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.util.AbstractList;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.util.Comparator;
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;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskB solver = new TaskB();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskB {
        ArrayList<int[]>[] adj;
        Mask[][] nodes;
        boolean[] set;
        int tot = 0;

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int N = in.nextInt();
            int M = in.nextInt();
            int k = in.nextInt();
            adj = new ArrayList[N];
            for (int i = 0; i < N; i++) {
                adj[i] = new ArrayList<>();
            }
            for (int i = 0; i < M; i++) {
                int u = in.nextInt() - 1;
                int v = in.nextInt() - 1;
                int w = in.nextInt();
                adj[u].add(new int[]{v, w});
            }
            for (int i = 0; i < N; i++) {
                Collections.sort(adj[i], new Comparator<int[]>() {

                    public int compare(int[] ints, int[] t1) {
                        return Integer.compare(ints[1], t1[1]);
                    }
                });
            }
            nodes = new Mask[k][k];
            for (int i = 0; i < k; i++) {
                for (int j = 0; j <= i; j++) {
                    nodes[i][j] = new Mask();
                }
            }
            for (int i = 0; i < N; i++) {
                for (int e = 0; e < adj[i].size(); e++) {
                    nodes[adj[i].size() - 1][e].add(adj[i].get(e)[0]);
                }
            }
            for (int i = 0; i < k; i++) {
                for (int j = 0; j <= i; j++) {
                    nodes[i][j].ready();
                    for (int c = j - 1; c >= 0; c--) {
                        if (nodes[i][j].equals(nodes[i][c])) {
                            break;
                        }
                    }
                }
            }
            set = new boolean[N];
            dfs(0, 1);
            out.println(tot);
        }

        void dfs(int L, int cur) {
            if (L == nodes.length) {
                tot += cur;
                return;
            }
            for (int i = 0; i <= L; i++) {
                boolean flag = false;
                if (!nodes[L][i].done) {
                    int last = -1;
                    for (int e : nodes[L][i].s) {
                        if (set[e]) {
                            flag = true;
                            last = e;
                            break;
                        } else {
                            set[e] = true;
                        }
                    }
                    if (!flag) {
                        dfs(L + 1, cur * nodes[L][i].cnt);
                    }
                    for (int e : nodes[L][i].s) {
                        if (e == last) {
                            break;
                        }
                        set[e] = false;
                    }
                }
            }
        }

        class Mask {
            ArrayList<Integer> s = new ArrayList<>();
            int cnt = 1;
            boolean done = false;

            void add(int a) {
                s.add(a);
            }

            void ready() {
                Collections.sort(s);
                for (int i = 1; i < s.size(); i++) {
                    if (s.get(i) == s.get(i - 1)) {
                        done = true;
                    }
                }
            }

            boolean equals(Mask s) {
                if (!done && !s.done) {
                    done = s.s.equals(this.s);
                    if (done) {
                        s.cnt += cnt;
                    }
                    return done;
                }
                return false;
            }

        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

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

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

    }
}

