You are given a tree (an undirected connected acyclic graph) consisting of n vertices and n - 1 edges. A number is written on each edge, each number is either 0 (let's call such edges 0-edges) or 1 (those are 1-edges).

Let's call an ordered pair of vertices (x, y) (x ≠ y) valid if, while traversing the simple path from x to y, we never go through a 0-edge after going through a 1-edge. Your task is to calculate the number of valid pairs in the tree.

Input

The first line contains one integer n (2 ≤ n ≤ 200000) — the number of vertices in the tree.

Then n - 1 lines follow, each denoting an edge of the tree. Each edge is represented by three integers x_i, y_i and c_i (1 ≤ x_i, y_i ≤ n, 0 ≤ c_i ≤ 1, x_i ≠ y_i) — the vertices connected by this edge and the number written on it, respectively.

It is guaranteed that the given edges form a tree.

Output

Print one integer — the number of valid pairs of vertices.

Example

Input


7
2 1 1
3 2 0
4 2 1
5 2 0
6 7 1
7 2 1


Output


34

Note

The picture corresponding to the first example:

<image>
#include <bits/stdc++.h>
using namespace std;
struct DSU {
  vector<int> par;
  void kc(int n) { par.assign(n + 1, -1); }
  int root(int u) {
    if (par[u] < 0) return u;
    return par[u] = root(par[u]);
  }
  void dsu(int u, int v) {
    u = root(u);
    v = root(v);
    if (u == v) return;
    if (par[u] > par[v]) swap(u, v);
    par[u] += par[v];
    par[v] = u;
  }
};
DSU dset[2];
int n;
void gogo() {
  cin >> n;
  dset[0].kc(n);
  dset[1].kc(n);
  for (int i = 1; i < n; ++i) {
    int u, v, c;
    cin >> u >> v >> c;
    dset[c].dsu(u, v);
  }
  long long ans = 0;
  for (int i = 1; i <= n; ++i) {
    ans += (long long)(-dset[0].par[dset[0].root(i)] - 1);
    ans += (long long)(-dset[1].par[dset[1].root(i)] - 1);
    ans += (long long)(-dset[0].par[dset[0].root(i)] - 1) *
           (-dset[1].par[dset[1].root(i)] - 1);
  }
  cout << ans;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  if (fopen("sol"
            ".inp",
            "r")) {
    freopen(
        "sol"
        ".inp",
        "r", stdin);
    freopen(
        "sol"
        ".out",
        "w", stdout);
  }
  gogo();
  return 0;
}
