// #include <bits/stdc++.h> #include <set> #include <map> #include <cmath> #include <deque> #include <queue> #include <vector> #include <iostream> #include <algorithm> #include <numeric> #include <chrono> using namespace std; 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() const int mod1 = 1e9 + 7, mod2 = 998244353, mod3 = 1e9 + 9; const int mod = mod1; const ll inf = 1e18; const int infint = 1e9; const string wsp = " "; const string tb = "\t"; const string rt = "\n"; const string alphabets = "abcdefghijklmnopqrstuvwxyz"; template <typename T> void show1dvec(const vector<T> &v) { if (v.size() == 0) return; int n = v.size() - 1; rep(i, n) cout << v[i] << wsp; cout << v[n] << rt; return; } 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> 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; } void show2dvec(const vector<string> &v) { int n = (int)v.size(); rep(i, n) cout << v[i] << rt; } template <typename T> void show2dvec(const vector<vector<T>> &v) { int n = v.size(); rep(i, n) show1dvec(v[i]); } 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 show1dpair(const vector<pair<T, S>> &v) { int n = v.size(); rep(i, n) cout << v[i].first << v[i].second << rt; return; } 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> void maxvec(vector<T> &v) { T s = v[0]; int n = v.size(); rep(i, n - 1) { if (s > v[i + 1]) { v[i + 1] = s; } s = v[i + 1]; } } 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; 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; } void make_frac_tables(VL &frac_list, VL &frac_inv_list) { rep(i, frac_list.size() - 1) { 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; } } 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 = -1; int subtree = 1; int check = 0; int scc = -1; VPLL children; VI parent_list; VPLL connect; ll visitfee; vector<TL3> max_cost_from_children; ll max_cost_from_parent; node() { parent = -1; weight = 0; depth = 0; degree = -1; subtree = 1; check = 0; children; parent_list; connect; max_cost_from_parent = 0; } }; 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; } }; 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 coordinate_compress(vector<T> &x, map<T, int> &zip, int &xs) { sort(x.begin(), x.end()); x.erase(unique(x.begin(), x.end()), x.end()); xs = x.size(); for (int i = 0; i < xs; i++) { zip[x[i]] = i; } } // 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; } // void djcstra(graph graphs, int s, int t) // { // const int n = graphs._n; // VL shortest(n, inf); // shortest[s] = 0; // priority_queue<pair<ll, int>> pq; // pq.push(make_pair(0, s)); // while (!pq.empty()) // { // auto [t, v] = pq.top(); // pq.pop(); // t = -t; // if (shortest[v] != t) // continue; // for (auto [u, c] : graphs.nodes[v].connect) // { // if (t + c < shortest[u]) // { // shortest[u] = t + c; // pq.push(make_pair(-(t + c), u)); // } // } // } // } class Unionfind { vector<int> p; public: Unionfind(int n) { for (int i = 0; i < n; i++) { p.push_back(i); } } 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]; } void unite(int x, int y) { x = find(x); y = find(y); if (x != y) { p[x] = y; } } bool isunion(int x, int y) { return find(x) == find(y); } void showtree() { cout << p; } }; template <typename T> class RangeMinorMaxorSumQuery // 0-index { T const intmax = infint; 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 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 0; 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 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: 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 = _v; } void add(int i, T x) { while (i <= n) { v[i] += x; i += i & -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; } class RangeSumQueryWithDelay // 0-index { ll const intmax = 2147483647; ll const intmin = 0; vector<ll> sgt; vector<ll> sgt_deray; int n; int k; public: RangeSumQueryWithDelay(int n1, int f = -1) { if (f == -1) f = intmax; else if (f == 0) f = intmin; int na = 1; int ka = 0; while (na < n1) { na *= 2; ka++; } for (int i = 0; i < 2 * na; i++) { sgt.push_back(f); sgt_deray.emplace_back(0); } n = na; k = ka; } void eval_add(int k, int l, int r) { if (sgt_deray[k] != 0) { sgt[k] += sgt_deray[k]; if (r - l > 1) { sgt_deray[2 * k] += sgt_deray[k] / 2; sgt_deray[2 * k + 1] += sgt_deray[k] / 2; } sgt_deray[k] = 0; } } void eval_update(int k, int l, int r) { if (sgt_deray[k] != intmax) { sgt[k] = sgt_deray[k]; if (r - l > 1) { sgt_deray[2 * k] = sgt_deray[k]; sgt_deray[2 * k + 1] = sgt_deray[k]; } sgt_deray[k] = intmax; } } void range_add(int a, int b, ll x, int k = 1, int l = 0, int r = -1) { if (r == -1) r = n; eval_add(k, l, r); //求める範囲とは違っても評価が行われることがある! if (r <= a || b <= l) return; if (a <= l && r <= b) { sgt_deray[k] += (r - l) * x; eval_add(k, l, r); } else { range_add(a, b, x, 2 * k, l, (l + r) / 2); range_add(a, b, x, 2 * k + 1, (l + r) / 2, r); sgt[k] = sgt[2 * k] + sgt[2 * k + 1]; } } void range_add_max(int a, int b, ll x, int k = 1, int l = 0, int r = -1) { if (r == -1) r = n; eval_update(k, l, r); //求める範囲とは違っても評価が行われることがある! if (r <= a || b <= l) return; if (a <= l && r <= b) { sgt_deray[k] += x; eval_update(k, l, r); } else { range_add_max(a, b, x, 2 * k, l, (l + r) / 2); range_add_max(a, b, x, 2 * k + 1, (l + r) / 2, r); sgt[k] = max(sgt[2 * k], sgt[2 * k + 1]); } } void range_update(int a, int b, ll x, int k = 1, int l = 0, int r = -1) { if (r == -1) r = n; eval_update(k, l, r); //求める範囲とは違っても評価が行われることがある! if (r <= a || b <= l) return; if (a <= l && r <= b) { sgt_deray[k] = x; eval_update(k, l, r); } else { range_update(a, b, x, 2 * k, l, (l + r) / 2); range_update(a, b, x, 2 * k + 1, (l + r) / 2, r); sgt[k] = sgt[2 * k] + sgt[2 * k + 1]; } } ll getsum(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; eval_add(k, l, r); if (a <= l && r <= b) { return (r - l) * sgt[k]; } else { auto v1 = getsum(a, b, 2 * k, l, (l + r) / 2); auto v2 = getsum(a, b, 2 * k + 1, (l + r) / 2, r); return v1 + v2; } } ll getmax(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; eval_update(k, l, r); if (a <= l && r <= b) { return sgt[k]; } else { auto v1 = getmax(a, b, 2 * k, l, (l + r) / 2); auto v2 = getmax(a, b, 2 * k + 1, (l + r) / 2, r); return max(v1, v2); } } ll 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; eval_update(k, l, r); if (a <= l && r <= b) { return sgt[k]; } else { auto v1 = get_min(a, b, 2 * k, l, (l + r) / 2); auto v2 = get_min(a, b, 2 * k + 1, (l + r) / 2, r); return min(v1, v2); } } void printsegtree() { for (int i = 0; i < 2 * n; i++) { cout << sgt[i] << " "; } cout << endl; for (int i = 0; i < 2 * n; i++) { cout << sgt_deray[i] << " "; } cout << endl; } }; // 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; } template <typename T> T mex(vector<T> v) { sort(allpt(v)); v.erase(unique(v.begin(), v.end()), v.end()); int ret = 0; for (auto x : v) { if (ret < x) return ret; ret++; } return ret; } // #define DEBUG int main() { 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 #ifdef DEBUG cout << "DEBUG MODE" << endl; // ifstream in("input.txt"); // for debug // cin.rdbuf(in.rdbuf()); // for debug chrono::system_clock::time_point timestart, timeend; // for debug timestart = std::chrono::system_clock::now(); // for debug #endif auto calc_func = [](ll x) { return (x * (x - 1) / 2) % mod; }; int n, a, b, c; cin >> n; vector<TI3> edges(n - 1); ll ans{0}; rep(i, n - 1) { cin >> a >> b >> c; --a, --b; edges[i] = make_tuple(a, b, c); } rep(i, 30) { auto p = 1ll << i; Unionfind uf(n); map<int, ll> uf_map; for (auto [a, b, c] : edges) { if (c & (1 << i)) uf.unite(a, b); } rep(j, n) uf_map[uf.find(j)]++; for (auto [_, v] : uf_map) { ans += p * calc_func(v); ans %= mod; } } cout << ans << rt; #ifdef DEBUG timeend = chrono::system_clock::now(); auto elapsed = chrono::duration_cast<chrono::milliseconds>(timeend - timestart) .count(); cout << "Time is " << elapsed << "ms" << std::endl; #endif return 0; }