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;
const int N = 2e5 + 10;
long long siz[2][N], par[2][N];
int get(int u, int w) {
  if (par[w][u] == u) return u;
  return par[w][u] = get(par[w][u], w);
}
void merge(int u, int v, int w) {
  int x = get(u, w);
  int y = get(v, w);
  if (siz[w][x] < siz[w][y]) {
    swap(x, y);
  }
  par[w][y] = x;
  siz[w][x] += siz[w][y];
}
void nikal_pehli_fursat_mai() {
  int n;
  cin >> n;
  for (int i = 1; i < n + 1; i++) {
    siz[0][i] = siz[1][i] = 1;
    par[0][i] = par[1][i] = i;
  }
  for (int i = 0; i < n - 1; i++) {
    int u, v, w;
    cin >> u >> v >> w;
    merge(u, v, w);
  }
  long long ans = 0;
  for (int i = 1; i < n + 1; i++) {
    if (par[0][i] == i) {
      ans += (siz[0][i] * siz[0][i] - siz[0][i]);
    }
    if (par[1][i] == i) {
      ans += (siz[1][i] * siz[1][i] - siz[1][i]);
    }
    ans += (siz[0][get(i, 0)] - 1) * (siz[1][get(i, 1)] - 1);
  }
  cout << ans << "\n";
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  int tc = 1;
  while (tc--) {
    nikal_pehli_fursat_mai();
  }
}
