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.util.*;
import java.lang.*;
import java.math.*;
import java.io.*;
import static java.lang.Math.*;
public class Solution{ 
    static InputReader sc;
    static PrintWriter wc;
    static class Pair{
        int x,y;
        Pair(int x,int y){
            this.x=x;
            this.y=y;
        }
    }
    static long arr[][]; 
    static ArrayList<Pair> graph[];
    static long res=0;
    static void dfs(int node, int par){
        for(Pair p: graph[node]){
            if(p.x!=par){
                dfs(p.x,node);
                if(p.y==0){
                    arr[node][0]+=arr[p.x][0]+1;
                    arr[node][1]+=arr[p.x][1]+arr[p.x][3]+1;
                }
                else{
                    arr[node][2]+=arr[p.x][2]+arr[p.x][0]+1;
                    arr[node][3]+=arr[p.x][3]+1;
                }
            }
        }
        res+=arr[node][0]+arr[node][1]+arr[node][2]+arr[node][3];
        for(Pair p: graph[node]){
            if(p.x!=par){
                if(p.y==0){
                    res+=(arr[p.x][0]+1)*(arr[node][1]+arr[node][3]-arr[p.x][1]-arr[p.x][3]-1);
                }
                else{
                    res+=(arr[p.x][2]+arr[p.x][0]+1)*(arr[node][3]-arr[p.x][3]-1);
                }
            }
        }
    }
    public static void main(String[] args) {
        sc=new InputReader(System.in);
        wc=new PrintWriter(System.out);
        int n=sc.nextInt();
        graph=new ArrayList[n+1];
        arr=new long[n+1][4];
        int i,a,b,w;
        for(i=0;i<=n;i++){
            graph[i]=new ArrayList<Pair>();
        }
        for(i=0;i<n-1;i++){
            a=sc.nextInt();
            b=sc.nextInt();
            w=sc.nextInt();
            graph[a].add(new Pair(b,w));
            graph[b].add(new Pair(a,w));
        }
        dfs(1,-1);
        /*for(i=1;i<=n;i++){
            wc.println(arr[i][0]+" "+arr[i][1]+" "+arr[i][2]+" "+arr[i][3]);
        }*/
        wc.println(res);
        wc.close();
    }
    static class InputReader {
        
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;
        
        public InputReader(InputStream stream)
        {
            this.stream = stream;
        }
        
        public int read()
        {
            if (numChars==-1) 
                throw new InputMismatchException();
            
            if (curChar >= numChars)
            {
                curChar = 0;
                try 
                {
                    numChars = stream.read(buf);
                }
                catch (IOException e)
                {
                    throw new InputMismatchException();
                }
                
                if(numChars <= 0)               
                    return -1;
            }
            return buf[curChar++];
        }
     
        public String nextLine()
        {
            BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
        public int nextInt()
        {
            int c = read();
            
            while(isSpaceChar(c)) 
                c = read();
            
            int sgn = 1;
            
            if (c == '-') 
            {
                sgn = -1;
                c = read();
            }
            
            int res = 0;
            do 
            {
                if(c<'0'||c>'9') 
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c)); 
            
            return res * sgn;
        }
        
        public long nextLong() 
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') 
            {
                sgn = -1;
                c = read();
            }
            long res = 0;
            
            do 
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));
                return res * sgn;
        }
        
        public double nextDouble() 
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') 
            {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') 
            {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') 
            {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) 
                {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }
        
        public String readString() 
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do 
            {
                res.appendCodePoint(c);
                c = read();
            } 
            while (!isSpaceChar(c));
            
            return res.toString();
        }
     
        public boolean isSpaceChar(int c) 
        {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
     
        public String next() 
        {
            return readString();
        }
        
        public interface SpaceCharFilter 
        {
            public boolean isSpaceChar(int ch);
        }
    }   
}