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>
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.HashSet;
import java.util.Set;
import java.util.StringTokenizer;

public class OZTree {

    static BufferedReader input;
    static StringTokenizer stoken = new StringTokenizer("");
    static String nextString() throws IOException {
        while (!stoken.hasMoreTokens()){
            String st = input.readLine();
            stoken = new StringTokenizer(st);
        }
        return stoken.nextToken();
    }
    static int nextInt() throws Exception {
        return Integer.parseInt(nextString());
    }


    static int[] zeroParent;
    static int[] zeroSize;
    static int[] oneParent;
    static int[] oneSize;

    static int parent(int v, int[] p){
        if(p[v] == v) return v;
        return p[v] = parent(p[v], p);
    }

    static void union(int a, int b, int[] p, int[] s) {
        a = parent(a, p);
        b = parent(b, p);
        if(a!=b) {
            p[b] = a;
            s[a]+=s[b];
        }
    }

    public static void main(String[] args) throws Exception {
        input = new BufferedReader(
                new InputStreamReader(System.in)
        );
        int n = nextInt();
        zeroParent = new int[n]; zeroSize = new int[n];
        oneParent = new int[n]; oneSize = new int[n];
        for(int i = 0; i<n; ++i) {
            zeroParent[i] = oneParent[i] = i;
            zeroSize[i] = oneSize[i] = 1;
        }
        for(int i = 1; i<n; ++i) {
            int x = nextInt() - 1;
            int y = nextInt() - 1;
            int c = nextInt();
            union(x, y, c==0?zeroParent:oneParent, c==0?zeroSize:oneSize);
        }
        Set<Integer> usedZ = new HashSet<>();
        Set<Integer> usedO = new HashSet<>();
        long ans = 0;
        for(int i = 0; i<n; ++i) {
            int z = parent(i, zeroParent);
            int o = parent(i, oneParent);
            ans+=(zeroSize[z]-1)*1L*(oneSize[o]-1);
            if(!usedZ.contains(z)) {
                usedZ.add(z);
                ans+=zeroSize[z]*(zeroSize[z]-1L);
            }
            if(!usedO.contains(o)) {
                usedO.add(o);
                ans+=oneSize[o]*(oneSize[o]-1L);
            }
        }
        System.out.println(ans);
    }
}
