#pragma region Macros #pragma GCC optimize("O3,unroll-loops") #pragma GCC target("sse,sse2,sse3,ssse3,sse4,fma,mmx,abm,bmi,bmi2,popcnt,lzcnt") #pragma GCC target("avx2") // CF, CodeChef, HOJ ではコメントアウト #include <bits/extc++.h> // #include <atcoder/all> // using namespace atcoder; using namespace std; using namespace __gnu_pbds; // #include <boost/multiprecision/cpp_dec_float.hpp> // #include <boost/multiprecision/cpp_int.hpp> // namespace mp = boost::multiprecision; // using lll = mp::cpp_int; // using lld = mp::cpp_dec_float_50; // 十進50桁. ldは19桁. // // using lld = mp::cpp_dec_float_100; // // using lld = mp::number<mp::cpp_dec_float<200>>; // lld Beps = 0.00000000000000000000000000000001; // 1e-32 // const bool equals(lld a, lld b) { return mp::fabs(a - b) < Beps; } #define pb emplace_back #define int ll #define endl '\n' using ll = long long; using ld = long double; const ld PI = acosl(-1); const int INF = 1 << 30; const ll INFL = 1LL << 61; const int MOD = 998244353; // const int MOD = 1000000007; const ld EPS = 1e-10; const bool equals(ld a, ld b) { return fabs((a) - (b)) < EPS; } const vector<int> dx = {0, 1, 0, -1, 1, 1, -1, -1, 0}; // → ↓ ← ↑ ↘ ↙ ↖ ↗ 自 const vector<int> dy = {1, 0, -1, 0, 1, -1, -1, 1, 0}; struct Edge { using cost_type = int; int from, to; cost_type cost; Edge() {} Edge(int to, cost_type cost) : to(to), cost(cost), from(-1) {} Edge(int from, int to, cost_type cost) : from(from), to(to), cost(cost) {} bool operator ==(const Edge &e) { return this->from == e.from && this->to == e.to && this->cost == e.cost; } bool operator !=(const Edge &e) { return this->from != e.from or this->to != e.to or this->cost != e.cost; } bool operator <(const Edge &e) { return this->cost < e.cost; } bool operator >(const Edge &e) { return this->cost > e.cost; } }; chrono::system_clock::time_point start; __attribute__((constructor)) void constructor() { ios::sync_with_stdio(false); cin.tie(nullptr); cout << fixed << setprecision(10); start = chrono::system_clock::now(); } struct RNG { using state_type = uint32_t; using result_type = uint32_t; state_type x = 123456789, y = 362436039, z = 521288629, w = 88675123; constexpr static double INV_MAX = 1.0 / 0xFFFFFFFF; // constexpr RNG(state_type seed = 88675123): w(seed) {} RNG() { auto now = chrono::high_resolution_clock::now(); w = static_cast<state_type>(now.time_since_epoch().count() & 0xFFFFFFFF); } constexpr result_type operator()() { state_type t = x ^ (x << 11); x = y, y = z, z = w; return w = (w ^ (w >> 19)) ^ (t ^ (t >> 8)); } constexpr result_type Int(state_type a) { // [0, a) return ((uint64_t) (*this)() * a) >> 32; } constexpr result_type Int(state_type a, state_type b) { // [a, b] return Int(b - a + 1) + a; } constexpr double prob() { // [0, 1] return (*this)() * INV_MAX; } constexpr double Double(double a, double b) { // [a, b] return prob() * (b - a) + a; } } rng; namespace bit_function { using i64 = ll; // using i64 = uint64_t; // bit演算, x==0の場合は例外処理した方がよさそう. 区間は [l, r) i64 lrmask(int l, int r) { return (1LL << r) - (1LL << l); } i64 sub_bit(i64 x, int l, int r) { i64 b = x & ((1LL << r) - (1LL << l)); return b >> l; } // r溢れ可 i64 bit_width(i64 x) { return 64 - __builtin_clzll(x) + (x == 0); } i64 popcount(i64 x) { return __builtin_popcountll(x); } i64 popcount(i64 x, int l, int r) { return __builtin_popcountll(sub_bit(x, l, r)); } i64 unpopcount(i64 x) { return bit_width(x) - __builtin_popcountll(x); } // 最上位bitより下のみ i64 unpopcount(i64 x, int l, int r) { return r - l - __builtin_popcountll(sub_bit(x, l, r)); } // 最上位bitより上も含まれうる bool is_pow2(i64 x) { return __builtin_popcountll(x) == 1; } // xが負のときは常にfalse bool is_pow4(i64 x) { return __builtin_popcountll(x) == 1 && __builtin_ctzll(x) % 2 == 0; } //bool is_pow4(ll x) { return __builtin_popcountll(x) == 1 && (x&0x55555555); } int top_bit(i64 x) { return 63 - __builtin_clzll(x);} // 2^kの位 (x > 0) int bot_bit(i64 x) { return __builtin_ctzll(x);} // 2^kの位 (x > 0) int next_bit(i64 x, int k) { // upper_bound x >>= (k + 1); int pos = k + 1; while (x > 0) { if (x & 1) return pos; x >>= 1; pos++; } return -1; } int prev_bit(i64 x, int k) { // k = min(k, bit_width(x)); ? int pos = 0; while (x > 0 && pos < k) { if (x & 1) { if (pos < k) return pos; } x >>= 1; pos++; } return -1; } int kth_bit(i64 x, int k) { // kは1-indexed int pos = 0, cnt = 0; while (x > 0) { if (x & 1) { cnt++; if (cnt == k) return pos; } x >>= 1; pos++; } return -1; } i64 msb(i64 x) { if (x == 0) return 0; return 1LL << (63 - __builtin_clzll(x)); } // mask i64 lsb(i64 x) { return (x & -x); } // mask int countl_zero(i64 x) { return __builtin_clzll(x); } int countl_one(i64 x) { // countl_oneと定義が異なるので注意 i64 ret = 0, k = 63 - __builtin_clzll(x); while (k != -1 && (x & (1LL << k))) { k--; ret++; } return ret; } int countr_zero(i64 x) { return __builtin_ctzll(x); } // x=0のとき64 int countr_one(i64 x) { int ret = 0; while (x & 1) { x >>= 1; ret++; } return ret; } // int countr_one(ll x) { return __builtin_popcount(x ^ (x & -~x)); i64 l_one(i64 x) { // 最上位で連なってる1のmask if (x == 0) return 0; i64 ret = 0, k = 63 - __builtin_clzll(x); while (k != -1 && (x & (1LL << k))) { ret += 1LL << k; k--; } return ret; } int floor_log2(i64 x) { return 63 - __builtin_clzll(x); } // top_bit int ceil_log2(i64 x) { return 64 - __builtin_clzll(x - 1); } i64 bit_floor(i64 x) { if (x == 0) return 0; return 1LL << (63 - __builtin_clzll(x)); } // msb i64 bit_ceil(i64 x) { if (x == 0) return 0; return 1LL << (64 - __builtin_clzll(x - 1)); } i64 rotl(i64 x, int k) { // 有効bit内でrotate. オーバーフロー注意 i64 w = bit_width(x); k %= w; return ((x << k) | (x >> (w - k))) & ((1LL << w) - 1); } // i64 rotl(i64 x, i64 l, i64 m, i64 r) {} i64 rotr(i64 x, int k) { i64 w = bit_width(x); k %= w; return ((x >> k) | (x << (w - k))) & ((1LL << w) - 1); } // i64 rotr(i64 x, i64 l, i64 m, i64 r) {} i64 bit_reverse(i64 x) { // 有効bit内で左右反転 i64 r = 0, w = bit_width(x); for (i64 i = 0; i < w; i++) r |= ((x >> i) & 1) << (w - i - 1); return r; } // i64 bit_reverse(i64 x, int l, int r) {} bool is_palindrome(i64 x) { return x == bit_reverse(x); } bool is_palindrome(i64 x, int l, int r) { i64 b = sub_bit(x, l, r); return b == bit_reverse(b); } i64 concat(i64 a, i64 b) { return (a << bit_width(b)) | b; } // オーバーフロー注意 i64 erase(i64 x, int l, int r) { return x >> r << l | x & ((1LL << l) - 1); } // [l, r) をカット i64 hamming(i64 a, i64 b) { return __builtin_popcountll(a ^ b); } i64 hamming(i64 a, i64 b, int l, int r) { return __builtin_popcountll(sub_bit(a, l, r) ^ sub_bit(b, l, r)); } i64 compcount(i64 x) { return (__builtin_popcountll(x ^ (x >> 1)) + (x & 1)) / 2; } i64 compcount2(i64 x) { return compcount(x & (x >> 1)); } // 長さ2以上の連結成分の個数 i64 adjacount(i64 x) { return __builtin_popcountll(x & (x >> 1)); } // 隣接する1のペアの個数 i64 next_combination(i64 x) { i64 t = x | (x - 1); return (t + 1) | (((~t & -~t) - 1) >> (__builtin_ctzll(x) + 1)); } } using namespace bit_function; namespace util_function { namespace Std = std; __int128_t POW(__int128_t x, int n) { __int128_t ret = 1; assert(n >= 0); if (x == 1 or n == 0) ret = 1; else if (x == -1 && n % 2 == 0) ret = 1; else if (x == -1) ret = -1; else if (n % 2 == 0) { // assert(x < INFL); ret = POW(x * x, n / 2); } else { // assert(x < INFL); ret = x * POW(x, n - 1); } return ret; } int per(int x, int y) { // x = qy + r (0 <= r < y) を満たすq assert(y != 0); if (x >= 0 && y > 0) return x / y; if (x >= 0 && y < 0) return x / y - (x % y < 0); if (x < 0 && y < 0) return x / y + (x % y < 0); return x / y - (x % y < 0); // (x < 0 && y > 0) } int mod(int x, int y) { // x = qy + r (0 <= r < y) を満たすr assert(y != 0); return x - y * per(x, y); } // https://yukicoder.me/problems/no/2781 int floor(int x, int y) { // (ld)x / y 以下の最大の整数 assert(y != 0); if (y < 0) x = -x, y = -y; return x >= 0 ? x / y : (x + 1) / y - 1; } int ceil(int x, int y) { // (ld)x / y 以上の最小の整数 assert(y != 0); if (y < 0) x = -x, y = -y; return x > 0 ? (x - 1) / y + 1 : x / y; } int round(int x, int y) { // (ld)x / y を小数第1位について四捨五入 assert(y != 0); if (x*y < 0) return -((abs(x) * 2 + abs(y)) / (abs(y) * 2)); // https://www.acmicpc.net/problem/2108 return (x * 2 + y) / (y * 2); } int round(int x, int y, int k) { // (ld)x / y を10^kの位に関して四捨五入 assert(y != 0 && k >= 0); if (k == 0) return (x * 2 + y) / (y * 2); x /= y * POW(10, k - 1); if (x % 10 >= 5) return (x + 10 - x % 10) * POW(10, k - 1); return x * POW(10, k - 1); } int round2(int x, int y) { // 五捨五超入 // 未verify assert(y != 0); if (y < 0) y = -y, x = -x; int z = x / y; if ((z * 2 + 1) * y <= y * 2) z++; return z; } int Floor(ld x) { // 未. 負数でも小さい方に丸める if (x > -EPS) return (int)(floorl(x + EPS) + EPS); return -(int)((ceill(-x - EPS)) + EPS); } int Ceil(ld x) { // 未. 負数でも大きい方に丸める if (x > EPS) return (int)(ceill(x - EPS) + EPS); return -(int)((floorl(-x + EPS)) + EPS); } int Round(ld x) { // 未. 負数でも.5の場合は大きい方に丸める if (x > EPS) return (int)(Std::round(x + EPS) + EPS); return (int)(Std::round(x + EPS) - EPS); } // int get(ld x, int k) { // 未. xの10^kの位の桁 // } ld floor(ld x, int k) { // xを10^kの位に関してflooring ld d = pow(10, -k); return Floor(x * d) / d; // 未verify } ld ceil(ld x, int k) { // xを10^kの位に関してceiling ld d = pow(10, -k); return Ceil(x * d) / d; // 未verify } ld round(ld x, int k) { // xを10^kの位に関して四捨五入. ld d = pow(10, -k); return Round(x * d) / d; } // int kth(int x, int y, int k) { // x / yの10^kの位の桁 // } int floor(ld x, ld y) { // 誤差対策TODO assert(!equals(y, 0)); return Std::floor(x / y); // floor(x) = ceil(x - 1) という話も } int ceil(ld x, ld y) { // 誤差対策TODO // ceil(p/q) = -floor(-(p/q))らしい assert(!equals(y, 0)); return Std::ceil(x / y); // ceil(x) = floor(x + 1) } int perl(ld x, ld y) { // x = qy + r (0 <= r < y, qは整数) を満たす q // 未verify. 誤差対策TODO. EPS外してもいいかも。 assert(!equals(y, 0)); if (x >= 0 && y > 0) return Std::floor(x / y)+EPS; if (x >= 0 && y < 0) return -Std::floor(x / fabs(y)); if (x < 0 && y < 0) return Std::floor(x / y) + (x - Std::floor(x/y)*y < -EPS); return Std::floor(x / y) - (x - Std::floor(x/y)*y < -EPS); // (x < 0 && y > 0) } ld modl(ld x, ld y) { // x = qy + r (0 <= r < y, qは整数) を満たす r // 未verify. 誤差対策TODO. -0.0が返りうる。 assert(!equals(y, 0)); if (x >= 0) return x - fabs(y)*fabs(per(x, y)); return x - fabs(y)*floor(x, fabs(y)); } int seisuu(ld x) { return (int)x; } // 整数部分. 誤差対策TODO int modf(ld x) { if (x < 0) return ceill(x); else return floorl(x); } // 正なら+EPS, 負なら-EPSしてから、文字列に直して小数点以下を捨てる? int seisuu(int x, int y) { assert(y != 0); return x / y; } int seisuu(ld x, ld y) { // 誤差対策TODO assert(!equals(y, 0)); return (int)(x / y); } int floor_log(int base, int x) { // log_base{x} のfloor assert(base >= 2); int ret = 0, now = 1; while (now <= x) { now *= base; if (now <= x) ret++; } return ret; } int ceil_log(int base, int x) { // log_base{x} のceil assert(base >= 2); int ret = 0, now = 1; while (now < x) { now *= base; ret++; } return ret; } template <class T> pair<T, T> max(const pair<T, T> &a, const pair<T, T> &b) { if (a.first > b.first or a.first == b.first && a.second > b.second) return a; return b; } template <class T> pair<T, T> min(const pair<T, T> &a, const pair<T, T> &b) { if (a.first < b.first or a.first == b.first && a.second < b.second) return a; return b; } template <class T> bool chmax(T &a, const T &b) { if (a < b) { a = b; return true; } return false; } template <class T> bool chmin(T &a, const T &b) { if (a > b) { a = b; return true; } return false; } template <class T> bool chmax(pair<T, T> &a, const pair<T, T> &b) { if (a.first < b.first or a.first == b.first && a.second < b.second) { a = b; return true; } return false; } template <class T> bool chmin(pair<T, T> &a, const pair<T, T> &b) { if (a.first > b.first or a.first == b.first && a.second > b.second) { a = b; return true; } return false; } template <class T> T mid(T a, T b, T c) { // 誤差対策TODO return a + b + c - Std::max({a, b, c}) - Std::min({a, b, c}); } template <typename T, typename... Args> void Sort(T& a, T& b, T& c, Args&... args) { vector<T> vec = {a, b, c, args...}; sort(vec.begin(), vec.end()); auto it = vec.begin(); a = *it++; b = *it++; c = *it++; int dummy[] = { (args = *it++, 0)... }; static_cast<void>(dummy); } template <typename T, typename... Args> void Sortr(T& a, T& b, T& c, Args&... args) { vector<T> vec = {a, b, c, args...}; sort(vec.rbegin(), vec.rend()); auto it = vec.begin(); a = *it++; b = *it++; c = *it++; int dummy[] = { (args = *it++, 0)... }; static_cast<void>(dummy); } template <class T> void sort(vector<T> &A, vector<T> &B) { vector<pair<T, T>> P(A.size()); for (int i = 0; i < A.size(); i++) P[i] = {A[i], B[i]}; sort(P.begin(), P.end()); for (int i = 0; i < A.size(); i++) A[i] = P[i].first, B[i] = P[i].second; } template <class T> void unique(vector<T> &A, vector<T> &B) { vector<T> A2, B2; A2.reserve(A.size()); B2.reserve(B.size()); for (int i = 0; i < A.size(); i++) { if (i == 0 or A[i] != A[i - 1] or B[i] != B[i - 1]) { A2.push_back(A[i]); B2.push_back(B[i]); } } } istream &operator >>(istream &is, __int128_t& x) { string S; is >> S; __int128_t ret = 0; int f = 1; if (S[0] == '-') f = -1; for (int i = 0; i < S.length(); i++) if ('0' <= S[i] && S[i] <= '9') ret = ret * 10 + S[i] - '0'; x = ret * f; return (is); } ostream &operator <<(ostream &os, __int128_t x) { ostream::sentry s(os); if (s) { __uint128_t tmp = x < 0 ? -x : x; char buffer[128]; char *d = end(buffer); do { --d; *d = "0123456789"[tmp % 10]; tmp /= 10; } while (tmp != 0); if (x < 0) { --d; *d = '-'; } int len = end(buffer) - d; if (os.rdbuf()->sputn(d, len) != len) os.setstate(ios_base::badbit); } return os; } __int128_t sto128(const string &S) { __int128_t ret = 0; int f = 1; if (S[0] == '-') f = -1; for (int i = 0; i < S.length(); i++) if ('0' <= S[i] && S[i] <= '9') ret = ret * 10 + S[i] - '0'; return ret * f; } __int128_t gcd(__int128_t a, __int128_t b) { return b ? gcd(b, a % b) : a; } __int128_t lcm(__int128_t a, __int128_t b) { return a / gcd(a, b) * b; // lcmが__int128_tに収まる必要あり } string to_string(double x, int k) { // 小数第k+1を四捨五入して小数第k位までを出力 // 切り捨てがほしい場合は to_string(x, k+1) として pop_back() すればよい? ostringstream os; os << fixed << setprecision(k) << x; return os.str(); } string to_string(__int128_t x) { string ret = ""; if (x < 0) { ret += "-"; x *= -1; } while (x) { ret += (char)('0' + x % 10); x /= 10; } reverse(ret.begin(), ret.end()); return ret; } string to_string(char c) { string s = ""; s += c; return s; } } using namespace util_function; 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); } }; template<class T> size_t HashCombine(const size_t seed,const T &v) { return seed^(hash<T>()(v)+0x9e3779b9+(seed<<6)+(seed>>2)); } template<class T,class S> struct hash<pair<T,S>>{ size_t operator()(const pair<T,S> &keyval) const noexcept { return HashCombine(hash<T>()(keyval.first), keyval.second); } }; template<class T> struct hash<vector<T>>{ size_t operator()(const vector<T> &keyval) const noexcept { size_t s=0; for (auto&& v: keyval) s=HashCombine(s,v); return s; } }; template<int N> struct HashTupleCore{ template<class Tuple> size_t operator()(const Tuple &keyval) const noexcept{ size_t s=HashTupleCore<N-1>()(keyval); return HashCombine(s,get<N-1>(keyval)); } }; template <> struct HashTupleCore<0>{ template<class Tuple> size_t operator()(const Tuple &keyval) const noexcept{ return 0; } }; template<class... Args> struct hash<tuple<Args...>>{ size_t operator()(const tuple<Args...> &keyval) const noexcept { return HashTupleCore<tuple_size<tuple<Args...>>::value>()(keyval); } }; template<typename T> class Compress { public: int sz = 0; vector<T> uniqV; Compress() {} template<typename... Vecs> Compress(const Vecs&... vecs) { (uniqV.insert(uniqV.end(), vecs.begin(), vecs.end()), ...); sort(uniqV.begin(), uniqV.end()); uniqV.erase(unique(uniqV.begin(), uniqV.end()), uniqV.end()); sz = uniqV.size(); } vector<int> zip(const vector<T> &V) { vector<int> ret(V.size()); for (int i = 0; i < V.size(); i++) { ret[i] = encode(V[i]); } return ret; } vector<T> unzip(const vector<int> &V) { vector<T> ret(V.size()); for (int i = 0; i < V.size(); i++) { ret[i] = decode(V[i]); } return ret; } int size() { return sz; } int encode(T x) { auto it = lower_bound(uniqV.begin(), uniqV.end(), x); return it - uniqV.begin(); } T decode(int x) { if (x < 0 or x >= uniqV.size()) return -1; // xが範囲外の場合 return uniqV[x]; } }; class UnionFind { public: UnionFind() = default; UnionFind(int N) : par(N), sz(N, 1) { iota(par.begin(), par.end(), 0); } int root(int x) { if (par[x] == x) return x; return (par[x] = root(par[x])); } bool unite(int x, int y) { int rx = root(x); int ry = root(y); if (rx == ry) return false; if (sz[rx] < sz[ry]) swap(rx, ry); sz[rx] += sz[ry]; par[ry] = rx; return true; } bool issame(int x, int y) { return (root(x) == root(y)); } int size(int x) { return sz[root(x)]; } vector<vector<int>> groups(int N) { vector<vector<int>> G(N); for (int x = 0; x < N; x++) { G[root(x)].push_back(x); } G.erase( remove_if(G.begin(), G.end(), [&](const vector<int>& V) { return V.empty(); }), G.end()); return G; } private: vector<int> par, sz; }; template<typename T> struct BIT { int N; vector<T> bit[2]; BIT(int N_, int x = 0) : N(N_ + 1) { bit[0].assign(N, 0); bit[1].assign(N, 0); if (x != 0) for (int i = 0; i < N; i++) add(i, x); } BIT(const vector<T> &A) : N(A.size() + 1) { bit[0].assign(N, 0); bit[1].assign(N, 0); for (int i = 0; i < (int)A.size(); i++) add(i, A[i]); } void add_sub(int p, int i, T x) { while (i < N) { bit[p][i] += x; i += (i & -i); } } void add(int l, int r, T x) { add_sub(0, l + 1, -x * l); add_sub(0, r + 1, x * r); add_sub(1, l + 1, x); add_sub(1, r + 1, -x); } void add(int i, T x) { add(i, i + 1, x); } T sum_sub(int p, int i) { T ret = T(0); while (i > 0) { ret += bit[p][i]; i -= (i & -i); } return ret; } T sum(int i) { return sum_sub(0, i) + sum_sub(1, i) * i; } T sum(int l, int r) { return sum(r) - sum(l); } T get(int i) { return sum(i, i + 1); } void set(int i, T x) { T s = get(i); add(i, -s + x); } }; template<int mod> class Modint { public: int val = 0; Modint(int x = 0) { while (x < 0) x += mod; val = x % mod; } Modint(const Modint &r) { val = r.val; } Modint operator -() { return Modint(-val); } // 単項 Modint operator +(const Modint &r) { return Modint(*this) += r; } Modint operator +(const int &q) { Modint r(q); return Modint(*this) += r; } Modint operator -(const Modint &r) { return Modint(*this) -= r; } Modint operator -(const int &q) { Modint r(q); return Modint(*this) -= r; } Modint operator *(const Modint &r) { return Modint(*this) *= r; } Modint operator *(const int &q) { Modint r(q); return Modint(*this) *= r; } Modint operator /(const Modint &r) { return Modint(*this) /= r; } Modint operator /(const int &q) { Modint r(q); return Modint(*this) /= r; } Modint& operator ++() { val++; if (val >= mod) val -= mod; return *this; } // 前置 Modint operator ++(signed) { ++*this; return *this; } // 後置 Modint& operator --() { val--; if (val < 0) val += mod; return *this; } Modint operator --(signed) { --*this; return *this; } Modint &operator +=(const Modint &r) { val += r.val; if (val >= mod) val -= mod; return *this; } Modint &operator +=(const int &q) { Modint r(q); val += r.val; if (val >= mod) val -= mod; return *this; } Modint &operator -=(const Modint &r) { if (val < r.val) val += mod; val -= r.val; return *this; } Modint &operator -=(const int &q) { Modint r(q); if (val < r.val) val += mod; val -= r.val; return *this; } Modint &operator *=(const Modint &r) { val = val * r.val % mod; return *this; } Modint &operator *=(const int &q) { Modint r(q); val = val * r.val % mod; return *this; } Modint &operator /=(const Modint &r) { int a = r.val, b = mod, u = 1, v = 0; while (b) {int t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v);} val = val * u % mod; if (val < 0) val += mod; return *this; } Modint &operator /=(const int &q) { Modint r(q); int a = r.val, b = mod, u = 1, v = 0; while (b) {int t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v);} val = val * u % mod; if (val < 0) val += mod; return *this; } bool operator ==(const Modint& r) { return this -> val == r.val; } bool operator !=(const Modint& r) { return this -> val != r.val; } bool operator <(const Modint& r) { return this -> val < r.val; } bool operator >(const Modint& r) { return this -> val > r.val; } friend istream &operator >>(istream &is, Modint& x) { int t; is >> t; x = t; return (is); } friend ostream &operator <<(ostream &os, const Modint& x) { return os << x.val; } }; using mint = Modint<MOD>; mint modpow(const mint &x, int n) { if (n < 0) return (mint)1 / modpow(x, -n); // 未verify assert(n >= 0); if (n == 0) return 1; mint t = modpow(x, n / 2); t = t * t; if (n & 1) t = t * x; return t; } int modpow(__int128_t x, int n, int mod) { if (n == 0 && mod == 1) return 0; assert(n >= 0 && mod > 0); // TODO: n <= -1 __int128_t ret = 1; while (n > 0) { if (n % 2 == 1) ret = ret * x % mod; x = x * x % mod; n /= 2; } return ret; } // int modinv(__int128_t x, int mod) { // // assert(mod > 0); // // assert(x > 0); // if (x == 1 or x == 0) return 1; // return mod - modinv(mod % x, mod) * (mod / x) % mod; // } vector<mint> _fac, _finv, _inv; void COMinit(int N) { _fac.resize(N + 1); _finv.resize(N + 1); _inv.resize(N + 1); _fac[0] = _fac[1] = 1; _finv[0] = _finv[1] = 1; _inv[1] = 1; for (int i = 2; i <= N; i++) { _fac[i] = _fac[i-1] * mint(i); _inv[i] = -_inv[MOD % i] * mint(MOD / i); _finv[i] = _finv[i - 1] * _inv[i]; } } mint FAC(int N) { if (N < 0) return 0; return _fac[N]; } mint FACinv(int N) { if (N < 0) return 0; return _finv[N]; } mint COM(int N, int K) { if (N < K) return 0; if (N < 0 or K < 0) return 0; return _fac[N] * _finv[K] * _finv[N - K]; } mint COMinv(int N, int K) { if (N < K) return 0; if (N < 0 or K < 0) return 0; return _finv[N] * _fac[K] * _fac[N - K]; } mint MCOM(const vector<int> &V) { int N = 0; for (int i = 0; i < V.size(); i++) N += V[i]; mint ret = _fac[N]; for (int i = 0; i < V.size(); i++) ret *= _finv[V[i]]; return ret; } mint PERM(int N, int K) { if (N < K) return 0; if (N < 0 or K < 0) return 0; return _fac[N] * _finv[N - K]; } mint NHK(int N, int K) { // initのサイズに注意 if (N == 0 && K == 0) return 1; return COM(N + K - 1, K); } #pragma endregion signed main() { int N, M; cin >> N >> M; vector<vector<int>> dist(N, vector<int>(N, INFL)); for (int i = 0; i < M; i++) { int u, v, c; cin >> u >> v >> c; u--; v--; dist[u][v] = min(dist[u][v], c); // dist[v][u] = min(dist[u][v], c); } for (int i = 0; i < N; i++) dist[i][i] = 0; for (int k = 0; k < N; k++) { for (int i = 0; i < N; i++) { for (int j = 0; j < N; j++) { if (dist[i][k] == INFL or dist[k][j] == INFL) continue; if (dist[i][j] > dist[i][k] + dist[k][j]) { dist[i][j] = dist[i][k] + dist[k][j]; } } } } for (int i = 0; i < N; i++) { int ans = 0; for (int j = 0; j < N; j++) { if (dist[i][j] == INFL) continue; ans += dist[i][j]; } cout << ans << endl; } }