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.*;

public class C {

	static ArrayList<Integer>[][] impacted;
	static int n, k, allHash, val[], set[][];
	static int MOD = 998244353;

	static int solve(int out, int hash) {
		if (out > k)
			return hash == allHash ? 1 : 0;
		int ans = 0;
		for (int choice = 1; choice <= out; choice++)
			ans += solve(out + 1, (hash + set[out][choice])%MOD);

		return ans;
	}

	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner();
		PrintWriter out = new PrintWriter(System.out);
		n = sc.nextInt();
		int m = sc.nextInt();
		k = sc.nextInt();
		ArrayList<int[]>[] adj = new ArrayList[n];
		for (int i = 0; i < n; i++)
			adj[i] = new ArrayList();
		val = new int[n];
		Random rand = new Random();
		for (int i = 0; i < n; i++) {
			val[i] = rand.nextInt(MOD);
			allHash=(allHash+val[i])%MOD;
		}
		impacted = new ArrayList[k + 1][k + 1];
		set=new int [k+1][k+1];
		for (int i = 0; i <= k; i++)
			for (int j = 0; j <= k; j++)
				impacted[i][j] = new ArrayList();
		int[] outDeg = new int[n];
		while (m-- > 0) {
			int u = sc.nextInt() - 1, v = sc.nextInt() - 1;
			int w = sc.nextInt();
			adj[u].add(new int[] { v, w });
			outDeg[u]++;
		}
		for (int i = 0; i < n; i++) {
			Collections.sort(adj[i], (x, y) -> x[1] - y[1]);
			ArrayList<Integer>[] curr = impacted[outDeg[i]];
			for (int j = 0; j < adj[i].size(); j++) {
				curr[j + 1].add(adj[i].get(j)[0]);
				set[outDeg[i]][j+1]+=val[adj[i].get(j)[0]];
				set[outDeg[i]][j+1]%=MOD;
			}
		}
		
		out.println(solve(1, 0));
		out.close();

	}

	static class Scanner {
		BufferedReader br;
		StringTokenizer st;

		Scanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		Scanner(String fileName) throws FileNotFoundException {
			br = new BufferedReader(new FileReader(fileName));
		}

		String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

		String nextLine() throws IOException {
			return br.readLine();
		}

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

		long nextLong() throws NumberFormatException, IOException {
			return Long.parseLong(next());
		}

		double nextDouble() throws NumberFormatException, IOException {
			return Double.parseDouble(next());
		}

		boolean ready() throws IOException {
			return br.ready();
		}

		int[] nxtArr(int n) throws IOException {
			int[] ans = new int[n];
			for (int i = 0; i < n; i++)
				ans[i] = nextInt();
			return ans;
		}

	}

	static void sort(int[] a) {
		shuffle(a);
		Arrays.sort(a);
	}

	static void shuffle(int[] a) {
		int n = a.length;
		Random rand = new Random();
		for (int i = 0; i < n; i++) {
			int tmpIdx = rand.nextInt(n);
			int tmp = a[i];
			a[i] = a[tmpIdx];
			a[tmpIdx] = tmp;
		}
	}

}