#line 1 "main.cpp" #pragma region Macros #include using namespace std; template inline bool chmax(T &a, T b) { if(a < b) { a = b; return 1; } return 0; } template inline bool chmin(T &a, T b) { if(a > b) { a = b; return 1; } return 0; } #ifdef DEBUG template ostream &operator<<(ostream &os, const pair &p) { os << '(' << p.first << ',' << p.second << ')'; return os; } template ostream &operator<<(ostream &os, const vector &v) { os << '{'; for(int i = 0; i < (int)v.size(); i++) { if(i) { os << ','; } os << v[i]; } os << '}'; return os; } void debugg() { cerr << endl; } template void debugg(const T &x, const Args &... args) { cerr << " " << x; debugg(args...); } #define debug(...) \ cerr << __LINE__ << " [" << #__VA_ARGS__ << "]: ", debugg(__VA_ARGS__) #define dump(x) cerr << __LINE__ << " " << #x << " = " << (x) << endl #else #define debug(...) (void(0)) #define dump(x) (void(0)) #endif struct Setup { Setup() { cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } __Setup; using ll = long long; #define OVERLOAD3(_1, _2, _3, name, ...) name #define ALL(v) (v).begin(), (v).end() #define RALL(v) (v).rbegin(), (v).rend() #define REP1(i, n) for(int i = 0; i < (n); i++) #define REP2(i, a, b) for(int i = (a); i < int(b); i++) #define REP(...) OVERLOAD3(__VA_ARGS__, REP2, REP1)(__VA_ARGS__) #define UNIQUE(v) sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end()) const int INF = 1 << 30; const ll LLINF = 1LL << 60; constexpr int MOD = 1000000007; constexpr int MOD2 = 998244353; const int dx[4] = {1, 0, -1, 0}; const int dy[4] = {0, 1, 0, -1}; void Case(int i) { cout << "Case #" << i << ": "; } int popcount(int x) { return __builtin_popcount(x); } ll popcount(ll x) { return __builtin_popcountll(x); } #pragma endregion Macros #line 1 "/home/siro53/kyo-pro/compro_library/math/modint.hpp" template struct ModInt { int x; ModInt() : x(0) {} ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {} ModInt &operator+=(const ModInt &p) { if((x += p.x) >= mod) x -= mod; return *this; } ModInt &operator-=(const ModInt &p) { if((x += mod - p.x) >= mod) x -= mod; return *this; } ModInt &operator*=(const ModInt &p) { x = (int)(1LL * x * p.x % mod); return *this; } ModInt &operator/=(const ModInt &p) { *this *= p.inv(); return *this; } ModInt operator-() const { return ModInt(-x); } ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; } ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; } ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; } ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; } bool operator==(const ModInt &p) const { return x == p.x; } bool operator!=(const ModInt &p) const { return x != p.x; } ModInt inv() const { int a = x, b = mod, u = 1, v = 0, t; while(b > 0) { t = a / b; swap(a -= t * b, b); swap(u -= t * v, v); } return ModInt(u); } ModInt pow(int64_t n) const { ModInt ret(1), mul(x); while(n > 0) { if(n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } friend ostream &operator<<(ostream &os, const ModInt &p) { return os << p.x; } friend istream &operator>>(istream &is, ModInt &a) { int64_t t; is >> t; a = ModInt(t); return (is); } static int get_mod() { return mod; } }; #line 76 "main.cpp" using mint = ModInt; #line 1 "/home/siro53/kyo-pro/compro_library/graph/re_rooting.hpp" template class re_rooting { private: int N; vector> G; vector> dp; S dfs1(int u, int p) { S res = e(); for(int i = 0; i < (int)G[u].size(); i++) { if(G[u][i] == p) continue; int v = G[u][i]; dp[u][i] = dfs1(v, u); res = merge(res, op(dp[u][i], v)); } return op2(res, u); } void dfs2(int u, int p, S from_par) { int sz = (int)G[u].size(); for(int i = 0; i < sz; i++) { if(G[u][i] == p) { dp[u][i] = from_par; break; } } vector rsum(sz + 1); rsum[sz] = e(); for(int i = sz-1; i >= 0; i--) { rsum[i] = merge(rsum[i+1], op(dp[u][i], G[u][i])); } S lsum = e(); for(int i = 0; i < sz; i++) { int v = G[u][i]; if(v != p) { S val = merge(lsum, rsum[i+1]); dfs2(v, u, op2(val, u)); } lsum = merge(lsum, op(dp[u][i], v)); } } void build(int root) { for(int i = 0; i < N; i++) dp[i].resize(G[i].size()); dfs1(root, -1); dfs2(root, -1, e()); } public: re_rooting(int N): N(N), G(N), dp(N) {} re_rooting(const vector>& G): N(G.size()), G(G), dp(G.size()) {} void add_edge(int u, int v) { G[u].emplace_back(v); G[v].emplace_back(u); } vector solve(int root = 0) { build(root); vector ans(N); for(int u = 0; u < N; u++) { S res = e(); for(int i = 0; i < (int)G[u].size(); i++) { res = merge(res, op(dp[u][i], G[u][i])); } ans[u] = op2(res, u); } return ans; } }; template struct Edge { int from, to; T cost; Edge() = default; Edge(int from, int to, T cost): from(from), to(to), cost(cost) {} operator int() const { return to; } }; template), S (*merge)(S, S), S (*op2)(S, int), S (*e)()> class re_rooting_edge { private: int N; vector>> G; vector> dp; S dfs1(int u, int p) { S res = e(); for(int i = 0; i < (int)G[u].size(); i++) { int v = G[u][i]; if(v == p) continue; dp[u][i] = dfs1(v, u); res = merge(res, op(dp[u][i], G[u][i])); } return op2(res, u); } void dfs2(int u, int p, S from_par) { int sz = (int)G[u].size(); for(int i = 0; i < sz; i++) { if(G[u][i] == p) { dp[u][i] = from_par; break; } } vector rsum(sz + 1); rsum[sz] = e(); for(int i = sz-1; i >= 0; i--) { rsum[i] = merge(rsum[i+1], op(dp[u][i], G[u][i])); } S lsum = e(); for(int i = 0; i < sz; i++) { int v = G[u][i]; if(v != p) { S val = merge(lsum, rsum[i+1]); dfs2(v, u, op2(val, u)); } lsum = merge(lsum, op(dp[u][i], G[u][i])); } } void build(int root) { for(int i = 0; i < N; i++) dp[i].resize(G[i].size()); dfs1(root, -1); dfs2(root, -1, e()); } public: re_rooting_edge(int N): N(N), G(N), dp(N) {} re_rooting_edge(const vector>>& G): N(G.size()), G(G), dp(G.size()) {} void add_edge(int u, int v, Cost cost) { G[u].emplace_back(u, v, cost); G[v].emplace_back(v, u, cost); } vector solve(int root = 0) { build(root); vector ans(N); for(int u = 0; u < N; u++) { S res = e(); for(int i = 0; i < (int)G[u].size(); i++) { res = merge(res, op(dp[u][i], G[u][i])); } ans[u] = op2(res, u); } return ans; } }; #line 78 "main.cpp" using S = tuple; using Cost = mint; S op(S x, Edge e) { auto [s2, d, sz] = x; return S(d*2*e.cost + s2 + e.cost*e.cost*(sz+1), d+e.cost*(sz+1), sz+1); } S merge(S x, S y) { auto [s2x, dx, szx] = x; auto [s2y, dy, szy] = y; return S(s2x + s2y, dx + dy, szx + szy); } S op2(S x, int id) { return x; } S e() { return {0, 0, 0}; } int main() { int N; cin >> N; re_rooting_edge re(N); REP(i, N-1) { int u, v, w; cin >> u >> v >> w; u--; v--; re.add_edge(u, v, w); } auto dp = re.solve(); mint ans = 0; REP(i, N) ans += get<0>(dp[i]); ans /= 2; cout << ans << endl; }