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>
int root[2][200001];
long long weight[2][200001];
int mark[2][200001];
int getRoot(int a, int type) {
  int result = 0;
  result = root[type][a];
  while (result != root[type][result]) result = root[type][result];
  root[type][a] = result;
  return result;
}
void connect(int a, int b, int type) {
  int ra = getRoot(a, type);
  int rb = getRoot(b, type);
  if (weight[type][ra] >= weight[type][rb]) {
    root[type][rb] = ra;
    weight[type][ra] += weight[type][rb];
  } else {
    root[type][ra] = rb;
    weight[type][rb] += weight[type][ra];
  }
}
int main() {
  long long ans = 0;
  int n;
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) {
    for (int j = 0; j < 2; j++) {
      root[j][i] = i;
      weight[j][i] = 1;
    }
  }
  for (int i = 1; i < n; i++) {
    int from, to, type;
    scanf("%d%d%d", &from, &to, &type);
    connect(from, to, type);
  }
  for (int i = 1; i <= n; i++) {
    for (int type = 0; type < 2; type++) {
      if (!mark[type][getRoot(i, type)]) {
        int root = getRoot(i, type);
        mark[type][getRoot(i, type)] = 1;
        ans += weight[type][root] * (weight[type][root] - 1);
      }
    }
    ans += (weight[0][getRoot(i, 0)] - 1) * (weight[1][getRoot(i, 1)] - 1);
  }
  printf("%lld\n", ans);
}
