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.util.*;
import java.io.*;

public class B1394 {

	static HashSet<Integer>[][] pos;

	public static int compare(boolean[] a, boolean[] b) {
		for (int i = 0; i < a.length; i++) {
			if (a[i] != b[i]) {
				return a[i] ? 1 : -1;
			}
		}
		return 0;
	}

	static boolean[] on;
	static int ans = 0;

	static TreeMap<Arr, Integer> tm;

	public static void solve(int idx, int set, int lim, int mode) {
		if (idx == lim) {

			if (mode == 1) {
				tm.put(new Arr(on.clone()), tm.getOrDefault(new Arr(on), 0) + 1);
			} else if (mode == 2) {
				boolean[] g = new boolean[on.length];
				for (int i = 0; i < g.length; i++) {
					g[i] = !on[i];
				}
//				System.err.println(Arrays.toString(g));
				ans += tm.getOrDefault(new Arr(g), 0);
			} else {
				if (set == on.length)
					ans++;
			}

			return;
		}
		loop: for (int i = 1; i <= idx; i++) {
			HashSet<Integer> cur = pos[idx][i];
			if (cur == null)
				continue;
			for (int x : cur) {
				if (on[x]) {
					continue loop;
				}
			}
			for (int x : cur) {
				on[x] = true;
			}
			solve(idx + 1, set + cur.size(), lim, mode);
			for (int x : cur) {
				on[x] = false;
			}
		}
	}

	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		int n = sc.nextInt();
		int m = sc.nextInt();
		int k = sc.nextInt();

		on = new boolean[n];
		int[] eu = new int[m];
		int[] ev = new int[m];
		ArrayList<Integer>[] adjList = new ArrayList[n];
		for (int i = 0; i < adjList.length; i++) {
			adjList[i] = new ArrayList<Integer>();
		}
		for (int i = 0; i < m; i++) {
			int u = sc.nextInt() - 1;
			int v = sc.nextInt() - 1;
			int w = sc.nextInt() - 1;
			eu[w] = u;
			ev[w] = v;
		}
		for (int i = 0; i < m; i++) {
			adjList[eu[i]].add(ev[i]);
		}

		pos = new HashSet[k + 1][k + 1];
		for (int i = 1; i < pos.length; i++) {
			for (int j = 1; j <= i; j++) {
				pos[i][j] = new HashSet<Integer>();
			}
		}

		for (int i = 0; i < n; i++) {
			int size = adjList[i].size();

			for (int j = 0; j < size; j++) {
				int x = adjList[i].get(j);
				if (pos[size][j + 1] != null && pos[size][j + 1].contains(x))
					pos[size][j + 1] = null;
				if (pos[size][j + 1] != null)
					pos[size][j + 1].add(x);
			}
		}
		tm = new TreeMap<Arr, Integer>();
		if (k <= 6) {
			solve(1, 0, k + 1, 3);
		} else {
			solve(1, 0, 7, 1);
//			System.out.println(tm);
			on = new boolean[n];
			solve(7, 0, k + 1, 2);
		}
//		pw.println(Arrays.deepToString(pos));
		pw.println(ans);
		pw.close();

	}

	static class Arr implements Comparable<Arr> {
		boolean[] arr;

		public Arr(boolean[] arr) {
			this.arr = arr;
		}

		public String toString() {
			return Arrays.toString(arr);
		}

		public int compareTo(Arr a) {
			return compare(arr, a.arr);
		}
	}

	static class Scanner {
		BufferedReader br;
		StringTokenizer st;

		public Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}

		public Scanner(FileReader f) {
			br = new BufferedReader(f);
		}

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

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

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

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

		public int[] nextIntArr(int n) throws IOException {
			int[] arr = new int[n];
			for (int i = 0; i < n; i++) {
				arr[i] = Integer.parseInt(next());
			}
			return arr;
		}

	}

}
