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;
long long w, w1, a[300005], b[300005], c[300005], sz1[300005], sz[300005],
    p[300005], p1[300005], n, ans;
map<long long, long long> fix, fix1;
int get_col1(int a) {
  if (a == p1[a]) return a;
  p1[a] = get_col1(p1[a]);
  return p1[a];
}
void col1(int a, int b) {
  a = get_col1(a);
  b = get_col1(b);
  if (sz1[a] > sz1[b]) swap(a, b);
  sz1[b] += sz1[a];
  sz1[a] = 0;
  p1[a] = b;
}
int get_col(int a) {
  if (a == p[a]) return a;
  p[a] = get_col(p[a]);
  return p[a];
}
void col(int a, int b) {
  a = get_col(a);
  b = get_col(b);
  if (sz[a] > sz[b]) swap(a, b);
  sz[b] += sz[a];
  sz[a] = 0;
  p[a] = b;
}
int main() {
  cin >> n;
  for (int i = 1; i <= n; i++) {
    sz[i] = sz1[i] = 1;
    p[i] = i;
    p1[i] = i;
  }
  for (int i = 1; i <= n - 1; i++) {
    cin >> a[i] >> b[i] >> c[i];
  }
  for (int i = 1; i <= n - 1; i++) {
    if (c[i] == 1) {
      col1(a[i], b[i]);
    } else {
      col(a[i], b[i]);
    }
  }
  for (int i = 1; i <= n; i++) {
    w1 = get_col1(i);
    w = get_col(i);
    if (fix1[w1] == 0) {
      ans += sz1[w1] * (sz1[w1] - 1);
      fix1[w1] = 1;
    }
    if (fix[w] == 0) {
      ans += sz[w] * (sz[w] - 1);
      fix[w] = 1;
    }
    if (sz[w] >= 1 && sz1[w1] >= 1) {
      ans += (sz[w] - 1) * (sz1[w1] - 1);
    }
  }
  cout << ans << endl;
}
