// #include <bits/stdc++.h> #include <algorithm> #include <atcoder/all> #include <bitset> #include <chrono> #include <cmath> #include <complex> #include <deque> #include <iomanip> #include <iostream> #include <limits> #include <map> #include <numeric> #include <queue> #include <random> #include <set> #include <vector> using namespace std; using namespace atcoder; using mint1 = modint1000000007; using mint2 = modint998244353; using ll = long long; using VI = vector<int>; using VL = vector<ll>; using VD = vector<double>; using VS = vector<string>; using VB = vector<bool>; using VVB = vector<vector<bool>>; using VVI = vector<VI>; using VVL = vector<VL>; using VVD = vector<VD>; using VVVI = vector<VVI>; using VVVL = vector<VVL>; using VVVD = vector<VVD>; using PII = std::pair<int, int>; using VPII = std::vector<std::pair<int, int>>; using PLL = std::pair<ll, ll>; using VPLL = std::vector<std::pair<ll, ll>>; using TI3 = std::tuple<int, int, int>; using TI4 = std::tuple<int, int, int, int>; using TL3 = std::tuple<ll, ll, ll>; using TL4 = std::tuple<ll, ll, ll, ll>; #define rep(i, n) for (int i = 0; i < (int)(n); i++) #define repr(i, n) for (int i = (int)(n)-1; i >= 0; i--) #define rep2(i, s, n) for (int i = (s); i < (int)(n); i++) #define repr2(i, g, n) for (int i = (int)(n)-1; i >= (g); i--) #define rep3(i, s, n, d) for (int i = (s); i < (int)(n); i += (d)) #define repr3(i, g, n, d) for (int i = (int)(n)-1; i >= (g); i -= (d)) #define allpt(v) (v).begin(), (v).end() #define allpt_c(v) (v).cbegin(), (v).cend() #define allpt_r(v) (v).rbegin(), (v).rend() #define allpt_cr(v) (v).crbegin(), (v).crend() constexpr int mod1 = 1e9 + 7, mod2 = 998244353, mod3 = 1e9 + 9; constexpr int mod = mod2; constexpr ll inf = 1e18; constexpr int infint = 1e9; constexpr double pi = 3.14159265359; bool test; const string wsp = " "; const string tb = "\t"; const string rt = "\n"; const string alphabets = "abcdefghijklmnopqrstuvwxyz"; std::random_device seed_gen; std::mt19937 engine(seed_gen()); // 乱数生成用メルセンヌ・ツイスタエンジン template <typename T> void operator++(vector<T> &v) { for (auto &x : v) ++x; } template <typename T> void operator--(vector<T> &v) { for (auto &x : v) --x; } template <typename T, typename S> void operator++(pair<T, S> &v) { ++v.first, ++v.second; } template <typename T, typename S> void operator--(pair<T, S> &v) { --v.first, --v.second; } int get1dcoodinate(int w, int i, int j) { return i * w + j; } template <typename T, typename S> istream &operator>>(istream &is, pair<T, S> &v) { is >> v.first >> v.second; return is; } template <typename T, typename S> ostream &operator<<(ostream &os, pair<T, S> &v) { os << v.first << wsp << v.second << rt; return os; } ostream &operator<<(ostream &os, modint &v) { os << v.val(); return os; } template <typename T> ostream &operator<<(ostream &os, const vector<T> &v) { if (v.size() == 0) return os; int n = (int)v.size() - 1; rep(i, n) os << v[i] << wsp; os << v[n] << rt; return os; } template <typename T> istream &operator>>(istream &is, vector<T> &v) { if (v.size() == 0) return is; int n = v.size(); rep(i, n) is >> v[i]; return is; } template <typename T> ostream &operator<<(ostream &os, const vector<vector<T>> &v) { if (v.size() == 0) return os; int n = (int)v.size(); rep(i, n) os << v[i]; return os; } template <typename T> istream &operator>>(istream &is, vector<vector<T>> &v) { if (v.size() == 0) return is; int n = v.size(); rep(i, n) is >> v[i]; return is; } template <typename T, typename S> istream &operator>>(istream &is, vector<pair<T, S>> &v) { if (v.size() == 0) return is; int n = v.size(); rep(i, n) is >> v[i].first >> v[i].second; return is; } template <typename T, typename S> ostream &operator<<(ostream &os, const vector<pair<T, S>> &v) { if (v.size() == 0) return os; int n = v.size(); rep(i, n) os << v[i].first << wsp << v[i].second << rt; return os; } template <class T> bool chmin(T &a, T b) { if (a > b) { a = b; return true; } return false; } template <class T> bool chmax(T &a, T b) { if (a < b) { a = b; return true; } return false; } template <typename T> void range_sort(vector<T> &arr, int l, int r) { sort(arr.begin() + l, arr.begin() + r); } template <typename T, typename S> void pairzip(const vector<pair<T, S>> &v, vector<T> &t, vector<T> &s) { int n = v.size(); rep(i, n) { t.push_back(v[i].first); s.push_back(v[i].second); } return; } template <typename T, typename S> bool myfind(T t, S s) { return find(t.cbegin(), t.cend(), s) != t.cend(); } bool check(int y, int x, int h, int w) { return 0 <= y && y < h && 0 <= x && x < w; } bool check(int y, int x, int h1, int h2, int w1, int w2) { return h1 <= y && y < h2 && w1 <= x && x < w2; } bool iskadomatsu(int a, int b, int c) { return (a != b && b != c && c != a) && ((a > b && b < c) || (a < b && b > c)); } template <typename T> bool iskadomatsu(vector<T> v) { T a = v[0], b = v[1], c = v[2]; return (a != b && b != c && c != a) && ((a > b && b < c) || (a < b && b > c)); } double euc_dist(PII a, PII b) { return sqrt(pow(a.first - b.first, 2) + pow(a.second - b.second, 2)); } // VS split(string s, char c) { // VS ret; // string part; // s += c; // rep(i, s.length()) { // if (s[i] == c) { // if (part != "") ret.emplace_back(part); // part = ""; // } else if (s[i] != c) { // part += s[i]; // } // } // return ret; // } VS split(string s, char c, char d = ' ') { VS ret; // reverse(allpt(s)); string part; s += c; rep(i, s.length()) { if (s[i] == c) { if (part != "") { // string t; // t += c; // ret.emplace_back(t); ret.emplace_back(part); } part = ""; } else { part += s[i]; } } return ret; } template <typename T, typename S, typename R> ll pow_mod(T p, S q, R _mod = 1ll) { ll ret = 1, r = p % _mod; while (q) { if (q % 2) ret *= r, ret %= _mod; r = (r * r) % _mod, q /= 2; } return ret % _mod; } template <typename T, typename S> ll pow_no_mod(T p, S q) { ll ret = 1, r = p; while (q) { if (q % 2) ret *= r; r = (r * r), q /= 2; } return ret; } pair<VL, VL> make_frac_tables(int n) { VL frac_list(n + 1, 1), frac_inv_list(n + 1, 1); rep(i, n) { frac_list[i + 1] *= frac_list[i] * (i + 1); frac_list[i + 1] %= mod; frac_inv_list[i + 1] *= frac_inv_list[i] * pow_mod(i + 1, mod - 2, mod); frac_inv_list[i + 1] %= mod; } return make_pair(frac_list, frac_inv_list); } ll perm(int a, int b, const VL &frac_list, const VL &frac_inv_list) { if (a < b) return 0; if (b < 0) return 0; ll ret = frac_list[a]; ret *= frac_inv_list[a - b]; ret %= mod; return ret; } ll comb(int a, int b, const VL &frac_list, const VL &frac_inv_list) { if (a < b) return 0; if (b < 0) return 0; ll ret = frac_list[a]; ret *= frac_inv_list[b]; ret %= mod; ret *= frac_inv_list[a - b]; ret %= mod; return ret; } struct vec2d { ll x; ll y; vec2d(ll _x, ll _y) { x = _x; y = _y; } ll dot(vec2d p) { return x * p.x + y * p.y; } vec2d diff(vec2d p) { return vec2d(x - p.x, y - p.y); } }; struct node { int parent = -1; ll weight = 0; int depth = 0; int degree = 0; int subtree = 0; int check = 0; int scc = -1; VPLL children; VI parent_list; VPLL connect; ll black_from_children; ll black_from_parent; node() { parent = -1; weight = 0; depth = 0; degree = 0; subtree = 0; check = 0; black_from_children = 1; black_from_parent = 1; } }; struct graph { int _n; int root = 0; vector<node> nodes; graph(int n) { _n = n; rep(i, _n) nodes.emplace_back(node()); } void getconnect_nocost() { ll a, b; cin >> a >> b; nodes[a].connect.emplace_back(b, 1); nodes[b].connect.emplace_back(a, 1); } void getconnect_cost() { ll a, b, c; cin >> a >> b >> c; nodes[a].connect.emplace_back(b, c); nodes[b].connect.emplace_back(a, c); } void getconnect_increment_nocost() { ll a, b; cin >> a >> b; a--, b--; nodes[a].connect.emplace_back(b, 1); nodes[b].connect.emplace_back(a, 1); } void getconnect_increment_cost() { ll a, b, c; cin >> a >> b >> c; a--, b--; nodes[a].connect.emplace_back(b, c); nodes[b].connect.emplace_back(a, c); } void showparent() { rep(i, _n - 1) cout << nodes[i].parent << wsp; cout << nodes[_n - 1].parent << rt; } void showweight() { rep(i, _n - 1) cout << nodes[i].weight << wsp; cout << nodes[_n - 1].weight << rt; } void showsubtree() { rep(i, _n - 1) cout << nodes[i].subtree << wsp; cout << nodes[_n - 1].subtree << rt; } void showdepth() { rep(i, _n - 1) cout << nodes[i].depth << wsp; cout << nodes[_n - 1].depth << rt; } // pair<VL, VI> djcstra(int s = 0) { // VL shortest(_n, inf); // VI prev(_n, -1); // shortest[s] = 0; // priority_queue<pair<ll, int>> pq; // pq.push(make_pair(0, s)); // while (!pq.empty()) { // auto [t, u] = pq.top(); // pq.pop(); // t = -t; // if (shortest[u] != t) continue; // for (auto [v, c] : nodes[u].connect) { // if (t + c < shortest[v]) { // shortest[v] = t + c; // prev[v] = u; // pq.push(make_pair(-(t + c), v)); // } // } // } // return make_pair(shortest, prev); // } pair<VL, VI> djcstra(int s = 0) { VL shortest(_n, inf); VI prev(_n, -1); shortest[s] = 0; priority_queue<pair<ll, int>> pq; pq.push(make_pair(0, s)); while (!pq.empty()) { auto [t, u] = pq.top(); pq.pop(); t = -t; if (shortest[u] != t) continue; for (auto [v, c] : nodes[u].connect) { if (t + c < shortest[v]) { shortest[v] = t + c; prev[v] = u; pq.push(make_pair(-(t + c), v)); } } } return make_pair(shortest, prev); } // pair<VL, VI> djcstra(VI s) { // VL shortest(_n, inf); // VI prev(_n, -1); // priority_queue<pair<ll, int>> pq; // for (auto x : s) { // shortest[x] = 0; // pq.push(make_pair(0, x)); // } // while (!pq.empty()) { // auto [t, u] = pq.top(); // pq.pop(); // t = -t; // if (shortest[u] != t) continue; // for (auto [v, c] : nodes[u].connect) { // if (t + c < shortest[v]) { // shortest[v] = t + c; // prev[v] = u; // pq.push(make_pair(-(t + c), v)); // } // } // } // return make_pair(shortest, prev); // } // VI djcstra(VI s, const VI x_list) { // VL shortest(_n, inf); // VI prev(_n, -1); // VI new_infection; // priority_queue<pair<ll, PII>> pq; // for (auto si : s) { // shortest[si] = 0; // pq.push(make_pair(0, make_pair(si, -x_list[si]))); // } // while (!pq.empty()) { // auto [t, p] = pq.top(); // auto [u, x] = p; // pq.pop(); // t = -t, x = -x; // if (shortest[u] != t) continue; // for (auto [v, d] : nodes[u].connect) { // if (t + d < shortest[v] && x >= d) { // shortest[v] = t + d; // prev[v] = u; // pq.push(make_pair(-(t + d), make_pair(v, -(x - d)))); // } // } // } // return new_infection; // } }; struct point { int x; int y; point() { x = 0; y = 0; } point(int _x, int _y) { x = _x; y = _y; } void pointinput() { int _x, _y; cin >> _x >> _y; x = _x; y = _y; } void pointinv() { swap(x, y); } }; istream &operator>>(istream &is, point &p) { is >> p.x >> p.y; return is; } ostream &operator<<(ostream &os, point &p) { os << p.x << wsp << p.y << rt; return os; } double pointseuc(point a, point b) { ll ax = a.x, bx = b.x, ay = a.y, by = b.y; return sqrt(pow(ax - bx, 2) + pow(ay - by, 2)); } ll pointseucsquare(point a, point b) { ll ax = a.x, bx = b.x, ay = a.y, by = b.y; return (ax - bx) * (ax - bx) + (ay - by) * (ay - by); } int pointsmanhattan(point a, point b) { return abs(a.x - b.x) + abs(a.y - b.y); } double dist_segment_point(TL3 segment, point p) { double a = get<0>(segment); double b = get<1>(segment); double c = get<2>(segment); return abs(a * p.x + b * p.y - c) / sqrt(a * a + b * b); } TL3 segment_parameter(point p, point q) { ll a, b, c; a = q.y - p.y; b = p.x - q.x; c = a * p.x + b * p.y; TL3 ret = (TL3){a, b, c}; // cout << a << b << c << rt; return ret; } int cross_check(TL3 segment, point p) { ll a = get<0>(segment); ll b = get<1>(segment); ll c = get<2>(segment); auto f = a * p.x + b * p.y - c; int ret; if (f > 0) ret = 1; if (f == 0) ret = 0; if (f < 0) ret = -1; return ret; } VI shave(int n) { VI v; if (n <= 1) return v; vector<bool> w(n + 1, true); int x; w[0] = w[1] = false; rep2(i, 2, n + 1) { if (w[i]) { x = i * 2; while (x <= n) { w[x] = false; x += i; } } } rep(i, n + 1) if (w[i]) v.emplace_back(i); return v; } bool iscross(point p1, point p2, point p3, point p4) { auto segment_1 = segment_parameter(p1, p2); auto segment_2 = segment_parameter(p3, p4); const double eps = 1e-6; bool ans{false}; if (cross_check(segment_1, p3) * cross_check(segment_1, p4) == 0 && cross_check(segment_2, p1) * cross_check(segment_2, p2) == 0) { auto xmin_1 = min(p1.x, p2.x) - eps; auto xmin_2 = min(p3.x, p4.x) - eps; auto xmax_1 = max(p1.x, p2.x) + eps; auto xmax_2 = max(p3.x, p4.x) + eps; auto ymin_1 = min(p1.y, p2.y) - eps; auto ymin_2 = min(p3.y, p4.y) - eps; auto ymax_1 = max(p1.y, p2.y) + eps; auto ymax_2 = max(p3.y, p4.y) + eps; if (xmin_1 <= p3.x && p3.x <= xmax_1 && ymin_1 <= p3.y && p3.y <= ymax_1) ans = true; if (xmin_1 <= p4.x && p4.x <= xmax_1 && ymin_1 <= p4.y && p4.y <= ymax_1) ans = true; if (xmin_2 <= p1.x && p1.x <= xmax_2 && ymin_2 <= p1.y && p1.y <= ymax_2) ans = true; if (xmin_2 <= p2.x && p2.x <= xmax_2 && ymin_2 <= p2.y && p2.y <= ymax_2) ans = true; } else if (cross_check(segment_1, p3) * cross_check(segment_1, p4) <= 0 && cross_check(segment_2, p1) * cross_check(segment_2, p2) <= 0) { ans = true; } return ans; } // int on_the_segment(point p, point q1, point q2) { // auto [a, b, c] = segment_parameter(q1, q2); // if (p.x < min(q1.x, q2.x) || max(q1.x, q2.x) < p.x) return 0; // if (p.y < min(q1.y, q2.y) || max(q1.y, q2.y) < p.y) return 0; // auto f = a * p.x + b * p.y - c; // return f == 0; // } void shave(vector<int> &v, int n) { if (n <= 1) return; vector<bool> w(n + 1, true); int x; w[0] = w[1] = false; rep2(i, 2, n + 1) { if (w[i]) { x = i * 2; while (x <= n) { w[x] = false; x += i; } } } rep(i, n + 1) if (w[i]) v.emplace_back(i); } template <typename T> void sort_and_unique(vector<T> &x) { sort(x.begin(), x.end()); x.erase(unique(x.begin(), x.end()), x.end()); } template <typename T> void coordinate_compress(vector<T> &x, map<T, int> &zip, int &xs) { sort_and_unique(x); xs = x.size(); for (int i = 0; i < xs; i++) zip[x[i]] = i; } template <typename T> pair<map<T, int>, int> coordinate_compress(vector<T> &x) { map<T, int> zip; sort_and_unique(x); int xs = x.size(); for (int i = 0; i < xs; i++) zip[x[i]] = i; return make_pair(zip, xs); } template <typename T> pair<map<T, int>, int> copy_coordinate_compress(vector<T> &x) { VI x_copy = x; auto [x_zip, xl] = coordinate_compress(x_copy); for (auto &v : x) v = x_zip[v]; return make_pair(x_zip, xl); } // ll getpalindrome(int l, int r, const string &s, VL &memo) { // if (r - l <= 1) return 1; // if (memo[l] != -1) return memo[l]; // ll ret{1}; // int n = (r - l) / 2; // string sl, sr; // rep(i, n) { // sl += s[l + i]; // sr += s[r - 1 - i]; // string rsr(i + 1, '0'); // reverse_copy(allpt_c(sr), rsr.begin()); // // cout << sl << wsp << sr << wsp << rsr << rt; // if (sl == rsr) { // ret += getpalindrome(l + i + 1, r - i - 1, s, memo); // ret %= mod; // } // } // memo[l] = ret; // return ret; // } // void getpalindrome(int l, int r, int n, const string &s, VVB &memo) { // if (r - l <= 1 || s[l] == s[r - 1]) { // memo[l][r] = true; // if (l > 0 && r < n) { // getpalindrome(l - 1, r + 1, n, s, memo); // } // } // return; // } class Unionfind { vector<int> p; vector<int> w; public: Unionfind(int n, int _w = 1) { for (int i = 0; i < n; i++) { p.emplace_back(i); w.emplace_back(_w); } } int find(int x) { while (p[x] != x) { p[x] = p[p[x]]; x = p[x]; } return x; } int getval(int x) { return p[x]; } int getweight(int x) { return w[find(x)]; } void setweight(int x, int _w) { w[find(x)] += _w; } void unite(int x, int y) { x = find(x); y = find(y); if (x != y) { p[x] = min(x, y); p[y] = min(x, y); w[min(x, y)] += w[max(x, y)]; w[max(x, y)] = 0; } } bool isunion(int x, int y) { return find(x) == find(y); } void showtree() { cout << p << w; } }; template <typename T> class RangeMinorMaxorSumQuery // 0-index { T const intmax = inf; T const intmin = 0; vector<T> sgt; int n; int k; public: RangeMinorMaxorSumQuery(int n1, T f) { int na = 1; int ka = 0; while (na < n1) { na *= 2; ka++; } for (int i = 0; i < 2 * na; i++) sgt.push_back(f); n = na; k = ka; } void update_min(int i, T x) { i += n; sgt[i] = x; while (i > 1) { i /= 2; sgt[i] = min(sgt[2 * i], sgt[2 * i + 1]); } } void update_max(int i, T x) { i += n; sgt[i] = x; while (i > 1) { i /= 2; sgt[i] = max(sgt[2 * i], sgt[2 * i + 1]); } } void update_sum(int i, T x) { i += n; sgt[i] = x; while (i > 1) { i /= 2; sgt[i] = sgt[2 * i] + sgt[2 * i + 1]; } } void update_gcd(int i, T x) { i += n; sgt[i] = x; while (i > 1) { i /= 2; sgt[i] = gcd(sgt[2 * i], sgt[2 * i + 1]); } } void add_sum(int i, T x) { i += n; sgt[i] += x; while (i > 1) { i /= 2; sgt[i] = sgt[2 * i] + sgt[2 * i + 1]; } } void add_min(int i, T x) { i += n; sgt[i] += x; while (i > 1) { i /= 2; sgt[i] = min(sgt[2 * i], sgt[2 * i + 1]); } } void add_max(int i, T x) { i += n; sgt[i] += x; while (i > 1) { i /= 2; sgt[i] = max(sgt[2 * i], sgt[2 * i + 1]); } } T get_min(int a, int b, int k = 1, int l = 0, int r = -1) // 閉区間 l <= x < r とする { if (r == -1) r = n; if (r <= a || b <= l) return inf; if (a == l && b == r) return sgt[k]; else return min(get_min(a, min(b, (l + r) / 2), 2 * k, l, (l + r) / 2), get_min(max(a, (l + r) / 2), b, 2 * k + 1, (l + r) / 2, r)); } T get_max(int a, int b, int k = 1, int l = 0, int r = -1) // 閉区間 l <= x < r とする { if (r == -1) r = n; if (r <= a || b <= l) return 0; if (a == l && b == r) return sgt[k]; else return max(get_max(a, min(b, (l + r) / 2), 2 * k, l, (l + r) / 2), get_max(max(a, (l + r) / 2), b, 2 * k + 1, (l + r) / 2, r)); } T get_sum(int a, int b, int k = 1, int l = 0, int r = -1) // 閉区間 l <= x < r とする { if (r == -1) r = n; if (r <= a || b <= l) return intmin; if (a == l && b == r) return sgt[k]; else return get_sum(a, min(b, (l + r) / 2), 2 * k, l, (l + r) / 2) + get_sum(max(a, (l + r) / 2), b, 2 * k + 1, (l + r) / 2, r); } T get_gcd(int a, int b, int k = 1, int l = 0, int r = -1) // 閉区間 l <= x < r とする { if (r == -1) r = n; if (r <= a || b <= l) return 0; if (a == l && b == r) return sgt[k]; else return gcd(get_gcd(a, min(b, (l + r) / 2), 2 * k, l, (l + r) / 2), get_gcd(max(a, (l + r) / 2), b, 2 * k + 1, (l + r) / 2, r)); } void update_xor(int i, T x) { i += n; sgt[i] = x; while (i > 1) { i /= 2; sgt[i] = sgt[2 * i] ^ sgt[2 * i + 1]; } } T get_xor(int a, int b, int k = 1, int l = 0, int r = -1) // 閉区間 l <= x < r とする { if (r == -1) r = n; if (r <= a || b <= l) return 0; if (a == l && b == r) return sgt[k]; else return get_xor(a, min(b, (l + r) / 2), 2 * k, l, (l + r) / 2) ^ get_xor(max(a, (l + r) / 2), b, 2 * k + 1, (l + r) / 2, r); } T operator[](int i) { return sgt[i + n]; } void printsegtree() { for (int i = 0; i < 2 * n; i++) { cout << sgt[i] << " "; } cout << endl; } }; template <typename T> class Bit_Index_Tree // 1-index { int n = 0; vector<T> v; public: void add(int i, T x) { while (i <= n) { v[i] += x; i += i & -i; } } Bit_Index_Tree(int _n, T x = 0) { n = _n; v.resize(n + 1); fill(allpt(v), x); } Bit_Index_Tree(vector<T> _v) { n = _v.size(); v.resize(n + 1); fill(allpt(v), 0); rep(i, n) add(i, v[i]); } T get_sum(int i) { T ret = 0; while (i > 0) { ret += v[i]; i -= i & -i; } return ret; } T get_range_sum(int l, int r) { // 半開区間 l <= x < r return get_sum(r) - get_sum(l); } }; // #define DEBUG VI smallest_prime_factors(int n) { VI ret(n + 1); iota(allpt(ret), 0); for (int i = 2; i * i <= n; i++) { if (ret[i] == i) { for (int j = i * i; j <= n; j += i) { if (ret[j] == j) ret[j] = i; } } } return ret; } // void dfs_1(graph &tree, int u) // { // cout << u << rt; // for (auto [v, _] : tree.nodes[u].connect) // if (v != tree.root && tree.nodes[v].parent == -1) // { // tree.nodes[v].parent = u; // dfs_1(tree, v); // tree.nodes[u].subtree += tree.nodes[v].subtree; // tree.nodes[u].children.emplace_back(PII(tree.nodes[v].subtree, // v)); // } // } // void dfs_2(graph &tree, int u, int d) // { // cout << u << wsp << d << rt; // sort(allpt_r(tree.nodes[u].children)); // rep(j, tree.nodes[u].children.size()) // { // auto [_, v] = tree.nodes[u].children[j]; // cout << (VI){u, (int)v, j}; // dfs_2(tree, v, j == 0 ? d : d + 1); // } // } template <typename T> class Matrix_n { int matsize; vector<vector<T>> mat; public: Matrix_n() { matsize = 0; vector<vector<T>> mat; } Matrix_n(int n) { matsize = n; mat.resize(n); rep(i, n) rep(j, n) mat[i].emplace_back(0); } Matrix_n(const vector<vector<T>> &inmat) { int n = inmat.size(); matsize = n; mat.resize(n); rep(i, n) { mat[i].resize(n); rep(j, n) { mat[i][j] = inmat[i][j]; } } } void identify() { rep(i, matsize) rep(j, matsize) { mat[i][j] = i == j ? 1 : 0; } } T getone(const int &i, const int &j) { return mat[i][j]; } int getsize() { return matsize; } const Matrix_n operator+(const Matrix_n &b) { Matrix_n ret(matsize); rep(i, matsize) rep(j, matsize) { ret.mat[i][j] = mat[i][j] + b.mat[i][j]; } return ret; } const Matrix_n operator-(const Matrix_n &b) { Matrix_n ret(matsize); rep(i, matsize) rep(j, matsize) { ret.mat[i][j] = mat[i][j] - b.mat[i][j]; } return ret; } const Matrix_n operator*(const Matrix_n &b) { Matrix_n ret(matsize); rep(i, matsize) rep(j, matsize) rep(k, matsize) { ret.mat[i][j] += mat[i][k] * b.mat[k][j]; ret.mat[i][j] %= mod; } return ret; } const Matrix_n operator%(const int &b) { Matrix_n ret(matsize); rep(i, matsize) rep(j, matsize) { ret.mat[i][j] = mat[i][j] % b; } return ret; } const Matrix_n operator+() { return *this; } const Matrix_n operator-() { Matrix_n ret(matsize); rep(i, matsize) rep(j, matsize) { ret.mat[i][j] = -mat[i][j]; } return ret; } Matrix_n &operator+=(const Matrix_n &b) { rep(i, matsize) rep(j, matsize) { mat[i][j] += b.mat[i][j]; } return *this; } Matrix_n &operator-=(const Matrix_n &b) { rep(i, matsize) rep(j, matsize) { mat[i][j] -= b.mat[i][j]; } return *this; } Matrix_n &operator%=(const int &b) { rep(i, matsize) rep(j, matsize) { mat[i][j] %= b; } return *this; } void showmat() { cout << mat; } }; template <typename T> Matrix_n<T> mat_pow_mod(Matrix_n<T> a, ll p, ll m = mod) { const int n = a.getsize(); Matrix_n<T> b(n); b.identify(); while (p > 0) { if (p % 2) { b = b * a; b %= m; } p /= 2; a = a * a; a %= m; } return b; } template <typename T> Matrix_n<T> mat_pow_no_mod(Matrix_n<T> a, ll p) { const int n = a.getsize(); Matrix_n<T> b(n); b.identify(); while (p > 0) { if (p % 2) { b = b * a; } p /= 2; a = a * a; } return b; } VL make_frac_k(int k, int l) { VL ret(l + 1, 1); rep(i, l) { ret[i + 1] = ret[i] * k; ret[i + 1] %= mod; } return ret; } template <typename T, typename S> void ans_print(T ans, T nodata, S printdata) { if (ans == nodata) { cout << printdata; } else { cout << ans; } cout << endl; } int mex(VI v) { sort_and_unique(v); int n = v.size(); rep(i, n) { if (v[i] != i) return i; } return n; } int main(int argc, char *argv[]) { // cin.tie(0); // ios::sync_with_stdio(false); // リアクティブ問題のときはコメントアウト int n, m, u, v, c; cin >> n >> m; const int a{n - 2}, b{n - 1}; graph normal_net(n), reverse_net(n); rep(_, m) { cin >> u >> v >> c; --u, --v; normal_net.nodes[u].connect.emplace_back(v, c); reverse_net.nodes[v].connect.emplace_back(u, c); } auto from_a = normal_net.djcstra(a).first; auto from_b = normal_net.djcstra(b).first; auto to_a = reverse_net.djcstra(a).first; auto to_b = reverse_net.djcstra(b).first; rep(i, n - 2) { auto ans = min(from_a[i] + to_a[b] + to_b[i], from_b[i] + to_b[a] + to_a[i]); cout << (ans >= inf ? -1 : ans) << rt; } return 0; }