Boboniu has a directed graph with n vertices and m edges.

The out-degree of each vertex is at most k.

Each edge has an integer weight between 1 and m. No two edges have equal weights.

Boboniu likes to walk on the graph with some specific rules, which is represented by a tuple (c_1,c_2,…,c_k). If he now stands on a vertex u with out-degree i, then he will go to the next vertex by the edge with the c_i-th (1≤ c_i≤ i) smallest weight among all edges outgoing from u.

Now Boboniu asks you to calculate the number of tuples (c_1,c_2,…,c_k) such that

  * 1≤ c_i≤ i for all i (1≤ i≤ k). 
  * Starting from any vertex u, it is possible to go back to u in finite time by walking on the graph under the described rules. 

Input

The first line contains three integers n, m and k (2≤ n≤ 2⋅ 10^5, 2≤ m≤ min(2⋅ 10^5,n(n-1) ), 1≤ k≤ 9).

Each of the next m lines contains three integers u, v and w (1≤ u,v≤ n,u≠ v,1≤ w≤ m), denoting an edge from u to v with weight w. It is guaranteed that there are no self-loops or multiple edges and each vertex has at least one edge starting from itself.

It is guaranteed that the out-degree of each vertex is at most k and no two edges have equal weight.

Output

Print one integer: the number of tuples.

Examples

Input


4 6 3
4 2 1
1 2 2
2 4 3
4 1 4
4 3 5
3 1 6


Output


2


Input


5 5 1
1 4 1
5 1 2
2 5 3
4 3 4
3 2 5


Output


1


Input


6 13 4
3 5 1
2 5 2
6 3 3
1 4 4
2 6 5
5 3 6
4 1 7
4 3 8
5 2 9
4 2 10
2 1 11
6 1 12
4 6 13


Output


1

Note

For the first example, there are two tuples: (1,1,3) and (1,2,3). The blue edges in the picture denote the c_i-th smallest edges for each vertex, which Boboniu chooses to go through.

<image>

For the third example, there's only one tuple: (1,2,2,2).

<image>

The out-degree of vertex u means the number of edges outgoing from u.
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

public class Task5 {
    ArrayList<int[]>[] adj;
    int[] targetNodeToNum;
    int mod;
    int targetSum;
    int n;
    int k;
    int[][] sumByOutdegreeAndK;

    public static void main(String[] args) throws IOException {
        new Task5().solve();
    }

    private void solve() throws IOException {
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);

        StringTokenizer tokenizer = new StringTokenizer(f.readLine());
        n = Integer.parseInt(tokenizer.nextToken());
        int m = Integer.parseInt(tokenizer.nextToken());
        k = Integer.parseInt(tokenizer.nextToken());

        adj = new ArrayList[n];
        for (int i = 0; i < n; i++) adj[i] = new ArrayList<int[]>();
        for (int i = 0; i < m; i++) {
            tokenizer = new StringTokenizer(f.readLine());
            int a = Integer.parseInt(tokenizer.nextToken()) - 1;
            int b = Integer.parseInt(tokenizer.nextToken()) - 1;
            int w = Integer.parseInt(tokenizer.nextToken());
            int[] ar1 = {b, w};
            adj[a].add(ar1);
        }

        for (int i = 0; i < n; i++) Collections.sort(adj[i], new ArrayComparator());

        mod = 1000000007;
        targetNodeToNum = new int[n];
        Random r = new Random();
        for (int i = 0; i < n; i++) targetNodeToNum[i] = r.nextInt(1000000000);
        for (int i = 0; i < n; i++) {
            targetSum += targetNodeToNum[i];
            targetSum %= mod;
        }

        sumByOutdegreeAndK = new int[k + 1][k];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < adj[i].size(); j++) {
                sumByOutdegreeAndK[adj[i].size()][j] += targetNodeToNum[adj[i].get(j)[0]];
                sumByOutdegreeAndK[adj[i].size()][j] %= mod;
            }
        }

        out.println(numberOfTuples(0, 0));

        out.close();
    }

    private static class ArrayComparator implements Comparator<int[]> {
        @Override
        public int compare(int[] o1, int[] o2) {
            return Integer.compare(o1[1], o2[1]);
        }
    }

    private int numberOfTuples(int index, int currSum) {
        if (index == k) {
            if (currSum == targetSum) {
                return 1;
            }
            return 0;
        }

        int res = 0;
        for (int i = 0; i <= index; i++) {
            res += numberOfTuples(index + 1, (currSum + sumByOutdegreeAndK[index + 1][i]) % mod);
        }

        return res;
    }
}
