#include #include #include #include using namespace std; const int LIM = 800008, LIM2 = 20; const int MOD = 1000000007; class UnionFind { int N; int root[LIM], rank[LIM], size[LIM]; void init(int _N) { N = _N; for (int i = 0; i < N; i++) { root[i] = i; size[i] = 1; } } public: UnionFind(int _N) { init(_N); } int find(int i) { if (root[i] != i) { root[i] = find(root[i]); } return root[i]; } bool merge(int i, int j) { i = find(i); j = find(j); if (i == j) { return false; } if (rank[i] > rank[j]) { swap(i, j); } root[i] = j; size[j] += size[i]; if (rank[i] == rank[j]) { rank[j]++; } return true; } int get_size(int i) { return size[find(i)]; } }; int N, ans, tot; vector> adj[LIM]; int dynU[LIM][LIM2 + 2]; // dynU[i][j] = # of nodes reachable up from i (through edge to parent) via capacity >= j edges int dynD[LIM][LIM2 + 2]; // dynD[i][j] = # of nodes reachable down from i via capacity >= j edges // Populate dynD. void recD(int i, int p) { for (int j = 1; j <= LIM2; j++) { dynD[i][j] = 1; } for (auto e : adj[i]) { int b = e.first, c = e.second; if (b == p) { continue; } recD(b, i); for (int j = 1; j <= c; j++) { dynD[i][j] += dynD[b][j]; } } } // Populate dynU (and answer). void recU(int i, int p) { for (auto e : adj[i]) { int b = e.first, c = e.second; if (b == p) { continue; } for (int j = 1; j <= LIM2; j++) { if (j <= c) { dynU[b][j] = (dynU[i][j] + dynD[i][j] - dynD[b][j] + MOD) % MOD; } else { dynU[b][j] = 0; } } int totE = tot, prev = 0; for (int j = c; j > 0; j--) { int curr = (long long)dynD[b][j]*dynU[b][j] % MOD; int cnt = (curr - prev + MOD) % MOD; int s = (long long)cnt*j % MOD; totE = (totE - s + MOD) % MOD; prev = curr; } ans = (long long)ans*totE % MOD; recU(b, i); } } int solve() { for (int i = 0; i < LIM; i++) { adj[i].clear(); } // Input. cin >> N; vector>> E; for (int i = 0; i < N - 1; i++) { int a, b, c; cin >> a >> b >> c; a--; b--; adj[a].push_back(make_pair(b, c)); adj[b].push_back(make_pair(a, c)); E.push_back(make_pair(c, make_pair(a, b))); } // Compute initial capacity sum. tot = 0; UnionFind U(N); sort(E.begin(), E.end()); for (int i = (int)E.size() - 1; i >= 0; i--) { int a = E[i].second.first, b = E[i].second.second, c = E[i].first; tot = (tot + (long long)c*U.get_size(a)*U.get_size(b)) % MOD; U.merge(a, b); } // Compute reduced capacity sums via DP. ans = 1; recD(0, -1); recU(0, -1); return ans; } int main() { int T; cin >> T; for (int t = 1; t <= T; t++) { cout << "Case #" << t << ": " << solve() << endl; } return 0; }