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.io.*;
import static java.lang.Math.*;
import java.math.BigInteger;
public class Main {
    static final long MOD = 1_000_000_007 , INF = 1_000_000_000_000_000L;
    static final int INf = 1_000_000_000;
    static FastReader reader;
    static PrintWriter writer;
    public static void main(String[] args) {
        Thread t = new Thread(null, new O(), "Integer.MAX_VALUE", 100000000);
        t.start();
    }
    static class O implements Runnable {
        public void run() {
            try {
                magic();
            }
            catch (Exception e) {
                e.printStackTrace();
                System.exit(1);
            }
        }
    }
    static class FastReader {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

        public FastReader() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public FastReader(String file_name) throws IOException {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public String readLine() throws IOException {
            byte[] buf = new byte[1000000];
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n') break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public int nextInt() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ') c = read();
            boolean neg = (c == '-');
            if (neg) c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg) return -ret;
            return ret;
        }

        public long nextLong() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ') c = read();
            boolean neg = (c == '-');
            if (neg) c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg) return -ret;
            return ret;
        }

        public double nextDouble() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ') c = read();
            boolean neg = (c == '-');
            if (neg) c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (c == '.') while ((c = read()) >= '0' && c <= '9') ret += (c - '0') / (div *= 10);
            if (neg) return -ret;
            return ret;
        }

        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1) buffer[0] = -1;
        }

        private byte read() throws IOException {
            if (bufferPointer == bytesRead) fillBuffer();
            return buffer[bufferPointer++];
        }

        public void close() throws IOException {
            if (din == null) return;
            din.close();
        }
    }
    static int n, dpInSubtree[][], dpOut[][];
    static ArrayList<Pair> adj[];
    static void magic() throws IOException {
        reader = new FastReader();
        writer = new PrintWriter(System.out, true);
        n = reader.nextInt();
        adj = new ArrayList[n+1];
        for(int i=1;i<=n;++i) {
            adj[i] = new ArrayList<>();
        }
        for(int i=1;i<n;++i) {
            int u = reader.nextInt(), v = reader.nextInt(), ty = reader.nextInt();
            adj[u].add(new Pair(v,ty));
            adj[v].add(new Pair(u, ty));
        }
        dpInSubtree = new int[n+1][2];
        dpOut = new int[n+1][2];
        dfs1(1,-1);
        dfs2(1,-1);
        long ans = 0;
        for(int i=1;i<=n;++i) {
            ans+=dpOut[i][0] + dpOut[i][1] + dpInSubtree[i][0] + dpInSubtree[i][1];
        }
        writer.println(ans);
    }
    static void dfs1(int x, int par) {
        for(Pair p : adj[x]) {
            if(p.x!=par) {
                dfs1(p.x, x);
                if(p.y==0) {
                    dpInSubtree[x][0] += dpInSubtree[p.x][0] + dpInSubtree[p.x][1]+1;
                }
                else {
                    dpInSubtree[x][1] += 1 + dpInSubtree[p.x][1];
                }
            }
        }
    }
    static void dfs2(int x, int par) {
        for(Pair p : adj[x]) {
            if(p.x==par) {
                if(p.y==0) {
                    dpOut[x][0] = 1 + dpOut[par][0] + dpOut[par][1] + dpInSubtree[par][0] + dpInSubtree[par][1] - dpInSubtree[x][0] - dpInSubtree[x][1] - 1;
                }
                else {
                    dpOut[x][1] = 1 + dpOut[par][1] + dpInSubtree[par][1] - dpInSubtree[x][1] - 1;
                }
            }
        }
        for(Pair p : adj[x]) {
            if(p.x!=par) {
                dfs2(p.x, x);
            }
        }
    }
    static class Pair implements Comparable<Pair>
    {
        int x,y;
        Pair(int x,int y)
        {
            this.x=x;
            this.y=y;
        }
        public int compareTo(Pair other)
        {
            if(this.x!=other.x)
                return this.x-other.x;
            return this.y-other.y;
        }
        public String toString()
        {
            return "("+x+","+y+")";
        }
    }
}