#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #ifdef LOCAL # include "debug_print.hpp" # define debug(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__) #else # define debug(...) (static_cast(0)) #endif using namespace std; #define rep(i,n) for(int i=0; i<(n); i++) #define rrep(i,n) for(int i=(n)-1; i>=0; i--) #define FOR(i,a,b) for(int i=(a); i<(b); i++) #define RFOR(i,a,b) for(int i=(b-1); i>=(a); i--) #define ALL(v) v.begin(), v.end() #define RALL(v) v.rbegin(), v.rend() #define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() ); #define pb push_back using ll = long long; using D = double; using LD = long double; using P = pair; template using PQ = priority_queue>; template using minPQ = priority_queue, greater>; templatebool chmax(T &a, const T &b) { if (abool chmin(T &a, const T &b) { if (b ostream &operator<<(ostream &os, const pair &p) { os << p.first << " " << p.second; return os; } template istream &operator>>(istream &is, pair &p) { is >> p.first >> p.second; return is; } template ostream &operator<<(ostream &os, const vector &v) { int s = (int)v.size(); for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i]; return os; } template istream &operator>>(istream &is, vector &v) { for (auto &x : v) is >> x; return is; } void in() {} template void in(T &t, U &...u) { cin >> t; in(u...); } void out() { cout << "\n"; } template void out(const T &t, const U &...u) { cout << t; if (sizeof...(u)) cout << sep; out(u...); } void outr() {} template void outr(const T &t, const U &...u) { cout << t; outr(u...); } template struct Fp { long long val; constexpr Fp(long long v = 0) noexcept : val(v % mod) { if (val < 0) val += mod; } constexpr int getmod() { return mod; } constexpr Fp operator - () const noexcept { return val ? mod - val : 0; } constexpr Fp operator + (const Fp& r) const noexcept { return Fp(*this) += r; } constexpr Fp operator - (const Fp& r) const noexcept { return Fp(*this) -= r; } constexpr Fp operator * (const Fp& r) const noexcept { return Fp(*this) *= r; } constexpr Fp operator / (const Fp& r) const noexcept { return Fp(*this) /= r; } constexpr Fp& operator += (const Fp& r) noexcept { val += r.val; if (val >= mod) val -= mod; return *this; } constexpr Fp& operator -= (const Fp& r) noexcept { val -= r.val; if (val < 0) val += mod; return *this; } constexpr Fp& operator *= (const Fp& r) noexcept { val = val * r.val % mod; return *this; } constexpr Fp& operator /= (const Fp& r) noexcept { long long a = r.val, b = mod, u = 1, v = 0; while (b) { long long 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; } constexpr bool operator == (const Fp& r) const noexcept { return this->val == r.val; } constexpr bool operator != (const Fp& r) const noexcept { return this->val != r.val; } friend constexpr istream& operator >> (istream &is, const Fp& x) noexcept { int val; is >> val; x = Fp(val); return is; } friend constexpr ostream& operator << (ostream &os, const Fp& x) noexcept { return os << x.val; } friend constexpr Fp modpow(const Fp &a, long long n) noexcept { if (n == 0) return 1; auto t = modpow(a, n / 2); t = t * t; if (n & 1) t = t * a; return t; } }; const int mod = 1e9+7; // const int mod = 998244353; using mint = Fp; const int MAX_N = 200005; struct var { mint dp1, dp2; int sz; var(mint dp1 = 0, mint dp2 = 0, int sz = 0): dp1(dp1), dp2(dp2), sz(sz) {} var merge(const var &a, mint w) const { mint ndp1 = dp1 + a.dp1 + w*a.sz; mint ndp2 = dp2 + a.dp2 + a.dp1*w*2 + w*w*a.sz; int nsz = sz + a.sz; return {ndp1, ndp2, nsz}; } var addRoot() const { return {dp1, dp2, sz+1}; } }; vector

g[MAX_N]; vector dp[MAX_N]; var ans[MAX_N]; var dfs1(int v, int p = -1) { var dpsum; dp[v] = vector (g[v].size()); rep(i, g[v].size()) { int u = g[v][i].first; if(u == p) continue; mint w = g[v][i].second; dp[v][i] = dfs1(u, v); dpsum = dpsum.merge(dp[v][i], w); } return dpsum.addRoot(); } void dfs2(int v, const var& dpParent = var(), int p = -1) { int deg = g[v].size(); rep(i, deg) if(g[v][i].first == p) dp[v][i] = dpParent; vector dpSum_Left(deg+1), dpSum_Right(deg+1); rep(i,deg) { mint w = g[v][i].second; dpSum_Left[i+1] = dpSum_Left[i].merge(dp[v][i], w); } rrep(i, deg) { mint w = g[v][i].second; dpSum_Right[i] = dpSum_Right[i+1].merge(dp[v][i],w); } ans[v] = dpSum_Left[deg].addRoot(); rep(i,deg) { int u = g[v][i].first; if(u == p) continue; var d = dpSum_Left[i].merge(dpSum_Right[i+1],0); dfs2(u, d.addRoot(), v); } } int main(){ ios_base::sync_with_stdio(false); cin.tie(nullptr); int n; in(n); rep(i,n-1) { int a,b,c; in(a,b,c); a--; b--; g[a].pb({b,c}); g[b].pb({a,c}); } dfs1(0); dfs2(0); mint res = 0; rep(i,n) res += ans[i].dp2; res /= 2; out(res); }