#include #include using namespace std; using namespace atcoder; using mint = modint1000000007; const int mod = 1000000007; //using mint = modint998244353; //const int mod = 998244353; //const int INF = 1e9; //const long long LINF = 1e18; //const bool debug = false; #define rep(i, n) for (int i = 0; i < (n); ++i) #define rep2(i,l,r)for(int i=(l);i<(r);++i) #define rrep(i, n) for (int i = (n-1); i >= 0; --i) #define rrep2(i,l,r)for(int i=(r-1);i>=(l);--i) #define all(x) (x).begin(),(x).end() #define allR(x) (x).rbegin(),(x).rend() #define endl "\n" #define P pair template inline bool chmax(A & a, const B & b) { if (a < b) { a = b; return true; } return false; } template inline bool chmin(A & a, const B & b) { if (a > b) { a = b; return true; } return false; } struct ReRooting { struct Edge { int to; mint cost; Edge(int _to, mint _cost) :to(_to), cost(_cost) {} }; struct Data { mint sump; mint sum; mint count; Data() :sump(0), sum(0), count(0) {} Data(mint _sump, mint _sum, mint _count) :sump(_sump), sum(_sum), count(_count) {} }; vector>g; vectordp; vectorans; int sz; ReRooting(int _sz) :sz(_sz) { g.resize(sz); dp.reserve(sz); ans.resize(sz); } void ReadGraph() { rep(i, sz - 1) { int a, b, c; cin >> a >> b >> c; a--; b--; g[a].push_back({ b,c }); g[b].push_back({ a,c }); } } Data merge(const Data &lh, const Data &rh, mint cost) { Data ret = lh; ret.sump += rh.sump + rh.sum * cost * 2 + cost * cost * (rh.count + 1); ret.sum += rh.sum + cost * (rh.count + 1); ret.count += rh.count + 1; return ret; } Data mergeSub(const Data &lh, const Data &rh) { Data ret = lh; ret.sump += rh.sump; ret.sum += rh.sum; ret.count += rh.count; return ret; } void dfs(int v, int p = -1) { Data val; for (auto e : g[v]) { if (p == e.to)continue; dfs(e.to, v); val = merge(val, dp[e.to], e.cost); } dp[v] = val; } void dfsR(int v, int p) { for (auto e : g[v]) ans[v] = merge(ans[v], dp[e.to], e.cost); vectorvdata; vectorvcost; for (auto e : g[v]) vdata.push_back(dp[e.to]), vcost.push_back(e.cost); int vsz = vdata.size(); vectorsumL(vsz + 1), sumR(vsz + 1); rep(i, vsz)sumL[i + 1] = merge(sumL[i], vdata[i], vcost[i]); rep(i, vsz)sumR[i + 1] = merge(sumR[i], vdata[vsz - i - 1], vcost[vsz - i - 1]); for (int i = 0; i < g[v].size(); ++i) { auto e = g[v][i]; if (p == e.to)continue; dp[v] = mergeSub(sumL[i], sumR[vsz - (i + 1)]); dfsR(e.to, v); } } void output() { mint out = 0; rep(i, sz)out += ans[i].sump; out *= inv_mod(2, mod); cout << out.val() << endl; } void solve() { ReadGraph(); dfs(0); dfsR(0, -1); output(); } }; int main() { ios::sync_with_stdio(false); cin.tie(nullptr); int n; cin >> n; ReRooting reroot(n); reroot.solve(); return 0; }