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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.List;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.util.Collections;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastScanner in = new FastScanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskB solver = new TaskB();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskB {
        int ans;
        boolean[][][][] forbidden;

        public void solve(int testNumber, FastScanner in, PrintWriter out) {
            int n = in.nextInt();
            int m = in.nextInt();
            int k = in.nextInt();
            List<Edge>[] edges = new List[n];
            List<Edge>[] edgesRev = new List[n];
            for (int i = 0; i < n; i++) {
                edges[i] = new ArrayList<>();
                edgesRev[i] = new ArrayList<>();
            }
            for (int i = 0; i < m; i++) {
                int a = in.nextInt() - 1;
                int b = in.nextInt() - 1;
                int c = in.nextInt() - 1;
                edges[a].add(new Edge(b, c));
                edgesRev[b].add(new Edge(a, -1));
            }
            for (int i = 0; i < n; i++) {
                Collections.sort(edges[i]);
                if (edges[i].size() == 0) {
                    throw new AssertionError();
                }
            }

            forbidden = new boolean[k][k][k][k];
            for (int i = 0; i < n; i++) {
                int[][] c = new int[k + 1][k];
                for (Edge r : edgesRev[i]) {
                    int j = r.dst;
                    int deg = edges[j].size();
                    for (int t = 0; t < deg; t++) {
                        if (edges[j].get(t).dst != i) {
                            continue;
                        }
                        ++c[deg][t];
                        if (c[deg][t] > 1) {
                            forbidden[deg - 1][t][deg - 1][t] = true;
                        }
                        break;
                    }
                }

                for (int deg0 = 1; deg0 <= k; deg0++) {
                    for (int pos0 = 0; pos0 < deg0; pos0++) {
                        if (c[deg0][pos0] == 0) {
                            continue;
                        }
                        for (int deg1 = deg0 + 1; deg1 <= k; deg1++) {
                            for (int pos1 = 0; pos1 < k; pos1++) {
                                if (c[deg1][pos1] == 0) {
                                    continue;
                                }
                                forbidden[deg0 - 1][pos0][deg1 - 1][pos1] = true;
                            }
                        }
                    }
                }
            }

            ans = 0;
            rec(0, k, new int[k]);
            out.println(ans);
        }

        private void rec(int pos, int k, int[] seq) {
            if (pos == k) {
                ++ans;
                return;
            }
            outer:
            for (int i = 0; i <= pos; i++) {
                if (forbidden[pos][i][pos][i]) {
                    continue;
                }
                for (int prevPos = 0; prevPos < pos; prevPos++) {
                    if (forbidden[prevPos][seq[prevPos]][pos][i]) {
                        continue outer;
                    }
                }
                seq[pos] = i;
                rec(pos + 1, k, seq);
            }
        }

        class Edge implements Comparable<Edge> {
            int dst;
            int weight;

            public Edge(int dst, int weight) {
                this.dst = dst;
                this.weight = weight;
            }

            public int compareTo(Edge o) {
                return weight - o.weight;
            }

        }

    }

    static class FastScanner {
        private BufferedReader in;
        private StringTokenizer st;

        public FastScanner(InputStream stream) {
            in = new BufferedReader(new InputStreamReader(stream));
        }

        public String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(in.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return st.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }
}

