, 3, 2, 2, 0, 0, 2, 3, 1, 4, 1, 1},
    {2, 1, 2, 2, 0, 0, 1, 3, 0, 0, 1, 3, 1, 4, 1, 1, 0, 5, 1, 4, 2, 3, 2, 3},
    {2, 1, 2, 2, 0, 1, 2, 5, 0, 2, 2, 1, 2, 5, 2, 3, 1, 3, 2, 0, 0, 4, 2, 0},
    {2, 1, 2, 2, 0, 2, 1, 3, 1, 3, 1, 1, 0, 0, 2, 5, 2, 1, 1, 2, 2, 2, 1, 4},
    {2, 1, 2, 2, 0, 2, 1, 3, 1, 4, 1, 5, 1, 0, 1, 2, 0, 0, 2, 4, 0, 0, 1, 5},
    {2, 1, 2, 2, 0, 3, 1, 2, 0, 0, 1, 1, 1, 4, 2, 1, 1, 5, 1, 1, 2, 2, 1, 0},
    {2, 1, 2, 2, 0, 3, 1, 2, 0, 0, 1, 5, 0, 4, 1, 1, 1, 2, 2, 1, 1, 3, 1, 3},
    {2, 1, 2, 2, 0, 4, 1, 3, 2, 4, 2, 1, 0, 0, 1, 5, 1, 3, 1, 1, 2, 2, 1, 4},
    {2, 1, 2, 3, 0, 2, 1, 1, 1, 4, 1, 4, 0, 5, 1, 3, 0, 0, 2, 4, 2, 3, 2, 1},
    {2, 1, 2, 4, 0, 1, 2, 5, 0, 4, 2, 0, 0, 3, 1, 2, 2, 2, 2, 2, 2, 3, 2, 3},
    {2, 1, 2, 4, 0, 3, 2, 5, 0, 3, 2, 5, 1, 5, 1, 1, 2, 4, 1, 5, 0, 0, 2, 2},
    {2, 1, 2, 4, 1, 4, 1, 2, 0, 1, 1, 4, 1, 3, 2, 2, 0, 5, 2, 0, 2, 2, 1, 3},
    {2, 1, 2, 4, 2, 3, 2, 5, 2, 5, 1, 0, 1, 4, 1, 5, 0, 2, 2, 1, 0, 3, 1, 4},
    {2, 1, 2, 5, 0, 3, 2, 2, 2, 3, 2, 3, 1, 0, 2, 1, 0, 4, 1, 0, 2, 4, 2, 0},
    {2, 1, 2, 5, 1, 2, 1, 2, 2, 4, 1, 0, 1, 5, 2, 4, 0, 3, 1, 5, 0, 0, 1, 4},
    {2, 2, 1, 0, 2, 3, 2, 0, 0, 5, 2, 2, 0, 3, 2, 0, 0, 1, 2, 2, 0, 5, 2, 4},
    {2, 2, 1, 1, 0, 3, 2, 4, 0, 2, 1, 1, 2, 4, 2, 1, 0, 5, 2, 0, 1, 1, 1, 4},
    {2, 2, 1, 1, 0, 3, 2, 5, 1, 1, 1, 1, 2, 5, 2, 0, 0, 2, 1, 2, 0, 2, 1, 4},
    {2, 2, 1, 3, 0, 5, 1, 1, 1, 1, 2, 0, 0, 4, 1, 0, 2, 0, 2, 3, 1, 3, 2, 2},
    {2, 2, 1, 4, 0, 0, 1, 3, 1, 4, 1, 5, 1, 4, 2, 5, 0, 1, 1, 1, 1, 1, 2, 1},
    {2, 2, 1, 4, 0, 3, 2, 4, 1, 1, 1, 5, 2, 4, 2, 0, 0, 2, 1, 1, 2, 0, 1, 0},
    {2, 2, 1, 4, 1, 2, 2, 4, 0, 5, 2, 3, 2, 1, 1, 5, 0, 0, 1, 3, 1, 4, 1, 2},
    {2, 2, 1, 5, 1, 4, 1, 2, 0, 3, 2, 5, 1, 5, 1, 4, 0, 3, 2, 2, 0, 0, 2, 1},
    {2, 2, 1, 5, 1, 4, 2, 5, 0, 1, 2, 2, 2, 5, 2, 4, 0, 3, 1, 0, 1, 0, 1, 4},
    {2, 2, 1, 5, 2, 0, 2, 5, 1, 4, 1, 4, 1, 5, 2, 4, 0, 3, 1, 5, 0, 1, 1, 4},
    {2, 2, 2, 0, 0, 1, 2, 2, 0, 5, 2, 3, 2, 1, 2, 1, 2, 4, 1, 0, 1, 0, 2, 4},
    {2, 2, 2, 1, 0, 0, 2, 2, 0, 4, 1, 3, 0, 5, 1, 1, 1, 1, 1, 2, 2, 3, 1, 5},
    {2, 2, 2, 1, 0, 0, 2, 3, 0, 5, 1, 3, 0, 5, 2, 5, 0, 0, 1, 3, 1, 1, 1, 4},
    {2, 2, 2, 1, 0, 2, 1, 3, 1, 3, 1, 1, 0, 5, 2, 0, 1, 0, 2, 3, 2, 1, 2, 4},
    {2, 2, 2, 1, 0, 5, 1, 4, 0, 3, 1, 2, 1, 1, 2, 2, 1, 5, 1, 5, 0, 0, 1, 1},
    {2, 2, 2, 2, 0, 1, 2, 4, 0, 3, 1, 2, 1, 4, 1, 4, 0, 0, 2, 5, 2, 1, 2, 1},
    {2, 2, 2, 2, 0, 3, 2, 4, 0, 2, 1, 5, 2, 5, 2, 4, 0, 0, 1, 4, 1, 1, 1, 1},
    {2, 2, 2, 2, 1, 0, 1, 3, 2, 5, 2, 2, 0, 1, 2, 3, 1, 3, 1, 5, 0, 4, 2, 5},
    {2, 2, 2, 2, 1, 2, 2, 3, 0, 5, 1, 3, 0, 0, 2, 4, 1, 1, 2, 4, 1, 3, 1, 2},
    {2, 2, 2, 2, 1, 3, 1, 3, 0, 0, 1, 1, 0, 3, 2, 5, 0, 4, 1, 2, 2, 4, 2, 4},
    {2, 2, 2, 2, 1, 3, 2, 4, 0, 1, 2, 0, 0, 5, 2, 2, 2, 0, 2, 3, 1, 4, 1, 3},
    {2, 2, 2, 2, 1, 4, 1, 2, 0, 0, 1, 5, 2, 5, 2, 5, 0, 3, 2, 4, 0, 1, 1, 4},
    {2, 2, 2, 2, 1, 5, 2, 4, 0, 0, 1, 1, 0, 3, 1, 2, 1, 3, 1, 3, 0, 5, 1, 4},
    {2, 2, 2, 2, 2, 4, 2, 2, 0, 3, 2, 5, 1, 4, 1, 2, 0, 0, 2, 4, 2, 1, 2, 1},
    {2, 2, 2, 3, 0, 0, 2, 4, 0, 5, 1, 3, 0, 0, 2, 4, 0, 5, 1, 2, 1, 1, 1, 2},
    {2, 2, 2, 3, 1, 4, 1, 2, 0, 1, 1, 4, 1, 5, 1, 5, 0, 0, 2, 2, 0, 0, 2, 4},
    {2, 2, 2, 3, 2, 3, 1, 1, 0, 5, 1, 4, 1, 1, 2, 2, 0, 0, 2, 4, 1, 4, 1, 2},
    {2, 2, 2, 4, 0, 0, 2, 2, 0, 5, 1, 3, 1, 0, 2, 1, 1, 3, 2, 0, 1, 1, 1, 1},
    {2, 2, 2, 4, 0, 5, 1, 4, 0, 1, 2, 3, 2, 1, 2, 1, 0, 0, 2, 2, 1, 4, 1, 2},
    {2, 2, 2, 4, 1, 4, 1, 4, 0, 1, 1, 3, 1, 0, 2, 5, 0, 0, 2, 2, 2, 5, 1, 2},
    {2, 2, 2, 4, 1, 4, 2, 5, 1, 3, 1, 4, 2, 5, 2, 5, 0, 0, 1, 2, 0, 1, 2, 0},
    {2, 2, 2, 4, 1, 5, 1, 2, 0, 1, 2, 5, 0, 2, 1, 5, 1, 3, 1, 3, 0, 0, 2, 2},
    {2, 2, 2, 5, 0, 0, 2, 1, 0, 4, 1, 3, 1, 0, 2, 2, 1, 1, 1, 1, 0, 4, 2, 0},
    {2, 2, 2, 5, 0, 2, 1, 5, 0, 3, 1, 4, 1, 5, 1, 2, 0, 0, 1, 1, 0, 0, 1, 1},
    {2, 2, 2, 5, 1, 0, 2, 0, 0, 4, 1, 1, 0, 4, 2, 1, 1, 5, 1, 0, 0, 0, 2, 3},
    {2, 2, 2, 5, 1, 5, 2, 2, 0, 1, 1, 2, 2, 4, 1, 3, 2, 3, 1, 5, 0, 0, 2, 3},
    {2, 2, 2, 5, 2, 4, 2, 4, 0, 3, 1, 1, 1, 5, 1, 2, 1, 2, 1, 5, 0, 0, 2, 1},
    {2, 3, 1, 1, 0, 0, 2, 1, 2, 4, 2, 4, 0, 5, 2, 2, 0, 4, 1, 3, 1, 1, 2, 3},
    {2, 3, 1, 1, 0, 0, 2, 3, 2, 4, 1, 1, 0, 4, 2, 2, 1, 1, 1, 5, 1, 0, 2, 1},
    {2, 3, 1, 2, 1, 4, 2, 3, 0, 1, 2, 4, 0, 5, 1, 3, 0, 0, 2, 2, 1, 2, 1, 4},
    {2, 3, 1, 2, 1, 5, 1, 4, 1, 1, 1, 0, 0, 1, 1, 5, 0, 1, 1, 1, 0, 0, 2, 4},
    {2, 3, 1, 2, 2, 0, 2, 2, 0, 1, 1, 0, 2, 4, 2, 4, 0, 5, 2, 3, 2, 2, 2, 0},
    {2, 3, 1, 3, 2, 5, 2, 1, 0, 0, 1, 4, 1, 4, 1, 3, 0, 5, 2, 1, 0, 4, 1, 2},
    {2, 3, 1, 4, 0, 1, 2, 3, 0, 0, 2, 2, 0, 5, 1, 3, 1, 1, 1, 1, 1, 2, 1, 2},
    {2, 3, 1, 4, 1, 4, 1, 2, 0, 1, 2, 2, 0, 5, 2, 4, 0, 0, 2, 3, 1, 2, 1, 3},
    {2, 3, 1, 4, 2, 0, 2, 3, 0, 5, 2, 2, 2, 2, 2, 5, 0, 1, 1, 2, 2, 4, 2, 4},
    {2, 3, 1, 5, 0, 1, 1, 3, 1, 1, 2, 1, 1, 4, 1, 2, 0, 0, 1, 4, 2, 5, 1, 4},
    {2, 3, 1, 5, 0, 1, 2, 5, 1, 1, 1, 1, 0, 4, 1, 3, 1, 5, 2, 3, 0, 0, 1, 2},
    {2, 3, 1, 5, 0, 4, 2, 0, 1, 1, 1, 5, 0, 2, 2, 1, 2, 3, 1, 1, 0, 3, 1, 0},
    {2, 3, 1, 5, 0, 4, 2, 1, 2, 1, 2, 0, 0, 3, 2, 2, 1, 2, 2, 5, 0, 4, 1, 2},
    {2, 3, 1, 5, 1, 2, 1, 2, 0, 4, 1, 0, 2, 1, 2, 5, 2, 5, 2, 3, 0, 1, 1, 5},
    {2, 3, 1, 5, 2, 1, 1, 3, 1, 4, 2, 3, 0, 2, 1, 4, 0, 0, 2, 1, 1, 2, 1, 2},
    {2, 3, 2, 0, 2, 2, 2, 2, 0, 5, 1, 4, 1, 4, 1, 1, 0, 1, 2, 0, 1, 0, 1, 2},
    {2, 3, 2, 1, 0, 0, 1, 5, 1, 1, 2, 3, 0, 2, 1, 1, 1, 5, 1, 3, 0, 2, 2, 4},
    {2, 3, 2, 1, 0, 0, 2, 2, 2, 2, 1, 1, 0, 4, 1, 3, 1, 1, 2, 5, 0, 4, 2, 0},
    {2, 3, 2, 1, 0, 1, 2, 5, 2, 1, 1, 1, 0, 3, 2, 2, 2, 5, 1, 5, 0, 4, 2, 0},
    {2, 3, 2, 1, 0, 2, 2, 4, 1, 4, 1, 1, 2, 1, 1, 4, 0, 3, 2, 5, 0, 2, 1, 0},
    {2, 3, 2, 1, 0, 2, 2, 5, 2, 5, 1, 1, 0, 1, 1, 5, 1, 1, 1, 0, 0, 4, 2, 1},
    {2, 3, 2, 1, 1, 2, 1, 5, 2, 5, 2, 5, 1, 4, 1, 5, 0, 2, 1, 4, 0, 3, 2, 0},
    {2, 3, 2, 2, 0, 0, 1, 1, 0, 0, 1, 5, 0, 4, 1, 1, 1, 2, 2, 3, 0, 4, 1, 3},
    {2, 3, 2, 2, 1, 4, 1, 3, 0, 4, 1, 5, 0, 1, 2, 2, 0, 0, 2, 3, 1, 2, 1, 1},
    {2, 3, 2, 2, 2, 1, 1, 3, 0, 0, 2, 1, 0, 4, 1, 5, 1, 2, 2, 3, 0, 0, 1, 0},
    {2, 3, 2, 2, 2, 4, 1, 2, 0, 1, 1, 3, 0, 0, 1, 5, 1, 2, 1, 3, 1, 1, 2, 4},
    {2, 3, 2, 2, 2, 5, 1, 2, 0, 1, 1, 5, 0, 0, 2, 5, 1, 0, 1, 3, 1, 2, 1, 4},
    {2, 3, 2, 3, 0, 0, 2, 2, 2, 3, 1, 1, 0, 3, 2, 4, 2, 5, 2, 5, 0, 5, 2, 1},
    {2, 3, 2, 3, 0, 0, 2, 4, 1, 0, 2, 1, 0, 5, 1, 1, 2, 5, 1, 2, 1, 1, 1, 3},
    {2, 3, 2, 3, 0, 0, 2, 5, 0, 4, 1, 1, 0, 2, 1, 3, 1, 1, 2, 1, 2, 2, 2, 2},
    {2, 3, 2, 3, 0, 5, 1, 3, 2, 2, 1, 1, 0, 5, 1, 2, 0, 0, 2, 4, 1, 4, 1, 4},
    {2, 3, 2, 3, 2, 0, 1, 1, 1, 5, 2, 4, 0, 3, 2, 5, 0, 2, 1, 1, 2, 4, 2, 0},
    {2, 3, 2, 3, 2, 4, 1, 4, 1, 2, 2, 4, 0, 1, 1, 5, 1, 5, 1, 2, 0, 3, 2, 0},
    {2, 3, 2, 3, 2, 5, 2, 5, 1, 4, 1, 4, 0, 3, 2, 4, 0, 1, 2, 0, 0, 2, 1, 5},
    {2, 3, 2, 4, 1, 0, 2, 1, 0, 0, 1, 1, 0, 5, 1, 1, 0, 0, 2, 3, 1, 4, 1, 2},
    {2, 3, 2, 5, 0, 1, 1, 4, 1, 0, 2, 3, 0, 2, 1, 3, 1, 2, 1, 2, 2, 1, 1, 3},
    {2, 3, 2, 5, 0, 1, 2, 3, 0, 0, 1, 3, 0, 2, 1, 4, 1, 1, 1, 1, 2, 2, 2, 2},
    {2, 3, 2, 5, 1, 2, 1, 2, 0, 4, 1, 3, 0, 2, 1, 5, 1, 5, 2, 3, 0, 0, 1, 1},
    {2, 3, 2, 5, 1, 2, 2, 3, 1, 0, 1, 2, 0, 4, 2, 5, 2, 5, 2, 2, 0, 1, 1, 5},
    {2, 4, 1, 1, 0, 0, 2, 2, 0, 2, 1, 5, 1, 2, 2, 4, 1, 1, 1, 3, 1, 0, 2, 1},
    {2, 4, 1, 1, 1, 3, 1, 3, 0, 0, 2, 5, 1, 2, 1, 2, 0, 3, 1, 5, 0, 3, 1, 5},
    {2, 4, 1, 1, 1, 5, 1, 5, 1, 3, 2, 3, 0, 0, 1, 4, 0, 2, 2, 4, 0, 5, 1, 3},
    {2, 4, 1, 1, 2, 2, 1, 4, 0, 3, 2, 1, 1, 1, 2, 2, 1, 5, 1, 5, 0, 0, 1, 2},
    {2, 4, 1, 3, 1, 3, 1, 3, 0, 5, 2, 0, 0, 3, 1, 2, 0, 4, 1, 1, 2, 2, 1, 4},
    {2, 4, 1, 3, 1, 3, 2, 2, 2, 5, 2, 5, 0, 0, 1, 4, 0, 1, 2, 3, 0, 5, 2, 4},
    {2, 4, 1, 3, 2, 2, 1, 4, 2, 3, 1, 1, 0, 0, 2, 2, 0, 5, 2, 3, 2, 1, 2, 4},
    {2, 4, 1, 4, 0, 1, 2, 2, 0, 0, 1, 2, 2, 1, 2, 1, 0, 5, 2, 3, 1, 2, 2, 4},
    {2, 4, 1, 4, 2, 3, 2, 2, 0, 2, 2, 4, 0, 3, 2, 5, 0, 0, 2, 1, 2, 2, 2, 3},
    {2, 4, 1, 5, 0, 1, 2, 0, 2, 1, 2, 4, 0, 2, 2, 2, 0, 4, 2, 3, 2, 1, 1, 1},
    {2, 4, 1, 5, 1, 2, 1, 2, 0, 3, 1, 5, 0, 3, 2, 4, 1, 5, 1, 1, 0, 0, 1, 4},
    {2, 4, 2, 0, 0, 1, 2, 4, 1, 0, 1, 3, 1, 1, 1, 5, 0, 2, 1, 5, 1, 2, 1, 1},
    {2, 4, 2, 1, 0, 0, 1, 1, 1, 3, 2, 4, 0, 0, 1, 1, 0, 2, 1, 5, 1, 0, 1, 5},
    {2, 4, 2, 2, 0, 1, 1, 3, 2, 1, 2, 1, 0, 5, 1, 4, 0, 0, 2, 2, 2, 3, 2, 4},
    {2, 4, 2, 2, 1, 2, 1, 2, 0, 0, 1, 3, 1, 5, 2, 4, 0, 1, 1, 4, 1, 3, 2, 5},
    {2, 4, 2, 2, 1, 5, 1, 4, 1, 3, 2, 5, 2, 2, 2, 4, 0, 1, 1, 5, 0, 0, 2, 5},
    {2, 4, 2, 2, 2, 2, 1, 2, 0, 0, 2, 5, 2, 5, 2, 4, 0, 3, 1, 4, 2, 1, 2, 1},
    {2, 4, 2, 3, 0, 5, 1, 1, 2, 0, 2, 5, 1, 1, 2, 4, 0, 3, 2, 2, 2, 4, 2, 1},
    {2, 4, 2, 3, 1, 0, 1, 5, 0, 0, 1, 1, 0, 0, 2, 4, 0, 5, 1, 1, 1, 3, 1, 2},
    {2, 4, 2, 3, 1, 1, 1, 4, 0, 0, 2, 4, 2, 3, 2, 2, 0, 5, 1, 2, 1, 2, 1, 1},
    {2, 4, 2, 3, 1, 2, 2, 4, 0, 0, 2, 5, 0, 0, 2, 5, 0, 1, 1, 4, 2, 5, 1, 3},
    {2, 4, 2, 3, 1, 3, 1, 3, 1, 0, 2, 2, 0, 0, 1, 5, 0, 1, 1, 4, 0, 4, 1, 2},
    {2, 4, 2, 4, 0, 0, 2, 3, 1, 1, 1, 5, 1, 3, 2, 1, 0, 2, 1, 1, 1, 5, 1, 4},
    {2, 4, 2, 4, 0, 2, 2, 0, 0, 5, 1, 1, 1, 2, 1, 2, 0, 4, 2, 1, 2, 1, 1, 3},
    {2, 4, 2, 4, 0, 2, 2, 1, 1, 3, 1, 1, 0, 5, 2, 3, 0, 4, 1, 3, 2, 1, 2, 0},
    {2, 4, 2, 4, 1, 2, 2, 1, 0, 1, 1, 3, 1, 5, 1, 5, 0, 4, 2, 2, 0, 5, 2, 0},
    {2, 4, 2, 4, 1, 5, 2, 0, 0, 1, 1, 5, 2, 1, 2, 1, 2, 2, 2, 2, 0, 4, 2, 3},
    {2, 4, 2, 4, 1, 5, 2, 2, 0, 0, 2, 2, 1, 1, 1, 4, 0, 3, 1, 2, 2, 2, 2, 2},
    {2, 4, 2, 4, 2, 2, 2, 2, 0, 4, 1, 5, 0, 1, 2, 0, 1, 3, 1, 2, 0, 1, 2, 3},
    {2, 4, 2, 4, 2, 3, 2, 0, 1, 1, 2, 5, 0, 4, 2, 0, 0, 2, 2, 3, 2, 2, 1, 1},
    {2, 4, 2, 4, 2, 3, 2, 2, 0, 1, 1, 2, 0, 5, 1, 3, 0, 4, 2, 3, 1, 2, 2, 0},
    {2, 4, 2, 5, 1, 2, 1, 4, 0, 0, 1, 5, 1, 5, 1, 2, 0, 1, 2, 4, 0, 3, 2, 2},
    {2, 4, 2, 5, 1, 5, 1, 3, 1, 0, 2, 1, 0, 0, 1, 2, 0, 1, 1, 2, 0, 0, 2, 4},
    {2, 4, 2, 5, 2, 2, 2, 2, 0, 2, 1, 3, 0, 0, 2, 0, 1, 3, 1, 4, 0, 1, 2, 1},
    {2, 5, 1, 1, 0, 2, 2, 5, 2, 5, 2, 1, 1, 0, 1, 5, 1, 1, 1, 1, 0, 4, 1, 3},
    {2, 5, 1, 2, 0, 2, 2, 0, 2, 4, 2, 3, 0, 5, 2, 5, 0, 5, 1, 1, 1, 1, 1, 4},
    {2, 5, 1, 2, 1, 0, 1, 4, 1, 4, 1, 1, 0, 0, 2, 2, 0, 4, 1, 3, 1, 3, 1, 1},
    {2, 5, 1, 2, 2, 0, 2, 0, 0, 1, 2, 5, 0, 4, 2, 2, 2, 2, 2, 3, 2, 3, 2, 4},
    {2, 5, 1, 3, 0, 4, 1, 3, 2, 1, 2, 3, 0, 2, 1, 5, 1, 3, 1, 0, 0, 4, 2, 1},
    {2, 5, 1, 3, 1, 2, 2, 2, 0, 4, 2, 2, 0, 0, 2, 3, 1, 3, 1, 2, 2, 1, 2, 5},
    {2, 5, 1, 3, 1, 3, 2, 4, 0, 1, 1, 0, 0, 0, 2, 5, 0, 0, 2, 2, 0, 1, 1, 2},
    {2, 5, 1, 4, 0, 1, 1, 5, 1, 3, 2, 0, 1, 1, 2, 4, 0, 0, 1, 2, 1, 4, 1, 3},
    {2, 5, 1, 4, 0, 3, 1, 3, 0, 5, 2, 3, 1, 4, 1, 1, 0, 0, 2, 2, 0, 3, 2, 4},
    {2, 5, 1, 4, 2, 0, 2, 4, 2, 3, 2, 3, 0, 3, 2, 1, 0, 0, 2, 4, 1, 4, 2, 2},
    {2, 5, 1, 5, 0, 0, 1, 0, 1, 3, 2, 1, 0, 0, 2, 5, 0, 3, 1, 2, 0, 2, 1, 4},
    {2, 5, 1, 5, 0, 1, 2, 5, 1, 3, 1, 3, 0, 3, 1, 4, 1, 1, 1, 1, 0, 0, 1, 2},
    {2, 5, 1, 5, 2, 4, 2, 4, 0, 4, 2, 1, 2, 2, 2, 2, 0, 2, 2, 5, 0, 0, 2, 3},
    {2, 5, 2, 0, 1, 4, 1, 4, 2, 3, 2, 3, 0, 3, 2, 4, 0, 1, 2, 0, 0, 5, 2, 2},
    {2, 5, 2, 0, 2, 3, 1, 2, 1, 3, 1, 5, 0, 4, 2, 5, 1, 0, 2, 1, 0, 3, 1, 1},
    {2, 5, 2, 1, 0, 0, 1, 5, 0, 0, 2, 3, 1, 1, 1, 0, 1, 2, 2, 5, 0, 4, 1, 1},
    {2, 5, 2, 1, 0, 4, 2, 5, 0, 3, 1, 2, 2, 1, 2, 2, 1, 2, 1, 5, 0, 0, 1, 1},
    {2, 5, 2, 1, 1, 4, 1, 3, 2, 1, 1, 4, 0, 0, 2, 5, 1, 3, 1, 1, 0, 2, 1, 5},
    {2, 5, 2, 1, 2, 2, 2, 1, 0, 2, 2, 0, 2, 4, 2, 1, 0, 5, 2, 0, 1, 3, 2, 4},
    {2, 5, 2, 2, 1, 2, 1, 4, 0, 0, 1, 5, 1, 4, 2, 5, 0, 3, 1, 2, 0, 1, 2, 4},
    {2, 5, 2, 2, 1, 2, 1, 4, 0, 3, 2, 0, 2, 4, 2, 5, 0, 1, 1, 2, 2, 0, 2, 4},
    {2, 5, 2, 2, 1, 3, 1, 3, 0, 0, 1, 2, 0, 4, 1, 5, 1, 2, 1, 1, 0, 3, 2, 5},
    {2, 5, 2, 3, 0, 1, 1, 2, 0, 0, 2, 2, 2, 1, 2, 1, 1, 2, 2, 5, 0, 4, 1, 5},
    {2, 5, 2, 3, 0, 1, 2, 5, 0, 0, 2, 2, 2, 1, 2, 1, 1, 2, 1, 2, 0, 4, 1, 5},
    {2, 5, 2, 3, 0, 2, 2, 3, 1, 3, 1, 1, 0, 0, 2, 1, 2, 1, 2, 1, 0, 2, 1, 4},
    {2, 5, 2, 3, 1, 4, 1, 5, 0, 4, 1, 4, 2, 1, 1, 4, 0, 0, 1, 4, 0, 1, 1, 2},
    {2, 5, 2, 3, 2, 1, 2, 3, 0, 0, 2, 2, 0, 4, 2, 1, 1, 2, 1, 5, 0, 4, 1, 5},
    {2, 5, 2, 4, 1, 4, 1, 2, 1, 3, 1, 4, 1, 5, 1, 4, 0, 0, 1, 5, 0, 1, 2, 2},
    {2, 5, 2, 4, 2, 2, 1, 3, 1, 5, 1, 5, 1, 4, 1, 5, 0, 0, 2, 1, 0, 3, 1, 4},
    {2, 5, 2, 5, 0, 1, 1, 3, 2, 3, 2, 3, 0, 2, 2, 0, 2, 1, 2, 1, 0, 5, 2, 4},
    {2, 5, 2, 5, 0, 1, 2, 2, 0, 0, 2, 2, 0, 4, 2, 3, 1, 1, 1, 1, 0, 5, 1, 3},
    {2, 5, 2, 5, 0, 1, 2, 3, 0, 2, 1, 5, 2, 2, 2, 2, 1, 1, 1, 1, 0, 0, 1, 4},
    {2, 5, 2, 5, 0, 2, 1, 1, 1, 3, 2, 1, 0, 5, 2, 0, 2, 1, 2, 3, 0, 4, 1, 3},
    {2, 5, 2, 5, 0, 2, 2, 3, 1, 1, 1, 3, 0, 4, 2, 0, 1, 3, 2, 1, 0, 5, 1, 1},
    {2, 5, 2, 5, 0, 4, 2, 0, 0, 3, 1, 2, 1, 1, 2, 2, 2, 2, 2, 1, 0, 5, 1, 1},
    {2, 5, 2, 5, 2, 2, 2, 2, 0, 2, 2, 0, 2, 4, 2, 1, 0, 5, 1, 4, 0, 3, 2, 4},
};
// END AUTO M6 AUTOMATA

static Automaton to_automaton(const array<int, 20>& raw) {
    Automaton a;
    for (int s = 0; s < M; ++s) {
        const int base = s * 4;
        a.act[s][0] = raw[base + 0];
        a.nxt[s][0] = raw[base + 1];
        a.act[s][1] = raw[base + 2];
        a.nxt[s][1] = raw[base + 3];
    }
    return a;
}

static Automaton6 to_automaton6(const array<int, 24>& raw) {
    Automaton6 a;
    for (int s = 0; s < Automaton6::M6; ++s) {
        const int base = s * 4;
        a.act[s][0] = raw[base + 0];
        a.nxt[s][0] = raw[base + 1];
        a.act[s][1] = raw[base + 2];
        a.nxt[s][1] = raw[base + 3];
    }
    return a;
}

static bool can_move(const Grid& g, int i, int j, int dir) {
    return !g.wall_ahead(i, j, dir);
}

static int char_to_action(char c) {
    if (c == 'F') return 0;
    if (c == 'R') return 1;
    return 2;
}

struct FallbackTrans {
    char a0;
    int b0;
    char a1;
    int b1;
};

static void dfs_build_tour(const Grid& g, int si, int sj, vector<int>& moves) {
    const int N = g.N;
    vector<char> vis(N * N, 0);

    auto dfs = [&](auto&& self, int u, int prev_dir) -> void {
        vis[u] = 1;
        const int i = u / N;
        const int j = u % N;

        int order[4];
        if (prev_dir < 0) {
            order[0] = 0;
            order[1] = 1;
            order[2] = 2;
            order[3] = 3;
        } else {
            order[0] = prev_dir;
            order[1] = (prev_dir + 1) & 3;
            order[2] = (prev_dir + 3) & 3;
            order[3] = (prev_dir + 2) & 3;
        }

        for (int t = 0; t < 4; t++) {
            const int d = order[t];
            if (!can_move(g, i, j, d)) continue;
            int ni = i, nj = j;
            g.step_forward(ni, nj, d);
            const int v = ni * N + nj;
            if (vis[v] != 0) continue;
            moves.push_back(d);
            self(self, v, d);
            moves.push_back((d + 2) & 3);
        }
    };

    dfs(dfs, si * N + sj, -1);
}

static OutputSolution build_dfs_fallback_solution(const Grid& g) {
    vector<int> moves;
    dfs_build_tour(g, 0, 0, moves);

    vector<FallbackTrans> tv;
    int cur_dir = 0;  // U

    for (int want : moves) {
        const int diff = (want - cur_dir) & 3;
        if (diff == 1) {
            tv.push_back({'R', (int)tv.size() + 1, 'R', (int)tv.size() + 1});
            cur_dir = (cur_dir + 1) & 3;
        } else if (diff == 2) {
            tv.push_back({'R', (int)tv.size() + 1, 'R', (int)tv.size() + 1});
            cur_dir = (cur_dir + 1) & 3;
            tv.push_back({'R', (int)tv.size() + 1, 'R', (int)tv.size() + 1});
            cur_dir = (cur_dir + 1) & 3;
        } else if (diff == 3) {
            tv.push_back({'L', (int)tv.size() + 1, 'L', (int)tv.size() + 1});
            cur_dir = (cur_dir + 3) & 3;
        }

        const int next = (int)tv.size() + 1;
        tv.push_back({'F', next, 'R', (int)tv.size()});
    }

    if (tv.empty()) {
        tv.push_back({'R', 0, 'R', 0});
    } else {
        tv.back().b0 = 0;
    }

    OutputSolution sol;
    sol.m = (int)tv.size();
    sol.start_i = 0;
    sol.start_j = 0;
    sol.start_dir = 0;
    sol.trans.reserve(tv.size());
    for (const auto& t : tv) {
        sol.trans.push_back(
            {char_to_action(t.a0), t.b0, char_to_action(t.a1), t.b1});
    }
    return sol;
}

static bitset<400> periodic_cells_for_robot(const Grid& g,
                                            const Precomp& p,
                                            const OutputSolution& robot) {
    const int m = robot.m;
    const int S = g.N * g.N * DIRS * m;
    vector<int> first_seen(S, -1);
    vector<int> cell_hist;
    cell_hist.reserve(S);

    auto encode = [&](int cell, int dir, int st) {
        return (((cell)*DIRS + dir) * m + st);
    };

    int cell = robot.start_i * g.N + robot.start_j;
    int dir = robot.start_dir;
    int st = 0;
    int step = 0;
    while (true) {
        const int code = encode(cell, dir, st);
        if (first_seen[code] != -1) {
            const int cyc_begin = first_seen[code];
            bitset<400> cells;
            for (int t = cyc_begin; t < (int)cell_hist.size(); t++) {
                cells.set(cell_hist[t], true);
            }
            return cells;
        }
        first_seen[code] = step++;
        cell_hist.push_back(cell);

        const bool w = p.wall[cell][dir];
        const int act = w ? robot.trans[st][2] : robot.trans[st][0];
        const int ns = w ? robot.trans[st][3] : robot.trans[st][1];
        if (act == 0) {
            if (w) {
                dir = (dir + 1) & 3;
            } else {
                cell = p.next_cell[cell][dir];
            }
        } else if (act == 1) {
            dir = (dir + 1) & 3;
        } else {
            dir = (dir + 3) & 3;
        }
        st = ns;
    }
}

static OutputSolution make_spin_robot(int i, int j) {
    OutputSolution sol;
    sol.m = 1;
    sol.start_i = i;
    sol.start_j = j;
    sol.start_dir = 0;
    sol.trans = {{array<int, 4>{1, 0, 1, 0}}};  // always turn right
    return sol;
}

static pair<vector<string>, vector<string>> zero_added_walls(const Grid& g) {
    return {vector<string>(g.N, string(g.N - 1, '0')),
            vector<string>(g.N - 1, string(g.N, '0'))};
}

static Grid merged_grid_with_added(const Grid& base,
                                   const vector<string>& add_v,
                                   const vector<string>& add_h) {
    Grid out = base;
    for (int i = 0; i < base.N; i++) {
        for (int j = 0; j < base.N - 1; j++) {
            if (add_v[i][j] == '1') out.v[i][j] = '1';
        }
    }
    for (int i = 0; i < base.N - 1; i++) {
        for (int j = 0; j < base.N; j++) {
            if (add_h[i][j] == '1') out.h[i][j] = '1';
        }
    }
    return out;
}

static int count_added_walls(const vector<string>& add_v,
                             const vector<string>& add_h) {
    int cnt = 0;
    for (const auto& s : add_v) {
        for (char c : s) cnt += (c == '1');
    }
    for (const auto& s : add_h) {
        for (char c : s) cnt += (c == '1');
    }
    return cnt;
}

struct BestManager {
    int A_K, A_M, A_W;
    const Grid& g;

    bool has_best = false;
    long long best_v = (1LL << 62);
    vector<OutputSolution> best_robots;
    vector<string> best_add_v;
    vector<string> best_add_h;

    BestManager(int A_K, int A_M, int A_W, const Grid& g)
        : A_K(A_K), A_M(A_M), A_W(A_W), g(g) {}

    long long score(int K, int sumM, int W) const {
        return 1LL * A_K * (K - 1) + 1LL * A_M * sumM + 1LL * A_W * W;
    }

    long long best_score() const { return best_v; }

    bool has_solution() const { return has_best; }

    void consider_candidate(const OutputSolution& primary,
                            const vector<string>& add_v,
                            const vector<string>& add_h) {
        Grid mg = merged_grid_with_added(g, add_v, add_h);
        Precomp mp = build_precomp(mg);
        bitset<400> covered = periodic_cells_for_robot(mg, mp, primary);
        vector<OutputSolution> robots{primary};

        if (A_K == 0) {
            for (int c = 0; c < mg.N * mg.N; c++) {
                if (covered.test(c)) continue;
                robots.push_back(make_spin_robot(c / mg.N, c % mg.N));
                covered.set(c, true);
            }
        }

        if ((int)covered.count() < mg.N * mg.N) return;

        long long K = (long long)robots.size();
        long long sumM = 0;
        for (const auto& r : robots) sumM += r.m;
        long long W = count_added_walls(add_v, add_h);
        long long V = score((int)K, (int)sumM, (int)W);

        if (!has_best || V < best_v) {
            has_best = true;
            best_v = V;
            best_robots = std::move(robots);
            best_add_v = add_v;
            best_add_h = add_h;
        }
    }

    void print_best() const {
        cout << best_robots.size() << '\n';
        for (const auto& sol : best_robots) {
            cout << sol.m << ' ' << sol.start_i << ' ' << sol.start_j << ' '
                 << dir_char(sol.start_dir) << '\n';
            for (const auto& t : sol.trans) {
                cout << action_char(t[0]) << ' ' << t[1] << ' ' << action_char(t[2])
                     << ' ' << t[3] << '\n';
            }
        }
        if (!best_add_v.empty() && !best_add_h.empty()) {
            for (const auto& s : best_add_v) cout << s << '\n';
            for (const auto& s : best_add_h) cout << s << '\n';
        } else {
            print_zero_added_walls(g);
        }
    }
};

static bool find4(const Grid& g,
                  OutputSolution& out,
                  const BestManager& manager,
                  const function<void(const OutputSolution&,
                                      const vector<string>&,
                                      const vector<string>&)>& submit) {
    if (manager.has_solution() && manager.best_score() <= manager.score(1, 4, 0)) {
        return false;
    }
    constexpr int M4 = 4;
    const int total_cells = g.N * g.N;
    auto [zv, zh] = zero_added_walls(g);
    Precomp p = build_precomp(g);
    int best_cov = -1;
    for (int wall_config = 0; wall_config < (1 << (3 * M4)); wall_config++) {
        Automaton4 aut;
        make_diagonal_automaton(aut, wall_config);
        int si = 0, sj = 0, sd = 0, ss = 0;
        const int cov = evaluate_m4_diagonal(g, p, aut, si, sj, sd, ss);
        if (cov > best_cov) {
            best_cov = cov;
            out = make_m4_solution(aut, si, sj, sd, ss);
            submit(out, zv, zh);
        }
        if (cov == total_cells) {
            out = make_m4_solution(aut, si, sj, sd, ss);
            submit(out, zv, zh);
            return true;
        }
    }
    return false;
}

static OutputSolution make_m5_solution(const Automaton& cand,
                                       const EvalResult& ev) {
    int s = 0, i = 0, j = 0, dir = 0;
    if (ev.best_start_node != -1) {
        decode_node(ev.best_start_node, s, i, j, dir);
    }
    OutputSolution sol;
    sol.m = M;
    sol.start_i = i;
    sol.start_j = j;
    sol.start_dir = dir;
    sol.trans.reserve(M);
    for (int st = 0; st < M; st++) {
        sol.trans.push_back(
            {cand.act[st][0], cand.nxt[st][0], cand.act[st][1], cand.nxt[st][1]});
    }
    return sol;
}

static bool find5(const Grid& g,
                  OutputSolution& out,
                  const BestManager& manager,
                  const function<void(const OutputSolution&,
                                      const vector<string>&,
                                      const vector<string>&)>& submit) {
    if (manager.has_solution() && manager.best_score() <= manager.score(1, 5, 0)) {
        return false;
    }
    auto [zv, zh] = zero_added_walls(g);
    Precomp p = build_precomp(g);
    int best_cov = -1;
    bool full = false;
    for (const auto& raw : kSeedAutomataRawM5) {
        const Automaton cand = to_automaton(raw);
        const EvalResult ev = evaluate(p, cand);
        if (ev.best_cov > best_cov) {
            best_cov = ev.best_cov;
            out = make_m5_solution(cand, ev);
            submit(out, zv, zh);
        }
        if (ev.best_cov == 400) full = true;
    }
    return full;
}

static void add_random_walls_for_B(const Grid& g,
                                   int wall_count,
                                   std::mt19937& rng,
                                   vector<string>& add_v,
                                   vector<string>& add_h) {
    const int edge_cnt = 2 * g.N * (g.N - 1);
    const int v_edges = g.N * (g.N - 1);
    std::uniform_int_distribution<int> dist_edge(0, edge_cnt - 1);
    int placed = 0;
    while (placed < wall_count) {
        int e = dist_edge(rng);
        if (e < v_edges) {
            int i = e / (g.N - 1);
            int j = e % (g.N - 1);
            if (add_v[i][j] == '1') continue;
            add_v[i][j] = '1';
        } else {
            e -= v_edges;
            int i = e / g.N;
            int j = e % g.N;
            if (add_h[i][j] == '1') continue;
            add_h[i][j] = '1';
        }
        placed++;
    }
}

static bool find5_with_random_one_wall_for_B(
    const Grid& g,
    std::chrono::steady_clock::time_point deadline,
    OutputSolution& out,
    const BestManager& manager,
    const function<void(const OutputSolution&,
                        const vector<string>&,
                        const vector<string>&)>& submit) {
    if (manager.has_solution() && manager.best_score() <= manager.score(1, 5, 1)) {
        return false;
    }
    std::mt19937 rng((uint32_t)chrono::high_resolution_clock::now()
                         .time_since_epoch()
                         .count());
    const int edge_cnt = 2 * g.N * (g.N - 1);
    const int v_edges = g.N * (g.N - 1);
    vector<int> edges(edge_cnt);
    iota(edges.begin(), edges.end(), 0);
    shuffle(edges.begin(), edges.end(), rng);

    for (int e : edges) {
        if (std::chrono::steady_clock::now() >= deadline) break;
        auto [add_v, add_h] = zero_added_walls(g);
        if (e < v_edges) {
            int i = e / (g.N - 1);
            int j = e % (g.N - 1);
            add_v[i][j] = '1';
        } else {
            int eh = e - v_edges;
            int i = eh / g.N;
            int j = eh % g.N;
            add_h[i][j] = '1';
        }

        Grid mg = merged_grid_with_added(g, add_v, add_h);
        OutputSolution tmp;
        auto submit_with_wall = [&](const OutputSolution& cand,
                                    const vector<string>&,
                                    const vector<string>&) {
            submit(cand, add_v, add_h);
        };
        if (find5(mg, tmp, manager, submit_with_wall)) {
            out = tmp;
            cerr << "FIND 5 + 1" << endl;
            return true;
        }
    }
    return false;
}

static bool find4_with_random_one_wall_for_B(
    const Grid& g,
    std::chrono::steady_clock::time_point deadline,
    OutputSolution& out,
    const BestManager& manager,
    const function<void(const OutputSolution&,
                        const vector<string>&,
                        const vector<string>&)>& submit) {
    if (manager.has_solution() && manager.best_score() <= manager.score(1, 4, 1)) {
        return false;
    }
    std::mt19937 rng((uint32_t)chrono::high_resolution_clock::now()
                         .time_since_epoch()
                         .count());
    const int edge_cnt = 2 * g.N * (g.N - 1);
    const int v_edges = g.N * (g.N - 1);
    vector<int> edges(edge_cnt);
    iota(edges.begin(), edges.end(), 0);
    shuffle(edges.begin(), edges.end(), rng);

    for (int e : edges) {
        if (std::chrono::steady_clock::now() >= deadline) break;
        auto [add_v, add_h] = zero_added_walls(g);
        if (e < v_edges) {
            int i = e / (g.N - 1);
            int j = e % (g.N - 1);
            add_v[i][j] = '1';
        } else {
            int eh = e - v_edges;
            int i = eh / g.N;
            int j = eh % g.N;
            add_h[i][j] = '1';
        }

        Grid mg = merged_grid_with_added(g, add_v, add_h);
        OutputSolution tmp;
        auto submit_with_wall = [&](const OutputSolution& cand,
                                    const vector<string>&,
                                    const vector<string>&) {
            submit(cand, add_v, add_h);
        };
        if (find4(mg, tmp, manager, submit_with_wall)) {
            out = tmp;
            cerr << "FIND 4 + 1" << endl;
            return true;
        }
    }
    return false;
}

static bool find4_with_random_two_wall_for_B(
    const Grid& g,
    std::chrono::steady_clock::time_point deadline,
    OutputSolution& out,
    const BestManager& manager,
    const function<void(const OutputSolution&,
                        const vector<string>&,
                        const vector<string>&)>& submit) {
    if (manager.has_solution() && manager.best_score() <= manager.score(1, 4, 2)) {
        return false;
    }
    std::mt19937 rng((uint32_t)chrono::high_resolution_clock::now()
                         .time_since_epoch()
                         .count());

    while (std::chrono::steady_clock::now() < deadline) {
        auto [add_v, add_h] = zero_added_walls(g);
        add_random_walls_for_B(g, 2, rng, add_v, add_h);

        Grid mg = merged_grid_with_added(g, add_v, add_h);
        OutputSolution tmp;
        auto submit_with_wall = [&](const OutputSolution& cand,
                                    const vector<string>&,
                                    const vector<string>&) {
            submit(cand, add_v, add_h);
        };
        if (find4(mg, tmp, manager, submit_with_wall)) {
            out = tmp;
            cerr << "FIND 4 + 2" << endl;
            return true;
        }
    }
    return false;
}

static void random_init_m6(Automaton6& a, std::mt19937& rng) {
    std::uniform_int_distribution<int> dist_state(0, Automaton6::M6 - 1);
    for (int s = 0; s < Automaton6::M6; s++) {
        std::uniform_int_distribution<int> dist_a0(0, 2);
        std::uniform_int_distribution<int> dist_a1(1, 2);
        a.act[s][0] = dist_a0(rng);
        a.nxt[s][0] = dist_state(rng);
        a.act[s][1] = dist_a1(rng);
        a.nxt[s][1] = dist_state(rng);
    }
}

static void mutate_once_m6(Automaton6& a, std::mt19937& rng) {
    std::uniform_int_distribution<int> dist_s(0, Automaton6::M6 - 1);
    std::uniform_int_distribution<int> dist_w(0, 1);
    std::uniform_int_distribution<int> dist_what(0, 1);  // 0:action,1:next
    const int s = dist_s(rng);
    const int w = dist_w(rng);
    if (dist_what(rng) == 0) {
        if (w == 0) {
            std::uniform_int_distribution<int> dist_a(0, 2);
            a.act[s][w] = dist_a(rng);
        } else {
            std::uniform_int_distribution<int> dist_a(1, 2);
            a.act[s][w] = dist_a(rng);
        }
    } else {
        std::uniform_int_distribution<int> dist_state(0, Automaton6::M6 - 1);
        a.nxt[s][w] = dist_state(rng);
    }
}

static OutputSolution make_m6_solution(const Automaton6& a,
                                       const EvalResult& ev) {
    int s = 0, i = 0, j = 0, dir = 0;
    if (ev.best_start_node != -1) {
        decode_node6(ev.best_start_node, s, i, j, dir);
    }
    OutputSolution sol;
    sol.m = Automaton6::M6;
    sol.start_i = i;
    sol.start_j = j;
    sol.start_dir = dir;
    sol.trans.reserve(Automaton6::M6);
    for (int st = 0; st < Automaton6::M6; st++) {
        sol.trans.push_back(
            {a.act[st][0], a.nxt[st][0], a.act[st][1], a.nxt[st][1]});
    }
    return sol;
}

static bool find6(const Grid& g,
                  OutputSolution& out,
                  const BestManager& manager,
                  const function<void(const OutputSolution&,
                                      const vector<string>&,
                                      const vector<string>&)>& submit) {
    if (manager.has_solution() && manager.best_score() <= manager.score(1, 6, 0)) {
        return false;
    }
    int best_cov = -1;
    auto [zv, zh] = zero_added_walls(g);
    Precomp p = build_precomp(g);
    EvalM6Workspace ws = init_m6_workspace();

    for (const auto& raw : kSeedAutomataRawM6) {
        Automaton6 cand = to_automaton6(raw);
        EvalResult ev = evaluate_m6_fast(p, cand, ws);
        if (ev.best_cov > best_cov) {
            best_cov = ev.best_cov;
            out = make_m6_solution(cand, ev);
            submit(out, zv, zh);
        }
        if (ev.best_cov == 400) return true;
    }
    return false;
}

static bool find6_by_sa(const Grid& g,
                        std::chrono::steady_clock::time_point deadline,
                        OutputSolution& out,
                        const BestManager& manager,
                        const function<void(const OutputSolution&,
                                            const vector<string>&,
                                            const vector<string>&)>& submit) {
    if (manager.has_solution() && manager.best_score() <= manager.score(1, 6, 0)) {
        return false;
    }
    std::mt19937 rng((uint32_t)chrono::high_resolution_clock::now()
                         .time_since_epoch()
                         .count());
    const int ITER = 10000;
    const double start_temp = 1.0;
    const double end_temp = 0.1;
    int best_cov = -1;
    auto [zv, zh] = zero_added_walls(g);
    Precomp p = build_precomp(g);
    EvalM6Workspace ws = init_m6_workspace();

    while (true) {
        if (std::chrono::steady_clock::now() >= deadline) break;

        Automaton6 cur_a;
        random_init_m6(cur_a, rng);
        EvalResult cur = evaluate_m6_fast(p, cur_a, ws);
        if (cur.best_cov == 400) {
            out = make_m6_solution(cur_a, cur);
            submit(out, zv, zh);
            return true;
        }
        if (cur.best_cov > best_cov) {
            best_cov = cur.best_cov;
            out = make_m6_solution(cur_a, cur);
            submit(out, zv, zh);
        }

        for (int it = 0; it < ITER; it++) {
            if (it % 100 == 0) {
                cerr << "find6 iter " << it << ", best_cov = " << best_cov << endl;
            }
            if (it % 100 == 0 && std::chrono::steady_clock::now() >= deadline) {
                break;
            }
            const double temp =
                start_temp + (end_temp - start_temp) * (double)it / ITER;

            Automaton6 cand = cur_a;
            for (int k = 0; k < 3; k++) mutate_once_m6(cand, rng);
            EvalResult ev = evaluate_m6_fast(p, cand, ws);
            if (ev.best_cov == 400) {
                out = make_m6_solution(cand, ev);
                submit(out, zv, zh);
                return true;
            }
            if (ev.best_cov > best_cov) {
                best_cov = ev.best_cov;
                out = make_m6_solution(cand, ev);
                submit(out, zv, zh);
            }

            bool accept = false;
            if (ev.best_cov >= cur.best_cov) {
                accept = true;
            } else {
                const double diff = (double)(ev.best_cov - cur.best_cov);
                const double prob = std::exp(diff / temp);
                accept = (prob > 1e-9 && (double)rng() / rng.max() < prob);
            }

            if (accept) {
                cur_a = std::move(cand);
                cur = ev;
            }
        }
    }
    return false;
}

int main() {
    // Time limit is 2 seconds
    const auto now = std::chrono::steady_clock::now();

    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    Grid g;
    int A_K = 0;
    int A_M = 0;
    int A_W = 0;
    cin >> g.N >> A_K >> A_M >> A_W;
    if (g.N != NMAX) {
        return 0;
    }

    g.v.resize(g.N);
    for (int i = 0; i < g.N; ++i) cin >> g.v[i];
    g.h.resize(g.N - 1);
    for (int i = 0; i < g.N - 1; ++i) cin >> g.h[i];

    BestManager manager(A_K, A_M, A_W, g);
    auto submit = [&](const OutputSolution& cand,
                      const vector<string>& add_v,
                      const vector<string>& add_h) {
        manager.consider_candidate(cand, add_v, add_h);
    };

    OutputSolution sol;
    find4(g, sol, manager, submit);

    {
        const auto b_deadline_2 = now + std::chrono::milliseconds(700);
        find4_with_random_one_wall_for_B(g, b_deadline_2, sol, manager, submit);
    }

    find5(g, sol, manager, submit);

    find6(g, sol, manager, submit);

    // B-only boost: if wall is cheaper than one state, try random +1/+2 walls.
    {
        const auto b_deadline_2 = now + std::chrono::milliseconds(1300);
        find4_with_random_two_wall_for_B(g, b_deadline_2, sol, manager, submit);
        const auto b_deadline_1 = now + std::chrono::milliseconds(1900);
        find5_with_random_one_wall_for_B(g, b_deadline_1, sol, manager, submit);
    }


    // Build fallback first as a safe baseline candidate.
    OutputSolution fallback = build_dfs_fallback_solution(g);
    auto [zv, zh] = zero_added_walls(g);
    submit(fallback, zv, zh);

    {
        const auto deadline = now + std::chrono::milliseconds(1950);
        find6_by_sa(g, deadline, sol, manager, submit);
    }

    manager.print_best();

    return 0;
}

Submission Info

Judge Result