Submission #38915876

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Source Code Expand

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T, typename V>
void ndarray(vector<T>& vec, const V& val, int len) { vec.assign(len, val); }
template <typename T, typename V, typename... Args> void ndarray(vector<T>& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); }
template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }
template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }
const std::vector<std::pair<int, int>> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <class T1, class T2> T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); }
template <class T1, class T2> std::pair<T1, T2> operator+(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first + r.first, l.second + r.second); }
template <class T1, class T2> std::pair<T1, T2> operator-(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first - r.first, l.second - r.second); }
template <class T> std::vector<T> sort_unique(std::vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <class T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }
template <class T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }
template <class IStream, class T> IStream &operator>>(IStream &is, std::vector<T> &vec) { for (auto &v : vec) is >> v; return is; }

template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec);
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr);
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const pair<T, U> &pa);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa);
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp);
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp);
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl);

template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
template <class... T> std::istream &operator>>(std::istream &is, std::tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; }
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";
#define dbg(x) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl
#define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl : std::cerr)
#else
#define dbg(x) ((void)0)
#define dbgif(cond, x) ((void)0)
#endif

template <class DistanceMatrix> std::vector<std::pair<int, int>> mst_edges(const DistanceMatrix &dist) {
    using T = decltype((*dist.adjacents(0).begin()).second);

    if (dist.n() <= 1) return {};

    std::vector<T> dp(dist.n(), std::numeric_limits<T>::max());
    std::vector<int> prv(dist.n(), -1);
    std::vector<int> used(dist.n());
    std::vector<std::pair<int, int>> ret(dist.n() - 1);

    for (int t = 0; t < dist.n(); ++t) {
        int x = std::min_element(dp.cbegin(), dp.cend()) - dp.cbegin();
        dp.at(x) = std::numeric_limits<T>::max();
        used.at(x) = 1;
        if (t > 0) ret.at(t - 1) = {prv.at(x), x};

        for (auto [y, len] : dist.adjacents(x)) {
            if (!used.at(y) and len < dp.at(y)) dp.at(y) = len, prv.at(y) = x;
        }
    }

    return ret;
}

// http://webhotel4.ruc.dk/~keld/research/LKH/LKH-2.0/DOC/LKH_REPORT.pdf, p.20
template <class DistanceMatrix> auto calc_lkh_alpha(const DistanceMatrix &dist) {
    using T = decltype((*dist.adjacents(0).begin()).second);

    std::vector<std::vector<int>> to(dist.n());

    for (auto [s, t] : mst_edges(dist)) {
        to.at(s).push_back(t);
        to.at(t).push_back(s);
    }

    std::vector ret(dist.n(), std::vector<T>(dist.n()));

    for (int s = 0; s < dist.n(); ++s) {
        auto rec = [&](auto &&self, int now, int prv, T hi) -> void {
            ret.at(s).at(now) = dist(s, now) - hi;
            for (int nxt : to.at(now)) {
                if (nxt == prv) continue;
                self(self, nxt, now, std::max(hi, dist(now, nxt)));
            }
        };
        rec(rec, s, -1, T());
    }

    // Determining special node for the 1-tree
    // Reference: p.26 of http://webhotel4.ruc.dk/~keld/research/LKH/LKH-2.0/DOC/LKH_REPORT.pdf
    int best_one = -1;
    T longest_2nd_nearest = T();

    for (int one = 0; one < dist.n(); ++one) {
        if (to.at(one).size() != 1) continue;
        const int ng = to.at(one).front();
        bool found = false;
        T second_nearest = T();

        for (auto [v, len] : dist.adjacents(one)) {
            if (v == ng) continue;
            if (!found) {
                found = true, second_nearest = len;
            } else if (len < second_nearest) {
                second_nearest = len;
            }
        }

        if (found and (best_one < 0 or second_nearest > longest_2nd_nearest)) best_one = one, longest_2nd_nearest = second_nearest;
    }

    if (best_one != -1) {
        for (auto [v, len] : dist.adjacents(best_one)) {
            if (v == to.at(best_one).front()) continue;
            ret.at(best_one).at(v) = ret.at(v).at(best_one) = len - longest_2nd_nearest;
        }
    }

    return ret;
}

template <class T> class dense_distance_matrix {
    int _n;
    std::vector<T> _d;

public:
    dense_distance_matrix(const std::vector<std::vector<T>> &distance_vecvec) : _n(distance_vecvec.size()) {
        _d.reserve(n() * n());
        for (const auto &vec : distance_vecvec) _d.insert(end(_d), begin(vec), end(vec));
    }

    template <class U> void apply_pi(const std::vector<U> &pi) {
        for (int i = 0; i < n(); ++i) {
            for (int j = 0; j < n(); ++j) _d.at(i * n() + j) += pi.at(i) + pi.at(j);
        }
    }

    int n() const noexcept { return _n; }

    T dist(int s, int t) const { return _d.at(s * n() + t); }
    T operator()(int s, int t) const { return dist(s, t); }

    struct adjacents_sequence {
        const dense_distance_matrix *ptr;
        int from;
        struct iterator {
            const dense_distance_matrix *ptr;
            int from;
            int to;
            iterator operator++() { return {ptr, from, to++}; }
            std::pair<int, T> operator*() const { return {to, ptr->dist(from, to)}; }
            bool operator!=(const iterator &rhs) const { return to != rhs.to or ptr != rhs.ptr or from != rhs.from; }
        };
        iterator begin() const { return iterator{ptr, from, 0}; }
        iterator end() const { return iterator{ptr, from, ptr->n()}; }
    };

    adjacents_sequence adjacents(int from) const { return {this, from}; }
};



template <class T> class csr_distance_matrix {

    int _rows = 0;
    std::vector<int> begins;
    std::vector<std::pair<int, T>> vals;

public:
    csr_distance_matrix() : csr_distance_matrix({}, 0) {}

    csr_distance_matrix(const std::vector<std::tuple<int, int, T>> &init, int rows) : _rows(rows), begins(rows + 1) {
        std::vector<int> degs(rows);
        for (const auto &p : init) ++degs.at(std::get<0>(p));

        for (int i = 0; i < rows; ++i) begins.at(i + 1) = begins.at(i) + degs.at(i);

        vals.resize(init.size(), std::make_pair(-1, T()));
        for (auto [i, j, w] : init) vals.at(begins.at(i + 1) - (degs.at(i)--)) = {j, w};
    }

    void apply_pi(const std::vector<T> &pi) {
        for (int i = 0; i < n(); ++i) {
            for (auto &[j, d] : adjacents(i)) d += pi.at(i) + pi.at(j);
        }
    }

    int n() const noexcept { return _rows; }

    struct adjacents_sequence {
        csr_distance_matrix *ptr;
        int from;

        using iterator = typename std::vector<std::pair<int, T>>::iterator;
        iterator begin() { return std::next(ptr->vals.begin(), ptr->begins.at(from)); }
        iterator end() { return std::next(ptr->vals.begin(), ptr->begins.at(from + 1)); }
    };

    struct const_adjacents_sequence {
        const csr_distance_matrix *ptr;
        const int from;

        using const_iterator = typename std::vector<std::pair<int, T>>::const_iterator;
        const_iterator begin() const { return std::next(ptr->vals.cbegin(), ptr->begins.at(from)); }
        const_iterator end() const { return std::next(ptr->vals.cbegin(), ptr->begins.at(from + 1)); }
    };

    adjacents_sequence adjacents(int from) { return {this, from}; }

    const_adjacents_sequence adjacents(int from) const { return {this, from}; }
    const_adjacents_sequence operator()(int from) const { return {this, from}; }
};

template <class DistanceMatrix>
auto build_adjacent_info(const DistanceMatrix &dist, int sz) {
    using T = decltype((*dist.adjacents(0).begin()).second);

    const std::vector<std::vector<T>> alpha = calc_lkh_alpha(dist);

    std::vector<std::tuple<int, int, T>> adjacent_edges;

    std::vector<std::tuple<T, T, int>> candidates;
    for (int i = 0; i < dist.n(); ++i) {
        candidates.clear();
        for (auto [j, d] : dist.adjacents(i)) {
            if (i != j) candidates.emplace_back(alpha.at(i).at(j), d, j);
        }

        const int final_sz = std::min<int>(sz, candidates.size());
        std::nth_element(candidates.begin(), candidates.begin() + final_sz, candidates.end());

        candidates.resize(final_sz);
        std::sort(candidates.begin(), candidates.end(), [&](const auto &l, const auto &r) { return std::get<1>(l) < std::get<1>(r); });
        for (auto [alpha, dij, j] : candidates) adjacent_edges.emplace_back(i, j, dij);
    }
    return csr_distance_matrix(adjacent_edges, dist.n());
}

template <class DistanceMatrix, class Adjacents> struct SymmetricTSP {
    DistanceMatrix dist;
    Adjacents adjacents;
    using T = decltype((*dist.adjacents(0).begin()).second);

    struct Solution {
        T cost;
        std::vector<int> path;

        template <class OStream> friend OStream &operator<<(OStream &os, const Solution &x) {
            os << "[cost=" << x.cost << ", path=(";
            for (int i : x.path) os << i << ",";
            return os << x.path.front() << ")]";
        }
    };

    T eval(const Solution &sol) const {
        T ret = T();
        int now = sol.path.back();
        for (int nxt : sol.path) ret += dist(now, nxt), now = nxt;
        return ret;
    }

    SymmetricTSP(const DistanceMatrix &distance_matrix, const Adjacents &adjacents) : dist(distance_matrix), adjacents(adjacents) {}

    Solution nearest_neighbor(int init) const {
        if (n() == 0) return {T(), {}};
        int now = init;
        std::vector<int> ret{now}, alive(n(), 1);
        T len = T();
        ret.reserve(n());
        alive.at(now) = 0;
        while (int(ret.size()) < n()) {
            int nxt = -1;
            for (int i = 0; i < n(); ++i) {
                if (alive.at(i) and (nxt < 0 or dist(now, i) < dist(now, nxt))) nxt = i;
            }
            ret.push_back(nxt);
            alive.at(nxt) = 0;
            len += dist(now, nxt);
            now = nxt;
        }
        len += dist(ret.back(), ret.front());
        return Solution{len, ret};
    }

    void two_opt(Solution &sol) const {
        static std::vector<int> v_to_i;
        v_to_i.resize(n());
        for (int i = 0; i < n(); ++i) v_to_i.at(sol.path.at(i)) = i;
        while (true) {
            bool updated = false;
            for (int i = 0; i < n() and !updated; ++i) {
                const int u = sol.path.at(i), nxtu = sol.path.at(modn(i + 1));
                const T dunxtu = dist(u, nxtu);

                for (auto [v, duv] : adjacents(u)) {
                    if (duv >= dunxtu) break;
                    int j = v_to_i.at(v), nxtv = sol.path.at(modn(j + 1));
                    T diff = duv + dist(nxtu, nxtv) - dunxtu - dist(v, nxtv);
                    if (diff < 0) {
                        sol.cost += diff;
                        int l, r;
                        if (modn(j - i) < modn(i - j)) {
                            l = modn(i + 1), r = j;
                        } else {
                            l = modn(j + 1), r = i;
                        }
                        while (l != r) {
                            std::swap(sol.path.at(l), sol.path.at(r));
                            v_to_i.at(sol.path.at(l)) = l;
                            v_to_i.at(sol.path.at(r)) = r;
                            l = modn(l + 1);
                            if (l == r) break;
                            r = modn(r - 1);
                        }
                        updated = true;
                        break;
                    }
                }
                if (updated) break;

                for (auto [nxtv, dnxtunxtv] : adjacents(nxtu)) {
                    if (dnxtunxtv >= dunxtu) break;
                    int j = modn(v_to_i.at(nxtv) - 1), v = sol.path.at(j);
                    T diff = dist(u, v) + dnxtunxtv - dunxtu - dist(v, nxtv);
                    if (diff < 0) {
                        sol.cost += diff;
                        int l, r;
                        if (modn(j - i) < modn(i - j)) {
                            l = modn(i + 1), r = j;
                        } else {
                            l = modn(j + 1), r = i;
                        }
                        while (l != r) {
                            std::swap(sol.path.at(l), sol.path.at(r));
                            v_to_i.at(sol.path.at(l)) = l;
                            v_to_i.at(sol.path.at(r)) = r;
                            l = modn(l + 1);
                            if (l == r) break;
                            r = modn(r - 1);
                        }
                        updated = true;
                        break;
                    }
                }
            }
            if (!updated) break;
        }
    }

    bool three_opt(Solution &sol) const {
        static std::vector<int> v_to_i;
        v_to_i.resize(n());
        for (int i = 0; i < n(); ++i) v_to_i.at(sol.path.at(i)) = i;

        auto check_uvw_order = [](int u, int v, int w) {
            int i = v_to_i.at(u);
            int j = v_to_i.at(v);
            int k = v_to_i.at(w);
            if (i < j and j < k) return true;
            if (j < k and k < i) return true;
            if (k < i and i < j) return true;
            return false;
        };

        auto rev = [&](const int u, const int v) -> void {
            int l = v_to_i.at(u), r = v_to_i.at(v);
            while (l != r) {
                std::swap(sol.path.at(l), sol.path.at(r));
                l = modn(l + 1);
                if (l == r) break;
                r = modn(r - 1);
            }
        };

        static int i = 0;
        for (int nseen = 0; nseen < n(); ++nseen, i = modn(i + 1)) {
            const int u = sol.path.at(modn(i - 1)), nxtu = sol.path.at(i);
            const T dunxtu = dist(u, nxtu);

            // type 1 / 3
            for (const auto &[nxtv, dunxtv] : adjacents(u)) {
                if (dunxtv >= dunxtu) break;
                const int v = sol.path.at(modn(v_to_i.at(nxtv) - 1));
                const T dvnxtv = dist(v, nxtv);

                // type 1
                for (const auto &[nxtw, dvnxtw] : adjacents(v)) {
                    if (nxtw == nxtv or nxtw == nxtu) continue;
                    if (dunxtv + dvnxtw >= dunxtu + dvnxtv) break;
                    const int w = sol.path.at(modn(v_to_i.at(nxtw) - 1));

                    if (!check_uvw_order(u, v, w)) continue;

                    const T current = dunxtu + dvnxtv + dist(w, nxtw);
                    if (T diff = dunxtv + dist(w, nxtu) + dvnxtw - current; diff < T()) {
                        sol.cost += diff;
                        rev(nxtu, v);
                        rev(nxtv, w);
                        rev(nxtw, u);
                        return true;
                    }
                }

                // type 3
                for (const auto &[w, dvw] : adjacents(v)) {
                    if (dunxtv + dvw >= dunxtu + dvnxtv) break;
                    if (!check_uvw_order(u, v, w)) continue;

                    const int nxtw = sol.path.at(modn(v_to_i.at(w) + 1));

                    const T current = dunxtu + dvnxtv + dist(w, nxtw);

                    if (T diff = dunxtv + dvw + dist(nxtu, nxtw) - current; diff < T()) {
                        sol.cost += diff;
                        rev(nxtw, u);
                        rev(nxtv, w);
                        return true;
                    }
                }
            }

            // type 2
            for (const auto &[nxtv, dnxtunxtv] : adjacents(nxtu)) {
                if (dnxtunxtv >= dunxtu) break;
                const int v = sol.path.at(modn(v_to_i.at(nxtv) - 1));
                const T dvnxtv = dist(v, nxtv);

                for (const auto &[nxtw, dvnxtw] : adjacents(v)) {
                    const int w = sol.path.at(modn(v_to_i.at(nxtw) - 1));
                    if (dnxtunxtv + dvnxtw >= dunxtu + dvnxtv) break;
                    if (!check_uvw_order(u, v, w)) continue;

                    const T current = dunxtu + dvnxtv + dist(w, nxtw);
                    if (T diff = dist(u, w) + dnxtunxtv + dvnxtw - current; diff < T()) {
                        sol.cost += diff;
                        rev(nxtu, v);
                        rev(nxtw, u);
                        return true;
                    }
                }
            }

            // type 4
            for (const auto &[v, duv] : adjacents(u)) {
                if (duv >= dunxtu) break;
                const int nxtv = sol.path.at(modn(v_to_i.at(v) + 1));
                const T dvnxtv = dist(v, nxtv);

                for (const auto &[nxtw, dnxtvnxtw] : adjacents(nxtv)) {
                    const int w = sol.path.at(modn(v_to_i.at(nxtw) - 1));
                    if (duv + dnxtvnxtw >= dunxtu + dvnxtv) break;
                    if (!check_uvw_order(u, v, w)) continue;

                    const T current = dunxtu + dvnxtv + dist(w, nxtw);
                    if (T diff = duv + dist(nxtu, w) + dnxtvnxtw - current; diff < T()) {
                        sol.cost += diff;
                        rev(nxtu, v);
                        rev(nxtv, w);
                        return true;
                    }
                }
            }
        }
        return false;
    }

    template <class Rng>
    bool double_bridge(Solution &sol, Rng &rng) const {
        if (n() < 8) return false;

        std::vector<int> &p = sol.path;
        int rand_rot = std::uniform_int_distribution<int>(0, n() - 1)(rng);
        std::rotate(p.begin(), p.begin() + rand_rot, p.end());

        static std::array<int, 3> arr;
        for (int &y : arr) y = std::uniform_int_distribution<int>(2, n() - 6)(rng);
        std::sort(arr.begin(), arr.end());
        const int i = arr.at(0), j = arr.at(1) + 2, k = arr.at(2) + 4;
        static std::array<T, 2> diffs;
        for (int d = 0; d < 2; ++d) {
            int u = p.at(n() - 1), nxtu = p.at(0);
            int v = p.at(i - 1), nxtv = p.at(i);
            int w = p.at(j - 1), nxtw = p.at(j);
            int x = p.at(k - 1), nxtx = p.at(k);
            diffs.at(d) = dist(u, nxtu) + dist(v, nxtv) + dist(w, nxtw) + dist(x, nxtx);
            if (d == 1) break;
            std::reverse(p.begin(), p.begin() + i);
            std::reverse(p.begin() + i, p.begin() + j);
            std::reverse(p.begin() + j, p.begin() + k);
            std::reverse(p.begin() + k, p.end());
        }
        sol.cost += diffs.at(1) - diffs.at(0);
        return true;
    }

    int n() const noexcept { return dist.n(); }
    int modn(int x) const noexcept {
        if (x < 0) return x + n();
        if (x >= n()) return x - n();
        return x;
    }
};

template <class T, class DistanceMatrix> std::pair<T, std::vector<int>> minimum_one_tree(const DistanceMatrix &dist, const std::vector<T> &pi) {

    assert(dist.n() > 2);
    std::vector<T> dp(dist.n(), std::numeric_limits<T>::max());
    std::vector<int> prv(dist.n(), -1);
    std::vector<int> used(dist.n());

    auto fix_v = [&](int x) -> void {
        dp.at(x) = std::numeric_limits<T>::max();
        used.at(x) = 1;
        for (auto [y, d] : dist.adjacents(x)) {
            if (used.at(y)) continue;
            if (T len = pi.at(x) + pi.at(y) + d; len < dp.at(y)) dp.at(y) = len, prv.at(y) = x;
        }
    };

    T W = T();
    std::vector<int> V(dist.n(), -2);

    fix_v(0);
    for (int t = 0; t < dist.n() - 1; ++t) {
        int i = std::min_element(dp.cbegin(), dp.cend()) - dp.cbegin();
        W += dp.at(i);
        ++V.at(i);
        ++V.at(prv.at(i));
        fix_v(i);
    }

    // p.26, http://webhotel4.ruc.dk/~keld/research/LKH/LKH-2.0/DOC/LKH_REPORT.pdf
    T wlo = T();
    int ilo = -1, jlo = -1;
    for (int i = 0; i < dist.n(); ++i) {
        if (V.at(i) != -1) continue;
        T tmp = T();
        int jtmp = -1;
        for (auto [j, d] : dist.adjacents(i)) {
            if (prv.at(i) == j or prv.at(j) == i or i == j) continue;
            if (T len = pi.at(i) + pi.at(j) + d; jtmp == -1 or tmp > len) tmp = len, jtmp = j;
        }
        if (jtmp != -1 and (ilo == -1 or wlo < tmp)) wlo = tmp, ilo = i, jlo = jtmp;
    }
    ++V.at(ilo);
    ++V.at(jlo);

    W += wlo - std::accumulate(pi.cbegin(), pi.cend(), T()) * 2;

    return {W, V};
}

// http://webhotel4.ruc.dk/~keld/research/LKH/LKH-2.0/DOC/LKH_REPORT.pdf
// p.26, p.33
template <class DistanceMatrix> auto held_karp_lower_bound(const DistanceMatrix &dist) {
    using T = decltype((*dist.adjacents(0).begin()).second);

    std::vector<T> best_pi(dist.n()), pi(dist.n());
    std::vector<int> V;
    T W;
    std::tie(W, V) = minimum_one_tree(dist, pi);
    if (std::count(V.cbegin(), V.cend(), 0) == dist.n()) return std::make_pair(W, pi);

    std::vector<int> lastV = V;

    T BestW = W;
    const int initial_period = (dist.n() + 1) / 2;
    bool is_initial_phase = true;
    int period = initial_period;

    const auto sparse_subgraph = build_adjacent_info(dist, 50);  // p.47

    for (long long t0 = 1; t0 > 0; period /= 2, t0 /= 2) {
        for (int p = 1; t0 > 0 and p <= period; ++p) {
            for (int i = 0; i < dist.n(); ++i) {
                if (V.at(i) != 0) pi.at(i) += t0 * (7 * V.at(i) + 3 * lastV.at(i)) / 10;
            }
            std::swap(lastV, V);
            std::tie(W, V) = minimum_one_tree(sparse_subgraph, pi);
            if (std::count(begin(V), begin(V) + dist.n(), 0) == dist.n()) return std::make_pair(W, pi);
            if (W > BestW) {
                BestW = W;
                best_pi = pi;
                if (is_initial_phase) t0 *= 2;
                if (p == period) period = std::min(period * 2, initial_period);

            } else if (is_initial_phase and p > period / 2) {
                is_initial_phase = false;
                p = 0;
                t0 = 3 * t0 / 4;
            }
        }
    }
    BestW = minimum_one_tree(dist, best_pi).first;
    return std::make_pair(BestW, best_pi);
}


int main() {
    int N;
    cin >> N;
    vector<long long> X(N), Y(N);
    constexpr long long Coeff = 10000LL;
    for (int i = 0; i < N; ++i) {
        cin >> X.at(i) >> Y.at(i);
        X.at(i) *= Coeff;
        Y.at(i) *= Coeff;
    }

    vector base_d(N, vector<long long>(N));
    for (int i = 0; i < N; ++i) {
        for (int j = 0; j < N; ++j) base_d.at(i).at(j) = roundl(hypot(X.at(i) - X.at(j), Y.at(i) - Y.at(j)));
    }

    dense_distance_matrix distance_matrix(base_d);
    auto adjacent_dmat = build_adjacent_info(distance_matrix, 20);
    SymmetricTSP tsp(distance_matrix, adjacent_dmat);
    decltype(tsp)::Solution best{1LL << 60, {}};
    best = tsp.nearest_neighbor(0);

    auto eval = [&](const auto &sol) -> long long {
        long long quad_sum = 0, sum = 0, len = 0;
        int now = sol.path.back();
        for (int nxt : sol.path) {
            quad_sum += base_d.at(now).at(nxt) * base_d.at(now).at(nxt);
            sum += base_d.at(now).at(nxt);
            ++len;
            now = nxt;
        }
        return len * quad_sum - sum * sum;
    };

    auto mean = [&](const auto &sol) -> long long {
        long long sum = 0, len = 0;
        int now = sol.path.back();
        for (int nxt : sol.path) {
            sum += base_d.at(now).at(nxt);
            ++len;
            now = nxt;
        }
        return len ? sum / len : 0;
    };

    auto best_ev = eval(best);

    long long initial_expected_mean = 500 * Coeff * 0.01;

    std::mt19937 mt(100);

    auto solve = [&](long long expected_mean) {
        dbg(expected_mean);
        vector D(N, vector<long long>(N));

        REP(_, 10) {
            REP(i, N) REP(j, N) D.at(i).at(j) = (base_d.at(i).at(j) - expected_mean) * (base_d.at(i).at(j) - expected_mean);
            distance_matrix = dense_distance_matrix(D);
            adjacent_dmat = build_adjacent_info(distance_matrix, 20);

            tsp = SymmetricTSP(distance_matrix, adjacent_dmat);
            auto sol = best;
            REP(_, 20) {
                tsp.double_bridge(sol, mt);
                do { tsp.two_opt(sol); } while (tsp.three_opt(sol));
                if (chmin(best_ev, eval(sol))) {
                    best = sol;
                    dbg(make_tuple(1.0 * expected_mean / (500 * Coeff), best_ev));
                }
            }
            expected_mean = mean(sol);
        }
    };

    REP(_, 5) {
        solve(initial_expected_mean * 56);
        solve(initial_expected_mean * 58);
        solve(initial_expected_mean * 60);
    }

    // FOR(l, 55, 70) solve(initial_expected_mean * l);
    dbg(best);
    dbg(best_ev);
    for (auto x : best.path) cout << x << '\n';
}

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