提出 #74271767

---

ソースコード 拡げる

#ifdef LOCAL
#include "pch.hpp"
#else // 2000 lines template starts here

#include<bits/stdc++.h>
#include <type_traits>

namespace atcoder {

namespace internal {

#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value ||
                                  std::is_same<T, __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_unsigned_int128 =
    typename std::conditional<std::is_same<T, __uint128_t>::value ||
                                  std::is_same<T, unsigned __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using make_unsigned_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value,
                              __uint128_t,
                              unsigned __int128>;

template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
                                                  is_signed_int128<T>::value ||
                                                  is_unsigned_int128<T>::value,
                                              std::true_type,
                                              std::false_type>::type;

template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
                                                 std::is_signed<T>::value) ||
                                                    is_signed_int128<T>::value,
                                                std::true_type,
                                                std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<(is_integral<T>::value &&
                               std::is_unsigned<T>::value) ||
                                  is_unsigned_int128<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<
    is_signed_int128<T>::value,
    make_unsigned_int128<T>,
    typename std::conditional<std::is_signed<T>::value,
                              std::make_unsigned<T>,
                              std::common_type<T>>::type>::type;
#endif

template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;

template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;

template <class T> using to_unsigned_t = typename to_unsigned<T>::type;

}  // namespace internal

}  // namespace atcoder


namespace atcoder {

template <class T> struct fenwick_tree {
    using U = internal::to_unsigned_t<T>;

  public:
    fenwick_tree() : _n(0) {}
    explicit fenwick_tree(int n) : _n(n), data(n) {}

    void add(int p, T x) {
        assert(0 <= p && p < _n);
        p++;
        while (p <= _n) {
            data[p - 1] += U(x);
            p += p & -p;
        }
    }

    T sum(int l, int r) {
        assert(0 <= l && l <= r && r <= _n);
        return sum(r) - sum(l);
    }

  private:
    int _n;
    std::vector<U> data;

    U sum(int r) {
        U s = 0;
        while (r > 0) {
            s += data[r - 1];
            r -= r & -r;
        }
        return s;
    }
};

}  // namespace atcoder

namespace atcoder {

namespace internal {

int ceil_pow2(int n) {
    int x = 0;
    while ((1U << x) < (unsigned int)(n)) x++;
    return x;
}

constexpr int bsf_constexpr(unsigned int n) {
    int x = 0;
    while (!(n & (1 << x))) x++;
    return x;
}

int bsf(unsigned int n) {
    return __builtin_ctz(n);
}

}  // namespace internal

}  // namespace atcoder


namespace atcoder {

template <class S, S (*op)(S, S), S (*e)()> struct segtree {
  public:
    segtree() : segtree(0) {}
    explicit segtree(int n) : segtree(std::vector<S>(n, e())) {}
    explicit segtree(const std::vector<S>& v) : _n(int(v.size())) {
        log = internal::ceil_pow2(_n);
        size = 1 << log;
        d = std::vector<S>(2 * size, e());
        for (int i = 0; i < _n; i++) d[size + i] = v[i];
        for (int i = size - 1; i >= 1; i--) {
            update(i);
        }
    }

    void set(int p, S x) {
        assert(0 <= p && p < _n);
        p += size;
        d[p] = x;
        for (int i = 1; i <= log; i++) update(p >> i);
    }

    S get(int p) const {
        assert(0 <= p && p < _n);
        return d[p + size];
    }

    S prod(int l, int r) const {
        assert(0 <= l && l <= r && r <= _n);
        S sml = e(), smr = e();
        l += size;
        r += size;

        while (l < r) {
            if (l & 1) sml = op(sml, d[l++]);
            if (r & 1) smr = op(d[--r], smr);
            l >>= 1;
            r >>= 1;
        }
        return op(sml, smr);
    }

    S all_prod() const { return d[1]; }

    template <bool (*f)(S)> int max_right(int l) const {
        return max_right(l, [](S x) { return f(x); });
    }
    template <class F> int max_right(int l, F f) const {
        assert(0 <= l && l <= _n);
        assert(f(e()));
        if (l == _n) return _n;
        l += size;
        S sm = e();
        do {
            while (l % 2 == 0) l >>= 1;
            if (!f(op(sm, d[l]))) {
                while (l < size) {
                    l = (2 * l);
                    if (f(op(sm, d[l]))) {
                        sm = op(sm, d[l]);
                        l++;
                    }
                }
                return l - size;
            }
            sm = op(sm, d[l]);
            l++;
        } while ((l & -l) != l);
        return _n;
    }

    template <bool (*f)(S)> int min_left(int r) const {
        return min_left(r, [](S x) { return f(x); });
    }
    template <class F> int min_left(int r, F f) const {
        assert(0 <= r && r <= _n);
        assert(f(e()));
        if (r == 0) return 0;
        r += size;
        S sm = e();
        do {
            r--;
            while (r > 1 && (r % 2)) r >>= 1;
            if (!f(op(d[r], sm))) {
                while (r < size) {
                    r = (2 * r + 1);
                    if (f(op(d[r], sm))) {
                        sm = op(d[r], sm);
                        r--;
                    }
                }
                return r + 1 - size;
            }
            sm = op(d[r], sm);
        } while ((r & -r) != r);
        return 0;
    }

  private:
    int _n, size, log;
    std::vector<S> d;

    void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }
};

}  // namespace atcoder

namespace atcoder {

template <class S,
          S (*op)(S, S),
          S (*e)(),
          class F,
          S (*mapping)(F, S),
          F (*composition)(F, F),
          F (*id)()>
struct lazy_segtree {
  public:
    lazy_segtree() : lazy_segtree(0) {}
    explicit lazy_segtree(int n) : lazy_segtree(std::vector<S>(n, e())) {}
    explicit lazy_segtree(const std::vector<S>& v) : _n(int(v.size())) {
        log = internal::ceil_pow2(_n);
        size = 1 << log;
        d = std::vector<S>(2 * size, e());
        lz = std::vector<F>(size, id());
        for (int i = 0; i < _n; i++) d[size + i] = v[i];
        for (int i = size - 1; i >= 1; i--) {
            update(i);
        }
    }

    void set(int p, S x) {
        assert(0 <= p && p < _n);
        p += size;
        for (int i = log; i >= 1; i--) push(p >> i);
        d[p] = x;
        for (int i = 1; i <= log; i++) update(p >> i);
    }

    S get(int p) {
        assert(0 <= p && p < _n);
        p += size;
        for (int i = log; i >= 1; i--) push(p >> i);
        return d[p];
    }

    S prod(int l, int r) {
        assert(0 <= l && l <= r && r <= _n);
        if (l == r) return e();

        l += size;
        r += size;

        for (int i = log; i >= 1; i--) {
            if (((l >> i) << i) != l) push(l >> i);
            if (((r >> i) << i) != r) push((r - 1) >> i);
        }

        S sml = e(), smr = e();
        while (l < r) {
            if (l & 1) sml = op(sml, d[l++]);
            if (r & 1) smr = op(d[--r], smr);
            l >>= 1;
            r >>= 1;
        }

        return op(sml, smr);
    }

    S all_prod() { return d[1]; }

    void apply(int p, F f) {
        assert(0 <= p && p < _n);
        p += size;
        for (int i = log; i >= 1; i--) push(p >> i);
        d[p] = mapping(f, d[p]);
        for (int i = 1; i <= log; i++) update(p >> i);
    }
    void apply(int l, int r, F f) {
        assert(0 <= l && l <= r && r <= _n);
        if (l == r) return;

        l += size;
        r += size;

        for (int i = log; i >= 1; i--) {
            if (((l >> i) << i) != l) push(l >> i);
            if (((r >> i) << i) != r) push((r - 1) >> i);
        }

        {
            int l2 = l, r2 = r;
            while (l < r) {
                if (l & 1) all_apply(l++, f);
                if (r & 1) all_apply(--r, f);
                l >>= 1;
                r >>= 1;
            }
            l = l2;
            r = r2;
        }

        for (int i = 1; i <= log; i++) {
            if (((l >> i) << i) != l) update(l >> i);
            if (((r >> i) << i) != r) update((r - 1) >> i);
        }
    }

    template <bool (*g)(S)> int max_right(int l) {
        return max_right(l, [](S x) { return g(x); });
    }
    template <class G> int max_right(int l, G g) {
        assert(0 <= l && l <= _n);
        assert(g(e()));
        if (l == _n) return _n;
        l += size;
        for (int i = log; i >= 1; i--) push(l >> i);
        S sm = e();
        do {
            while (l % 2 == 0) l >>= 1;
            if (!g(op(sm, d[l]))) {
                while (l < size) {
                    push(l);
                    l = (2 * l);
                    if (g(op(sm, d[l]))) {
                        sm = op(sm, d[l]);
                        l++;
                    }
                }
                return l - size;
            }
            sm = op(sm, d[l]);
            l++;
        } while ((l & -l) != l);
        return _n;
    }

    template <bool (*g)(S)> int min_left(int r) {
        return min_left(r, [](S x) { return g(x); });
    }
    template <class G> int min_left(int r, G g) {
        assert(0 <= r && r <= _n);
        assert(g(e()));
        if (r == 0) return 0;
        r += size;
        for (int i = log; i >= 1; i--) push((r - 1) >> i);
        S sm = e();
        do {
            r--;
            while (r > 1 && (r % 2)) r >>= 1;
            if (!g(op(d[r], sm))) {
                while (r < size) {
                    push(r);
                    r = (2 * r + 1);
                    if (g(op(d[r], sm))) {
                        sm = op(d[r], sm);
                        r--;
                    }
                }
                return r + 1 - size;
            }
            sm = op(d[r], sm);
        } while ((r & -r) != r);
        return 0;
    }

  private:
    int _n, size, log;
    std::vector<S> d;
    std::vector<F> lz;

    void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }
    void all_apply(int k, F f) {
        d[k] = mapping(f, d[k]);
        if (k < size) lz[k] = composition(f, lz[k]);
    }
    void push(int k) {
        all_apply(2 * k, lz[k]);
        all_apply(2 * k + 1, lz[k]);
        lz[k] = id();
    }
};

}  // namespace atcoder

namespace atcoder {

namespace internal {

std::vector<int> sa_naive(const std::vector<int>& s) {
    int n = int(s.size());
    std::vector<int> sa(n);
    std::iota(sa.begin(), sa.end(), 0);
    std::sort(sa.begin(), sa.end(), [&](int l, int r) {
        if (l == r) return false;
        while (l < n && r < n) {
            if (s[l] != s[r]) return s[l] < s[r];
            l++;
            r++;
        }
        return l == n;
    });
    return sa;
}

std::vector<int> sa_doubling(const std::vector<int>& s) {
    int n = int(s.size());
    std::vector<int> sa(n), rnk = s, tmp(n);
    std::iota(sa.begin(), sa.end(), 0);
    for (int k = 1; k < n; k *= 2) {
        auto cmp = [&](int x, int y) {
            if (rnk[x] != rnk[y]) return rnk[x] < rnk[y];
            int rx = x + k < n ? rnk[x + k] : -1;
            int ry = y + k < n ? rnk[y + k] : -1;
            return rx < ry;
        };
        std::sort(sa.begin(), sa.end(), cmp);
        tmp[sa[0]] = 0;
        for (int i = 1; i < n; i++) {
            tmp[sa[i]] = tmp[sa[i - 1]] + (cmp(sa[i - 1], sa[i]) ? 1 : 0);
        }
        std::swap(tmp, rnk);
    }
    return sa;
}

template <int THRESHOLD_NAIVE = 10, int THRESHOLD_DOUBLING = 40>
std::vector<int> sa_is(const std::vector<int>& s, int upper) {
    int n = int(s.size());
    if (n == 0) return {};
    if (n == 1) return {0};
    if (n == 2) {
        if (s[0] < s[1]) {
            return {0, 1};
        } else {
            return {1, 0};
        }
    }
    if (n < THRESHOLD_NAIVE) {
        return sa_naive(s);
    }
    if (n < THRESHOLD_DOUBLING) {
        return sa_doubling(s);
    }

    std::vector<int> sa(n);
    std::vector<bool> ls(n);
    for (int i = n - 2; i >= 0; i--) {
        ls[i] = (s[i] == s[i + 1]) ? ls[i + 1] : (s[i] < s[i + 1]);
    }
    std::vector<int> sum_l(upper + 1), sum_s(upper + 1);
    for (int i = 0; i < n; i++) {
        if (!ls[i]) {
            sum_s[s[i]]++;
        } else {
            sum_l[s[i] + 1]++;
        }
    }
    for (int i = 0; i <= upper; i++) {
        sum_s[i] += sum_l[i];
        if (i < upper) sum_l[i + 1] += sum_s[i];
    }

    auto induce = [&](const std::vector<int>& lms) {
        std::fill(sa.begin(), sa.end(), -1);
        std::vector<int> buf(upper + 1);
        std::copy(sum_s.begin(), sum_s.end(), buf.begin());
        for (auto d : lms) {
            if (d == n) continue;
            sa[buf[s[d]]++] = d;
        }
        std::copy(sum_l.begin(), sum_l.end(), buf.begin());
        sa[buf[s[n - 1]]++] = n - 1;
        for (int i = 0; i < n; i++) {
            int v = sa[i];
            if (v >= 1 && !ls[v - 1]) {
                sa[buf[s[v - 1]]++] = v - 1;
            }
        }
        std::copy(sum_l.begin(), sum_l.end(), buf.begin());
        for (int i = n - 1; i >= 0; i--) {
            int v = sa[i];
            if (v >= 1 && ls[v - 1]) {
                sa[--buf[s[v - 1] + 1]] = v - 1;
            }
        }
    };

    std::vector<int> lms_map(n + 1, -1);
    int m = 0;
    for (int i = 1; i < n; i++) {
        if (!ls[i - 1] && ls[i]) {
            lms_map[i] = m++;
        }
    }
    std::vector<int> lms;
    lms.reserve(m);
    for (int i = 1; i < n; i++) {
        if (!ls[i - 1] && ls[i]) {
            lms.push_back(i);
        }
    }

    induce(lms);

    if (m) {
        std::vector<int> sorted_lms;
        sorted_lms.reserve(m);
        for (int v : sa) {
            if (lms_map[v] != -1) sorted_lms.push_back(v);
        }
        std::vector<int> rec_s(m);
        int rec_upper = 0;
        rec_s[lms_map[sorted_lms[0]]] = 0;
        for (int i = 1; i < m; i++) {
            int l = sorted_lms[i - 1], r = sorted_lms[i];
            int end_l = (lms_map[l] + 1 < m) ? lms[lms_map[l] + 1] : n;
            int end_r = (lms_map[r] + 1 < m) ? lms[lms_map[r] + 1] : n;
            bool same = true;
            if (end_l - l != end_r - r) {
                same = false;
            } else {
                while (l < end_l) {
                    if (s[l] != s[r]) {
                        break;
                    }
                    l++;
                    r++;
                }
                if (l == n || s[l] != s[r]) same = false;
            }
            if (!same) rec_upper++;
            rec_s[lms_map[sorted_lms[i]]] = rec_upper;
        }

        auto rec_sa =
            sa_is<THRESHOLD_NAIVE, THRESHOLD_DOUBLING>(rec_s, rec_upper);

        for (int i = 0; i < m; i++) {
            sorted_lms[i] = lms[rec_sa[i]];
        }
        induce(sorted_lms);
    }
    return sa;
}

}  // namespace internal

std::vector<int> suffix_array(const std::vector<int>& s, int upper) {
    assert(0 <= upper);
    for (int d : s) {
        assert(0 <= d && d <= upper);
    }
    auto sa = internal::sa_is(s, upper);
    return sa;
}

template <class T> std::vector<int> suffix_array(const std::vector<T>& s) {
    int n = int(s.size());
    std::vector<int> idx(n);
    iota(idx.begin(), idx.end(), 0);
    sort(idx.begin(), idx.end(), [&](int l, int r) { return s[l] < s[r]; });
    std::vector<int> s2(n);
    int now = 0;
    for (int i = 0; i < n; i++) {
        if (i && s[idx[i - 1]] != s[idx[i]]) now++;
        s2[idx[i]] = now;
    }
    return internal::sa_is(s2, now);
}

std::vector<int> suffix_array(const std::string& s) {
    int n = int(s.size());
    std::vector<int> s2(n);
    for (int i = 0; i < n; i++) {
        s2[i] = s[i];
    }
    return internal::sa_is(s2, 255);
}

template <class T>
std::vector<int> lcp_array(const std::vector<T>& s,
                           const std::vector<int>& sa) {
    int n = int(s.size());
    assert(n >= 1);
    std::vector<int> rnk(n);
    for (int i = 0; i < n; i++) {
        rnk[sa[i]] = i;
    }
    std::vector<int> lcp(n - 1);
    int h = 0;
    for (int i = 0; i < n; i++) {
        if (h > 0) h--;
        if (rnk[i] == 0) continue;
        int j = sa[rnk[i] - 1];
        for (; j + h < n && i + h < n; h++) {
            if (s[j + h] != s[i + h]) break;
        }
        lcp[rnk[i] - 1] = h;
    }
    return lcp;
}

std::vector<int> lcp_array(const std::string& s, const std::vector<int>& sa) {
    int n = int(s.size());
    std::vector<int> s2(n);
    for (int i = 0; i < n; i++) {
        s2[i] = s[i];
    }
    return lcp_array(s2, sa);
}

template <class T> std::vector<int> z_algorithm(const std::vector<T>& s) {
    int n = int(s.size());
    if (n == 0) return {};
    std::vector<int> z(n);
    z[0] = 0;
    for (int i = 1, j = 0; i < n; i++) {
        int& k = z[i];
        k = (j + z[j] <= i) ? 0 : std::min(j + z[j] - i, z[i - j]);
        while (i + k < n && s[k] == s[i + k]) k++;
        if (j + z[j] < i + z[i]) j = i;
    }
    z[0] = n;
    return z;
}

std::vector<int> z_algorithm(const std::string& s) {
    int n = int(s.size());
    std::vector<int> s2(n);
    for (int i = 0; i < n; i++) {
        s2[i] = s[i];
    }
    return z_algorithm(s2);
}

}  // namespace atcoder

namespace atcoder {

namespace internal {

constexpr long long safe_mod(long long x, long long m) {
    x %= m;
    if (x < 0) x += m;
    return x;
}

struct barrett {
    unsigned int _m;
    unsigned long long im;

    explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}

    unsigned int umod() const { return _m; }

    unsigned int mul(unsigned int a, unsigned int b) const {

        unsigned long long z = a;
        z *= b;
#ifdef _MSC_VER
        unsigned long long x;
        _umul128(z, im, &x);
#else
        unsigned long long x =
            (unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
        unsigned int v = (unsigned int)(z - x * _m);
        if (_m <= v) v += _m;
        return v;
    }
};

constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
    if (m == 1) return 0;
    unsigned int _m = (unsigned int)(m);
    unsigned long long r = 1;
    unsigned long long y = safe_mod(x, m);
    while (n) {
        if (n & 1) r = (r * y) % _m;
        y = (y * y) % _m;
        n >>= 1;
    }
    return r;
}

constexpr bool is_prime_constexpr(int n) {
    if (n <= 1) return false;
    if (n == 2 || n == 7 || n == 61) return true;
    if (n % 2 == 0) return false;
    long long d = n - 1;
    while (d % 2 == 0) d /= 2;
    constexpr long long bases[3] = {2, 7, 61};
    for (long long a : bases) {
        long long t = d;
        long long y = pow_mod_constexpr(a, t, n);
        while (t != n - 1 && y != 1 && y != n - 1) {
            y = y * y % n;
            t <<= 1;
        }
        if (y != n - 1 && t % 2 == 0) {
            return false;
        }
    }
    return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);

constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
    a = safe_mod(a, b);
    if (a == 0) return {b, 0};

    long long s = b, t = a;
    long long m0 = 0, m1 = 1;

    while (t) {
        long long u = s / t;
        s -= t * u;
        m0 -= m1 * u;  // |m1 * u| <= |m1| * s <= b


        auto tmp = s;
        s = t;
        t = tmp;
        tmp = m0;
        m0 = m1;
        m1 = tmp;
    }
    if (m0 < 0) m0 += b / s;
    return {s, m0};
}

constexpr int primitive_root_constexpr(int m) {
    if (m == 2) return 1;
    if (m == 167772161) return 3;
    if (m == 469762049) return 3;
    if (m == 754974721) return 11;
    if (m == 998244353) return 3;
    int divs[20] = {};
    divs[0] = 2;
    int cnt = 1;
    int x = (m - 1) / 2;
    while (x % 2 == 0) x /= 2;
    for (int i = 3; (long long)(i)*i <= x; i += 2) {
        if (x % i == 0) {
            divs[cnt++] = i;
            while (x % i == 0) {
                x /= i;
            }
        }
    }
    if (x > 1) {
        divs[cnt++] = x;
    }
    for (int g = 2;; g++) {
        bool ok = true;
        for (int i = 0; i < cnt; i++) {
            if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
                ok = false;
                break;
            }
        }
        if (ok) return g;
    }
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);

unsigned long long floor_sum_unsigned(unsigned long long n,
                                      unsigned long long m,
                                      unsigned long long a,
                                      unsigned long long b) {
    unsigned long long ans = 0;
    while (true) {
        if (a >= m) {
            ans += n * (n - 1) / 2 * (a / m);
            a %= m;
        }
        if (b >= m) {
            ans += n * (b / m);
            b %= m;
        }

        unsigned long long y_max = a * n + b;
        if (y_max < m) break;
        n = (unsigned long long)(y_max / m);
        b = (unsigned long long)(y_max % m);
        std::swap(m, a);
    }
    return ans;
}

}  // namespace internal

}  // namespace atcoder


namespace atcoder {

long long pow_mod(long long x, long long n, int m) {
    assert(0 <= n && 1 <= m);
    if (m == 1) return 0;
    internal::barrett bt((unsigned int)(m));
    unsigned int r = 1, y = (unsigned int)(internal::safe_mod(x, m));
    while (n) {
        if (n & 1) r = bt.mul(r, y);
        y = bt.mul(y, y);
        n >>= 1;
    }
    return r;
}

long long inv_mod(long long x, long long m) {
    assert(1 <= m);
    auto z = internal::inv_gcd(x, m);
    assert(z.first == 1);
    return z.second;
}

std::pair<long long, long long> crt(const std::vector<long long>& r,
                                    const std::vector<long long>& m) {
    assert(r.size() == m.size());
    int n = int(r.size());
    long long r0 = 0, m0 = 1;
    for (int i = 0; i < n; i++) {
        assert(1 <= m[i]);
        long long r1 = internal::safe_mod(r[i], m[i]), m1 = m[i];
        if (m0 < m1) {
            std::swap(r0, r1);
            std::swap(m0, m1);
        }
        if (m0 % m1 == 0) {
            if (r0 % m1 != r1) return {0, 0};
            continue;
        }


        long long g, im;
        std::tie(g, im) = internal::inv_gcd(m0, m1);

        long long u1 = (m1 / g);
        if ((r1 - r0) % g) return {0, 0};

        long long x = (r1 - r0) / g % u1 * im % u1;

        r0 += x * m0;
        m0 *= u1;  // -> lcm(m0, m1)
        if (r0 < 0) r0 += m0;
    }
    return {r0, m0};
}

long long floor_sum(long long n, long long m, long long a, long long b) {
    assert(0 <= n && n < (1LL << 32));
    assert(1 <= m && m < (1LL << 32));
    unsigned long long ans = 0;
    if (a < 0) {
        unsigned long long a2 = internal::safe_mod(a, m);
        ans -= 1ULL * n * (n - 1) / 2 * ((a2 - a) / m);
        a = a2;
    }
    if (b < 0) {
        unsigned long long b2 = internal::safe_mod(b, m);
        ans -= 1ULL * n * ((b2 - b) / m);
        b = b2;
    }
    return ans + internal::floor_sum_unsigned(n, m, a, b);
}

}  // namespace atcoder

namespace atcoder {

namespace internal {

struct modint_base {};
struct static_modint_base : modint_base {};

template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;

}  // namespace internal

template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : internal::static_modint_base {
    using mint = static_modint;

  public:
    static constexpr int mod() { return m; }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }

    static_modint() : _v(0) {}
    template <class T, internal::is_signed_int_t<T>* = nullptr>
    static_modint(T v) {
        long long x = (long long)(v % (long long)(umod()));
        if (x < 0) x += umod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T>* = nullptr>
    static_modint(T v) {
        _v = (unsigned int)(v % umod());
    }

    unsigned int val() const { return _v; }

    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }

    mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v -= rhs._v;
        if (_v >= umod()) _v += umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        unsigned long long z = _v;
        z *= rhs._v;
        _v = (unsigned int)(z % umod());
        return *this;
    }
    mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }

    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }

    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        if (prime) {
            assert(_v);
            return pow(umod() - 2);
        } else {
            auto eg = internal::inv_gcd(_v, m);
            assert(eg.first == 1);
            return eg.second;
        }
    }

    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }

  private:
    unsigned int _v;
    static constexpr unsigned int umod() { return m; }
    static constexpr bool prime = internal::is_prime<m>;
};

template <int id> struct dynamic_modint : internal::modint_base {
    using mint = dynamic_modint;

  public:
    static int mod() { return (int)(bt.umod()); }
    static void set_mod(int m) {
        assert(1 <= m);
        bt = internal::barrett(m);
    }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }

    dynamic_modint() : _v(0) {}
    template <class T, internal::is_signed_int_t<T>* = nullptr>
    dynamic_modint(T v) {
        long long x = (long long)(v % (long long)(mod()));
        if (x < 0) x += mod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T>* = nullptr>
    dynamic_modint(T v) {
        _v = (unsigned int)(v % mod());
    }

    unsigned int val() const { return _v; }

    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }

    mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v += mod() - rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        _v = bt.mul(_v, rhs._v);
        return *this;
    }
    mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }

    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }

    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        auto eg = internal::inv_gcd(_v, mod());
        assert(eg.first == 1);
        return eg.second;
    }

    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }

  private:
    unsigned int _v;
    static internal::barrett bt;
    static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt(998244353);

using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;

namespace internal {

template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;

template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;

template <class> struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};

template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;

}  // namespace internal

}  // namespace atcoder

namespace atcoder {
namespace internal {

template <class E> struct csr {
    std::vector<int> start;
    std::vector<E> elist;
    explicit csr(int n, const std::vector<std::pair<int, E>>& edges)
        : start(n + 1), elist(edges.size()) {
        for (auto e : edges) {
            start[e.first + 1]++;
        }
        for (int i = 1; i <= n; i++) {
            start[i] += start[i - 1];
        }
        auto counter = start;
        for (auto e : edges) {
            elist[counter[e.first]++] = e.second;
        }
    }
};

}  // namespace internal

}  // namespace atcoder


namespace atcoder {
namespace internal {

struct scc_graph {
  public:
    explicit scc_graph(int n) : _n(n) {}

    int num_vertices() { return _n; }

    void add_edge(int from, int to) { edges.push_back({from, {to}}); }

    std::pair<int, std::vector<int>> scc_ids() {
        auto g = csr<edge>(_n, edges);
        int now_ord = 0, group_num = 0;
        std::vector<int> visited, low(_n), ord(_n, -1), ids(_n);
        visited.reserve(_n);
        auto dfs = [&](auto self, int v) -> void {
            low[v] = ord[v] = now_ord++;
            visited.push_back(v);
            for (int i = g.start[v]; i < g.start[v + 1]; i++) {
                auto to = g.elist[i].to;
                if (ord[to] == -1) {
                    self(self, to);
                    low[v] = std::min(low[v], low[to]);
                } else {
                    low[v] = std::min(low[v], ord[to]);
                }
            }
            if (low[v] == ord[v]) {
                while (true) {
                    int u = visited.back();
                    visited.pop_back();
                    ord[u] = _n;
                    ids[u] = group_num;
                    if (u == v) break;
                }
                group_num++;
            }
        };
        for (int i = 0; i < _n; i++) {
            if (ord[i] == -1) dfs(dfs, i);
        }
        for (auto& x : ids) {
            x = group_num - 1 - x;
        }
        return {group_num, ids};
    }

    std::vector<std::vector<int>> scc() {
        auto ids = scc_ids();
        int group_num = ids.first;
        std::vector<int> counts(group_num);
        for (auto x : ids.second) counts[x]++;
        std::vector<std::vector<int>> groups(ids.first);
        for (int i = 0; i < group_num; i++) {
            groups[i].reserve(counts[i]);
        }
        for (int i = 0; i < _n; i++) {
            groups[ids.second[i]].push_back(i);
        }
        return groups;
    }

  private:
    int _n;
    struct edge {
        int to;
    };
    std::vector<std::pair<int, edge>> edges;
};

}  // namespace internal

}  // namespace atcoder


namespace atcoder {

struct scc_graph {
  public:
    scc_graph() : internal(0) {}
    explicit scc_graph(int n) : internal(n) {}

    void add_edge(int from, int to) {
        int n = internal.num_vertices();
        assert(0 <= from && from < n);
        assert(0 <= to && to < n);
        internal.add_edge(from, to);
    }

    std::vector<std::vector<int>> scc() { return internal.scc(); }

  private:
    internal::scc_graph internal;
};

}  // namespace atcoder

namespace atcoder {

struct two_sat {
  public:
    two_sat() : _n(0), scc(0) {}
    explicit two_sat(int n) : _n(n), _answer(n), scc(2 * n) {}

    void add_clause(int i, bool f, int j, bool g) {
        assert(0 <= i && i < _n);
        assert(0 <= j && j < _n);
        scc.add_edge(2 * i + (f ? 0 : 1), 2 * j + (g ? 1 : 0));
        scc.add_edge(2 * j + (g ? 0 : 1), 2 * i + (f ? 1 : 0));
    }
    bool satisfiable() {
        auto id = scc.scc_ids().second;
        for (int i = 0; i < _n; i++) {
            if (id[2 * i] == id[2 * i + 1]) return false;
            _answer[i] = id[2 * i] < id[2 * i + 1];
        }
        return true;
    }
    std::vector<bool> answer() { return _answer; }

  private:
    int _n;
    std::vector<bool> _answer;
    internal::scc_graph scc;
};

}  // namespace atcoder

using namespace atcoder;

// #pragma GCC optimize("O3,unroll-loops")
// #pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
#include <bits/stdc++.h>
// #define endl "\n"
using ll = long long;
#define int ll
#define PI 3.14159265359

using namespace std;
using mint = modint;

using ld = long double;
using vi = vector<ll>;
using vvi = vector<vi>;
using vm = vector<mint>;
using vvm = vector<vm>;
using pii = pair<ll,ll>;
using vp = vector<pii>;
using vvp = vector<vp>;
using vs = vector<string>;
using vvs = vector<vs>;
using ti3 = tuple<ll,ll,ll>;
using vti3 = vector<ti3>;
using i128 = __int128;

i128 parse_i128(const std::string &s) {
    if (s == "0") return 0;
    bool neg = false;
    int i = 0;

    if (s[0] == '-') {
        neg = true;
        i = 1;
    }

    i128 x = 0;
    for (; i < (int)s.size(); i++) {
        x = x * 10 + (s[i] - '0');
    }

    return neg ? -x : x;
}

std::istream& operator>>(std::istream& is, i128 &x) {
    std::string s;
    is >> s;
    x = parse_i128(s);
    return is;
}

std::string to_string_i128(i128 x) {
    if (x == 0) return "0";
    bool neg = false;
    if (x < 0) {
        neg = true;
        x = -x;
    }
    std::string s;
    while (x > 0) {
        int digit = x % 10;
        s.push_back('0' + digit);
        x /= 10;
    }
    if (neg) s.push_back('-');
    std::reverse(s.begin(), s.end());
    return s;
}

std::ostream& operator<<(std::ostream& os, i128 x) {
    return os << to_string_i128(x);
}

struct custom_hash {
    static uint64_t splitmix64(uint64_t x) {
        x += 0x9e3779b97f4a7c15;
        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
        x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
        return x ^ (x >> 31);
    } 
    size_t operator()(uint64_t x) const {
        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
        return splitmix64(x + FIXED_RANDOM);
    }
    size_t operator()(pair<uint64_t,uint64_t> x) const {
        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
        return splitmix64(x.first + FIXED_RANDOM)^(splitmix64(x.second + FIXED_RANDOM) >> 1);
    }
    size_t operator()(vi const& vec) const {
        size_t seed = vec.size();
        for(auto& i : vec) {
            seed ^= i + 0x9e3779b9 + (seed << 6) + (seed >> 2);
        }
        return seed;
    }
};

struct range {
    struct iterator {
        int value;
        int step;
        int stop;

        int operator*() const { return value; }

        iterator& operator++() {
            value += step;
            return *this;
        }

        bool operator!=(const iterator& other) const {
            (void)other; // end iterator unused
            return step > 0 ? value < stop : value > stop;
        }
    };

    int start, stop, step;

    range(int stop) : start(0), stop(stop), step(1) {}

    range(int start, int stop) : start(start), stop(stop), step(1) {}

    range(int start, int stop, int step) : start(start), stop(stop), step(step) {
        assert(step != 0 && "range() step must not be zero");
    }

    iterator begin() const { return {start, step, stop}; }
    iterator end()   const { return {stop,  step, stop}; }
};

template<int D, typename T>
struct Vec : public vector<Vec<D - 1, T>> {
  static_assert(D >= 1, "Vector dimension must be greater than zero!");
  template<typename... Args>
  Vec(int n = 0, Args... args) : vector<Vec<D - 1, T>>(n, Vec<D - 1, T>(args...)) {}
};

template<typename T>
struct Vec<1, T> : public vector<T> {
  Vec(int n = 0, const T& val = T()) : vector<T>(n, val) {}
};

template<typename T>
void printv(vector<T> v) {
    for (auto e : v) {
        cout << e << " ";
    }   cout << "\n";
}
 
template<typename T>
void printvv(vector<T> vv) {
    for (int i=0; i<vv.size(); i++) {
        cout << i << ": ";
        for (auto e : vv[i]) {
            cout << e << " ";
        }   cout << "\n";
    }
}

template<typename T>
void ri(T &x) {
    cin >> x;
}
template<typename T, typename... Args>
void ri(T &x, Args&... args) {
    ri(x);
    ri(args...) ;
}
template<typename T>
void ri(vector<T> &v) {
    for (auto &x : v) {
        cin >> x;
    }
}
template<typename T, typename... Args>
void ri(vector<T> &v, Args&... args) {
    ri(v);
    ri(args...);
}

template<typename T>
void po(T x) {
    cout << x << "\n";
}
void po(mint x) {
    cout << x.val() << "\n";
}
template<typename T, typename... Args>
void po(T x, Args... args) {
    cout << x << " ";
    po(args...) ;
}
template<typename T>
void po(vector<T> &a) {
    int sz = a.size();
    for (int i=0; i<sz; i++) {
        cout << a[i] << ((i==sz-1)?"\n":" ");
    }
}
void po(vector<mint> &a) {
    int sz = a.size();
    for (int i=0; i<sz; i++) {
        cout << a[i].val() << ((i==sz-1)?"\n":" ");
    }
}

void __print(int x) {cerr << x;}
void __print(signed x) {cerr << x;}
void __print(long x) {cerr << x;}
void __print(unsigned x) {cerr << x;}
void __print(unsigned long x) {cerr << x;}
void __print(unsigned long long x) {cerr << x;}
void __print(float x) {cerr << x;}
void __print(double x) {cerr << x;}
void __print(long double x) {cerr << x;}
void __print(char x) {cerr << '\'' << x << '\'';}
void __print(const char *x) {cerr << '\"' << x << '\"';}
void __print(const string &x) {cerr << '\"' << x << '\"';}
void __print(bool x) {cerr << (x ? "true" : "false");}
void __print(i128 x) {cerr << x;}
void __print(mint x) {cerr << x.val();}

template<typename T, typename V>
void __print(const pair<T, V> &x) {cerr << '{'; __print(x.first); cerr << ','; __print(x.second); cerr << '}';}
template<typename T1, typename T2, typename T3>
void __print(const tuple<T1, T2, T3> &x) {cerr << '{'; __print(get<0>(x)); cerr << ','; __print(get<1>(x)); cerr << ','; __print(get<2>(x)); cerr << '}';}
template<typename T1, typename T2, typename T3, typename T4>
void __print(const tuple<T1, T2, T3, T4> &x) {cerr << '{'; __print(get<0>(x)); cerr << ','; __print(get<1>(x)); cerr << ','; __print(get<2>(x)); cerr << ','; __print(get<3>(x)); cerr << '}';}
template<typename T>
void __print(const T &x) {int f = 0; cerr << '{'; for (auto &i: x) cerr << (f++ ? "," : ""), __print(i); cerr << "}";}
template<typename T1, typename T2>
void __print(map<T1,T2> &mp) {for (auto [k,v] : mp) {cerr << '{'; __print(k); cerr << ':'; __print(v); cerr << '}';}}
void _print() {cerr << "]\n";}
template <typename T, typename... V>
void _print(T t, V... v) {__print(t); if (sizeof...(v)) cerr << ", "; _print(v...);}
#ifndef ONLINE_JUDGE
#define debug(x...) cerr << "[" << #x << "] = ["; _print(x)
#else
#define debug(x...)
#endif

int cnt_leq_x(vi &a, int x) {
    return upper_bound(a.begin(), a.end(), x) - a.begin();
}

int cnt_leq_x(vi &a, int x, int lo, int hi) {
    return upper_bound(a.begin()+lo, a.begin()+hi, x) - a.begin()+lo;
}

int cnt_lt_x(vi &a, int x) {
    return lower_bound(a.begin(), a.end(), x) - a.begin();
}

int cnt_lt_x(vi &a, int x, int lo, int hi) {
    return lower_bound(a.begin()+lo, a.begin()+hi, x) - a.begin()+lo;
}

int cnt_geq_x(vi &a, int x) {
    return a.end() - lower_bound(a.begin(), a.end(), x);
}

int cnt_geq_x(vi &a, int x, int lo, int hi) {
    return a.begin()+hi - lower_bound(a.begin()+lo, a.begin()+hi, x);
}

int cnt_gt_x(vi &a, int x) {
    return a.end() - upper_bound(a.begin(), a.end(), x);
}

int cnt_gt_x(vi &a, int x, int lo, int hi) {
    return a.begin()+hi - upper_bound(a.begin()+lo, a.begin()+hi, x);
}

bool mul_overflow(int a, int b) {
    int c;
    return __builtin_mul_overflow(a, b, &c);
}

template<typename T>
int popcount(T x) {return __builtin_popcountll(x);}

template<typename T>
T sum(vector<T> &a) {
    T ret = 0;
    for (auto v : a) ret += v;
    return ret;
}

template<typename T>
T max(vector<T> &a) {
    return *max_element(a.begin(), a.end());
}

template<typename T>
T min(vector<T> &a) {
    return *min_element(a.begin(), a.end());
}

template<typename T> 
pair<T,int> max_idx(vector<T> &a) {
    int n = a.size();
    vector<pair<T,int>> b(n);
    for (int i=0; i<n; i++) {
        b[i] = {a[i], i};
    }
    return *max_element(b.begin(), b.end());
}

template<typename T> 
pair<T,int> min_idx(vector<T> &a) {
    int n = a.size();
    vector<pair<T,int>> b(n);
    for (int i=0; i<n; i++) {
        b[i] = {a[i], i};
    }
    return *min_element(b.begin(), b.end());
}

int ceil_div(int a, int b) {
    return (a + b - 1) / b;
}

int int_pow(int base, int exp) {
    int res = 1;
    while (exp) {
        if (exp & 1) res *= base;
        exp >>= 1;
        base *= base;
    }
    return res;
}

int highest_power_of_2(int n) {
    while((n & (n-1)) != 0){
        n = n & (n-1);
    }
    return n;
}

int msb_pos(int x) {
    if (x==0) return -1;
    int y = __builtin_clzll(x);
    int ret = 63 - y;
    return ret;
}

template<typename T1, typename T2>
void chmax(T1 &x, T2 y) { if (x < y) x = y; }

template<typename T1, typename T2>
void chmin(T1 &x, T2 y) { if (x > y) x = y; }

template<typename T>
void asort(vector<T> &a) {sort(a.begin(), a.end());}

template<typename T>
void dsort(vector<T> &a) {sort(a.rbegin(), a.rend());}

template<typename T>
void reverse(vector<T> &a) {reverse(a.begin(), a.end());}

template<typename T>
set<T> get_set(vector<T> &a) {
    set<T> ret(a.begin(), a.end());
    return ret;
}

template<typename T>
vector<T> get_unique(vector<T> a) {
    sort(a.begin(), a.end());
    a.erase(unique(a.begin(), a.end()), a.end());
    return a;
}

template<typename T>
using min_pq = priority_queue<T, vector<T>, greater<T>>;
template<typename T>
using max_pq = priority_queue<T>;

int ccw(pii p1, pii p2, pii p3) {
    auto [x1,y1] = p1;
    auto [x2,y2] = p2;
    auto [x3,y3] = p3;
    return (x2-x1)*(y3-y1) - (x3-x1)*(y2-y1);
}

pii extgcd(int a, int b) {
    if (b==0) return {1,0};
    int q = a / b;
    auto [x,y] = extgcd(b,a-b*q);
    return {y,x-q*y};
}

vector<string> split_str(string s, const char delim = ' ') {
    vector<string> ret;
    stringstream ss(s);
    string t;
    while (getline(ss, t, delim)) {
        ret.push_back(t);
    }
    return ret;
}

struct dsu {
  public:
    dsu() : _n(0) {}
    dsu(int n) : _n(n), parent_or_size(n, -1) {}

    int merge(int a, int b) {
        assert(0 <= a && a < _n);
        assert(0 <= b && b < _n);
        int x = leader(a), y = leader(b);
        if (x == y) return x;
        if (-parent_or_size[x] < -parent_or_size[y]) std::swap(x, y);
        parent_or_size[x] += parent_or_size[y];
        parent_or_size[y] = x;
        return x;
    }

    bool same(int a, int b) {
        assert(0 <= a && a < _n);
        assert(0 <= b && b < _n);
        return leader(a) == leader(b);
    }

    int leader(int a) {
        assert(0 <= a && a < _n);
        if (parent_or_size[a] < 0) return a;
        return parent_or_size[a] = leader(parent_or_size[a]);
    }

    int size(int a) {
        assert(0 <= a && a < _n);
        return -parent_or_size[leader(a)];
    }

    std::vector<std::vector<int>> groups() {
        std::vector<int> leader_buf(_n), group_size(_n);
        for (int i = 0; i < _n; i++) {
            leader_buf[i] = leader(i);
            group_size[leader_buf[i]]++;
        }
        std::vector<std::vector<int>> result(_n);
        for (int i = 0; i < _n; i++) {
            result[i].reserve(group_size[i]);
        }
        for (int i = 0; i < _n; i++) {
            result[leader_buf[i]].push_back(i);
        }
        result.erase(
            std::remove_if(result.begin(), result.end(),
                [&](const std::vector<int>& v) { return v.empty(); }),
            result.end());
        return result;
    }

  private:
    int _n;
    std::vector<int> parent_or_size;
};

class Trie {
    public:

    bool leaf;
    Trie* ch[26];

    Trie() {
        this->leaf = false;
        for (int i=0; i<26; i++) {
            this->ch[i] = nullptr;
        }
    }
    
    ~Trie() {
        for (int i = 0; i < 26; i++) {
            if (ch[i]) delete ch[i];
        }
    }

    void insert(string s) {
        Trie* node = this;

        for (int i=0; i<(int)s.size(); i++) {
            int idx = s[i] - 'a';
            if (node->ch[idx] == nullptr) node->ch[idx] = new Trie();
            node = node->ch[idx];
        }
        node->leaf = true;
    }

    bool search(string key) {
        Trie* node = this;
        for (int i = 0; i <(int)key.size(); i++) {
            int idx = key[i] - 'a';
            if (!node->ch[idx]) return false;
            node = node->ch[idx];
        }
        return (node->leaf);
    }
};

template<typename T>
vector<vector<T>> mat_id(int n) {
    vector<vector<T>> ret(n, vector<T>(n));
    for (int i=0; i<n; i++) {
        ret[i][i] = 1;
    }
    return ret;
}

template<typename T>
vector<vector<T>> mat_mul(vector<vector<T>> &a, vector<vector<T>> &b) {
    int n = a.size();
    vector<vector<T>> ret(n, vector<T>(n));
    for (int i=0; i<n; i++) {
        for (int j=0; j<n; j++) {
            for (int k=0; k<n; k++) {
                ret[i][j] += a[i][k] * b[k][j];
            }
        }
    }
    return ret;
}

template<typename T>
vector<vector<T>> mat_exp(vector<vector<T>> a, int e) {
    int n = a.size();
    auto ret = mat_id<T>(n);
    while (e) {
        if (e&1) ret = mat_mul(ret, a);
        e >>= 1;
        a = mat_mul(a,a);
    }
    return ret;
}

////////////////////////////////////
 
vector<mint> fact;
vector<mint> finv;
 
void init_fact(int fact_sz, int finv_sz) {
    assert(fact_sz >= finv_sz);
    fact.resize(fact_sz+1,1);
    finv.resize(finv_sz+1);
    for (int i=1; i<=fact_sz; i++) {
        fact[i] = fact[i-1] * i;
    }
    finv[finv_sz] = fact[finv_sz].inv();
    for (int i=finv_sz; i>0; i--) {
        finv[i-1] = finv[i] * i;
    }
}

void init_fact(int sz) {
    init_fact(sz,sz);
}
 
mint ncr(int n, int r) {
    if (r < 0 || r > n) return mint(0);
    mint numer = fact[n];
    mint denom = finv[r] * finv[n-r];
    return numer * denom;
}

////////////////////////////////////

vi primes;
vi spf; 
void init_spf(int n) {
    spf.resize(n+1);
    for (int i=2; i <= n; i++) {
        if (spf[i] == 0) {
            spf[i] = i;
            primes.push_back(i);
        }
        for (int j = 0; i * primes[j] <= n; j++) {
            spf[i * primes[j]] = primes[j];
            if (primes[j] == spf[i]) {
                break;
            }
        }
    }
}

vi get_pfactors(int x) {
    vector<int> ret;
    while (x != 1) {
        ret.push_back(spf[x]);
        x = x / spf[x];
    }
    return ret;
}

////////////////////////////////////

struct rabin_karp {
    size_t n;
    i128 B, P;                          // base and modulus for this instance
    inline static const i128 defaultP = (1ll << 61) - 1;

    static std::mt19937_64 rng;         // shared RNG for all instances

    std::vector<i128> pw;               // pw[i] = B^i mod P
    std::vector<i128> h;                // prefix hashes

    // --- helper: get a random base in [1000, sqrt(P)] ---
    static i128 random_base(i128 P) {
        std::uniform_int_distribution<long long> dist(
            1000,
            (long long)std::sqrt((long double)P)
        );
        return dist(rng);
    }

    // --- helper for string → vector<int> ---
    static std::vector<int> to_vec(const std::string &s) {
        std::vector<int> a(s.size());
        for (int i = 0; i < (int)s.size(); i++) {
            a[i] = (unsigned char)s[i];
        }
        return a;
    }

    // --- core constructor: explicit base + modulus ---
    rabin_karp(const std::vector<int> &a, i128 B, i128 P = defaultP)
        : n(a.size()), B(B), P(P), pw(n + 1, 1), h(n + 1, 0) {

        // pw[i] = B^i mod P
        for (int i = 1; i <= (int)n; i++) {
            pw[i] = (pw[i - 1] * B) % P;
        }

        // backward-style prefix hash:
        // h[i+1] = h[i]*B + a[i]   (mod P)
        for (int i = 0; i < (int)n; i++) {
            h[i+1] = ((h[i] * B )%P + a[i]) % P;
        }
    }

    // --- convenience constructor: random base, given modulus (or defaultP) ---
    rabin_karp(const std::vector<int> &a, i128 P = defaultP)
        : rabin_karp(a, random_base(P), P) {}

    // --- string constructor: explicit base B, explicit P ---
    rabin_karp(const std::string &s, i128 B, i128 P)
        : rabin_karp(to_vec(s), B, P) {}

    // --- convenience constructor: random base, given modulus (or defaultP) ---
    rabin_karp(const std::string &s, i128 P = defaultP)
        : rabin_karp(to_vec(s), random_base(P), P) {}

    // hash of substring [l, r] (0-indexed, inclusive)
    i128 query(int l, int r) const {
        assert(0 <= l && l <= r && (size_t)r < n);
        int len = r - l + 1;

        // x = h[r+1] - h[l] * B^len
        i128 x = h[r + 1] - ( (__int128)h[l] * pw[len] ) % P;
        x %= P;
        if (x < 0) x += P;
        return x;
    }

    // optional helpers if you want to inspect parameters
    i128 base() const { return B; }
    i128 mod()  const { return P; }
};

// static RNG definition
std::mt19937_64 rabin_karp::rng(
    std::chrono::steady_clock::now().time_since_epoch().count()
);

////////////////////////////////////

template<typename T> T op_max(T x, T y) {return max(x,y);}
template<typename T> T op_min(T x, T y) {return min(x,y);}

template<typename T,  T (*op)(T, T)>
struct sparse_table {
    int n,m;
    vector<vector<T>> table;

    inline T merge(T x, T y) {
        return op(x, y);
    }

    sparse_table(vector<T> &a) {
        n = a.size();
        m = __lg(n) + 1;
        table.assign(m, vector<T>(n));
        for (int i = 0; i < n; i++) table[0][i] = a[i];
        for (int i = 1; i < m; i++) {
            for (int j = 0; j + (1<<i) <= n; j++) {
                table[i][j] = merge(table[i-1][j], table[i-1][j + (1<<(i-1))]);
            }
        }
    }

    T query(int l, int r) {
        // l, r : inclusive
        assert(l<=r && 0<=l && r< n);
        int u = __lg(r-l+1);
        return merge(table[u][l], table[u][r-(1<<u)+1]);
    }

    T query(int l, int r, T e) {
        // e for identity
        l = max(l,0ll);
        r = min(r,n-1);
        int u = __lg(r-l+1);
        if (l<=r) return merge(table[u][l], table[u][r-(1<<u)+1]);
        else return e;
    }
};

template<typename T> using max_spt = sparse_table<T,op_max>;
template<typename T> using min_spt = sparse_table<T,op_min>;

////////////////////////////////////

struct LCA {
    vi height, euler, pw2, lg2, idx;
    vvp sptable;
    int n, logn;

    LCA(vector<vector<int>> &adj, int root = 0) {
        n = adj.size();
        logn = ceil(log2(n))+1;
        height.resize(n);
        euler.reserve(2*n);
        idx.resize(n);
        sptable.assign(logn, vp(2*n));
        pw2.assign(logn, 1);
        for (int k=1; k<logn; k++) pw2[k] = 2*pw2[k-1];
        lg2.assign(2*n, -1);
        for(int k=0; k<logn; k++) {
            if(pw2[k] < 2*n) lg2[pw2[k]] = k;
        }
        for(int i=1; i<2*n; i++) {
            if(lg2[i] == -1) lg2[i] = lg2[i-1];
        }

        dfs(adj, root, -1);
        int m = euler.size();
        
        for(int i=0; i<m; i++) {
            sptable[0][i] = {height[euler[i]], euler[i]};
        }
        for(int k=1; k<logn; k++){
            for(int i=0; i<m; i++){
                if(i+pw2[k-1] > m) continue;
                sptable[k][i] = min(sptable[k-1][i], sptable[k-1][i+pw2[k-1]]);
            }
        }    
    }

    void dfs(vector<vector<int>> &adj, int u, int p, int h = 0) {
        height[u] = h;
        idx[u] = euler.size();
        euler.push_back(u);
        for (auto v : adj[u]) {
            if (v == p) continue;
            dfs(adj, v, u, h + 1);
            euler.push_back(u);
        }
    }

    int query(int u, int v) {
        int l = idx[u], r = idx[v];
        if(l > r) swap(l,r);
        int k = lg2[r-l+1];
        return min(sptable[k][l], sptable[k][r-pw2[k]+1]).second;
    }
};

////////////////////////////////////

// <lazy segtree prototype>

// using S = pii;
// using F = pii;

// S op(S a, S b) {
//     auto [x,u] = a;
//     auto [y,v] = b;
//     return {x+y,u+v};
// }
 
// S e() {
//     return {0,0};
// }
 
// S mapping(F f, S s) {
//     auto [a,b] = f;
//     auto [x,y] = s;
//     return {a*x + b*y, y};
// }
 
// F composition(F f, F g) {
//     auto [a,b] = g;
//     auto [c,d] = f;
//     return {c*a, c*b+d};
// }

// F id () {
//     return {1,0};
// }

// lazy_segtree<S, op, e, F, mapping, composition, id> seg(n);

////////////////////////////////////

#endif // 2000 lines template ends here

void io_util() {
    #ifdef LOCAL
    // freopen("input.txt", "r", stdin);
    // freopen("output.txt", "w", stdout);
    #endif
    cin.tie(0)->sync_with_stdio(0);
    cout.precision(17);
}

////////////////////////////////////

mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());

void solve(); 
signed main() {
    io_util();
    mint::set_mod(998244353);
    // mint::set_mod(1e9+7);
    int tc = 1;
    // ri(tc);
    // cin.ignore(numeric_limits<streamsize>::max(), '\n'); // flush the newline
    for (int i=1; i<=tc; i++) {
        // cout << "Case #" << i << ": ";
        solve();
    }
    return 0;
}

void solve() {
    int n; ri(n);
    vvi a(n, vi(n));
    for (int i=0; i<n; i++) {
        for (int j=0; j<n; j++) {
            if (i < j) {
                ri(a[i][j]);
            }
        }
    }
    bool ans = false;
    for (int i=0; i<n; i++) {
        for (int j=i+1; j<n; j++) {
            for (int k=j+1; k<n; k++) {
                if (a[i][j] + a[j][k] < a[i][k]) ans = true;
            }
        }
    }
    po(ans?"Yes":"No");
}

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