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.*;
import java.util.*;

/*
polyakoff
*/

public class Main {

    static FastReader in;
    static PrintWriter out;
    static Random rand = new Random();
    static final int oo = (int) 2e9;
    static final long OO = (long) 4e18;
    static final int MOD = (int) 1e9 + 7;
    static long P = 37;

    static int n, m, k, cnt = 0;
    static ArrayList<Pair>[] g;
    static long[][] hh;
    static long ideal;

    static class Pair {
        int v, w;

        Pair(int v, int w) {
            this.v = v;
            this.w = w;
        }
    }

    static long pow(long a, long b) {
        long res = 1;
        while (b > 0) {
            if ((b & 1) == 1)
                res = (res * a) % MOD;
            a = (a * a) % MOD;
            b >>= 1;
        }
        return res;
    }

    static long add(long a, long b) {
        return (a + b) % MOD;
    }

    static void go(int i, long h) {
        if (i > k) {
            if (h == ideal)
                cnt++;
            return;
        }
        for (int j = 0; j < i; j++)
            go(i + 1, add(h, hh[i][j]));
    }

    static void solve() {
        n = in.nextInt();
        m = in.nextInt();
        k = in.nextInt();

        g = new ArrayList[n]; Arrays.setAll(g, i -> new ArrayList<>());
        for (int i = 0; i < m; i++) {
            int u = in.nextInt() - 1;
            int v = in.nextInt() - 1;
            int w = in.nextInt();
            g[u].add(new Pair(v, w));
        }

        for (int i = 0; i < n; i++)
            Collections.sort(g[i], (o1, o2) -> o1.w - o2.w);

        hh = new long[k + 1][];
        for (int i = 1; i <= k; i++)
            hh[i] = new long[i];
        for (int i = 0; i < n; i++) {
            int sz = g[i].size();
            for (int j = 0; j < sz; j++)
                hh[sz][j] = add(hh[sz][j], pow(P, g[i].get(j).v));
        }

        for (int i = 0; i < n; i++)
            ideal = add(ideal, pow(P, i));

        go(1, 0);

        out.println(cnt);


    }

    public static void main(String[] args) throws FileNotFoundException {
        in = new FastReader(System.in);
//        in = new FastReader(new FileInputStream("sometext.txt"));
        out = new PrintWriter(System.out);
//        out = new PrintWriter(new FileOutputStream("output.txt"));

        int T = 1;
//        T = in.nextInt();
        while (T-- > 0)
            solve();

//        Thread thread = new Thread(null, () -> {
//            solve();
//        }, "Main", 1 << 28);
//        thread.start();
//        try {
//            thread.join();
//        } catch (InterruptedException e) {
//            e.printStackTrace();
//        }

//        out.flush();
        out.close();
    }

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        FastReader(InputStream is) {
            br = new BufferedReader(new InputStreamReader(is));
        }

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

        Long nextLong() {
            return Long.parseLong(next());
        }

        Double nextDouble() {
            return Double.parseDouble(next());
        }

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                st = new StringTokenizer(nextLine());
            }
            return st.nextToken();
        }

        String nextLine() {
            String s = "";
            try {
                s = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return s;
        }
    }

    static void dbg(Object... args) {
        for (Object arg : args)
            out.print(arg + " ");
        out.println();
    }

}