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.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.StringTokenizer;

public class Solution {
    private static class Edge {
        int to, w;

        public Edge(int to, int w) {
            this.to = to;
            this.w = w;
        }
    }

    public static void main(String[] args) throws IOException {
        BufferedReader rd = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(rd.readLine());
        int n = Integer.parseInt(st.nextToken());
        int m = Integer.parseInt(st.nextToken());
        int k = Integer.parseInt(st.nextToken());
        ArrayList<Edge>[] G = new ArrayList[n];
        for (int i = 0; i < n; i++) {
            G[i] = new ArrayList<>();
        }
        for (int i = 0; i < m; i++) {
            st = new StringTokenizer(rd.readLine());
            int u = Integer.parseInt(st.nextToken()) - 1, v = Integer.parseInt(st.nextToken()) - 1;
            int w = Integer.parseInt(st.nextToken());
            G[u].add(new Edge(v, w));
        }
        if (k == 1) {
            int[] r = new int[n];
            for (int i = 0; i < n; i++) {
                int v = G[i].get(0).to;
                if (r[v] > 0) {
                    System.out.println(0);
                    return;
                }
                r[v]++;
            }
            System.out.println(1);
            return;
        }
        for (int i = 0; i < n; i++) {
            Collections.sort(G[i], (x, y) -> Integer.compare(x.w, y.w));
        }
        int[][][][] b = new int[10][10][10][10];
        ArrayList<Integer>[] groups = new ArrayList[k + 1];
        for (int i = 1; i <= k; i++) {
            groups[i] = new ArrayList<>();
        }
        for (int i = 0; i < n; i++) {
            int deg = G[i].size();
            groups[deg].add(i);
        }
        // SET[i][x] -> group i, ci = x: all nodes after moving from group i along nodes with ci=x.
        int[][][] sets = new int[10][10][n];
        for (int i = 1; i <= k; i++) {
            for (int x = 0; x < i; x++) {
                sets[i][x] = setFrom(i, x, G, groups);
            }
        }
        for (int i = 1; i <= k; i++) {
            for (int x = 0; x < i; x++) {
                for (int j = i + 1; j <= k; j++) {
                    for (int y = 0; y < j; y++) {
                        b[i][x][j][y] = isOk(i, x, j, y, G, sets) ? 1 : 0;
                    }
                }
            }
        }
        System.out.println(recursiveCount(new int[k + 1], 1, b, k));
    }

    private static int recursiveCount(int[] c, int pos, int[][][][] b, int k) {
        if (pos == k + 1) {
            for (int i = 1; i <= k; i++) {
                for (int j = i + 1; j <= k; j++) {
                    if (b[i][c[i]][j][c[j]] == 0) return 0;
                }
            }
            return 1;
        }
        int ans = 0;
        for (int i = 0; i < pos; i++) {
            c[pos] = i;
            ans += recursiveCount(c, pos + 1, b, k);
        }
        return ans;
    }

    // ci = x
    private static int[] setFrom(int i, int x, ArrayList<Edge>[] G, ArrayList<Integer>[] groups) {
        int[] res = new int[G.length];
        for (int nd : groups[i]) {
            res[G[nd].get(x).to]++;
            if (res[G[nd].get(x).to] > 1) return null;
        }
        return res;
    }

    // ci=x, cj=y.
    private static boolean isOk(int i, int x, int j, int y, ArrayList<Edge>[] G, int[][][] sets) {
        int[] s1 = sets[i][x], s2 = sets[j][y];
        if (s1 == null || s2 == null) return false;
        for (int t = 0; t < G.length; t++) {
            if (s1[t] > 0 && s2[t] > 0) {
                return false;
            }
        }
        return true;
    }
}
