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.OutputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.io.BufferedOutputStream;
import java.util.HashSet;
import java.io.UncheckedIOException;
import java.util.List;
import java.nio.charset.Charset;
import java.util.StringTokenizer;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.BufferedReader;
import java.util.Comparator;
import java.io.InputStream;

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

    static class BBoboniuWalksOnGraph {
        public void solve(int testNumber, LightScanner in, LightWriter out) {
            int n = in.ints(), m = in.ints(), k = in.ints();
            BBoboniuWalksOnGraph.Node[] nodes = new BBoboniuWalksOnGraph.Node[n];
            for (int i = 0; i < n; i++) nodes[i] = new BBoboniuWalksOnGraph.Node(i);
            for (int i = 0; i < m; i++) {
                int u = in.ints() - 1, v = in.ints() - 1, w = in.ints();
                nodes[u].nat.add(new BBoboniuWalksOnGraph.Edge(w, nodes[v]));
            }
            boolean[][][][] ng = new boolean[k][9][k][9];
            boolean[][] ng2 = new boolean[k][9];
            for (int i = 0; i < n; i++) {
                int s = nodes[i].nat.size();
                nodes[i].s = s;
                nodes[i].nat.sort(Comparator.comparing(e -> e.w));
                for (int j = 0; j < s; j++) {
                    BBoboniuWalksOnGraph.Node dest = nodes[i].nat.get(j).node;
                    BBoboniuWalksOnGraph.Constraint c = new BBoboniuWalksOnGraph.Constraint(s - 1, j);
                    if (dest.rev.contains(c)) {
                        ng2[c.x][c.y] = true;
                    } else dest.rev.add(c);
                }
            }
            List<BBoboniuWalksOnGraph.Constraint> constraints = new ArrayList<>();
            for (int i = 0; i < n; i++) {
                constraints.clear();
                constraints.addAll(nodes[i].rev);
                int s = constraints.size();
                for (int j = 0; j < s; j++) {
                    for (int l = 0; l < j; l++) {
                        BBoboniuWalksOnGraph.Constraint c1 = constraints.get(j);
                        BBoboniuWalksOnGraph.Constraint c2 = constraints.get(l);
                        ng[c1.x][c1.y][c2.x][c2.y] = true;
                        ng[c2.x][c2.y][c1.x][c1.y] = true;
                    }
                }
            }

            out.ans(dfs(new int[k], 0, k, ng, ng2)).ln();
        }

        private static int dfs(int[] pre, int n, int k, boolean[][][][] ng, boolean[][] ng2) {
            if (n == k) return 1;
            int res = 0;
            outer:
            for (int i = 0; i <= n; i++) {
                if (ng2[n][i]) continue;
                for (int j = 0; j < n; j++) {
                    if (ng[j][pre[j]][n][i]) continue outer;
                }
                pre[n] = i;
                res += dfs(pre, n + 1, k, ng, ng2);
            }
            return res;
        }

        private static class Node {
            int i;
            int s;
            List<BBoboniuWalksOnGraph.Edge> nat = new ArrayList<>();
            HashSet<BBoboniuWalksOnGraph.Constraint> rev = new HashSet<>();

            Node(int i) {
                this.i = i;
            }

        }

        private static class Edge {
            int w;
            int x;
            int y;
            BBoboniuWalksOnGraph.Node node;

            Edge(BBoboniuWalksOnGraph.Node to, int x, int y) {
                this.node = to;
                this.x = x;
                this.y = y;
            }

            Edge(int w, BBoboniuWalksOnGraph.Node to) {
                this.w = w;
                this.node = to;
            }

        }

        private static class Constraint {
            int x;
            int y;

            public Constraint(int x, int y) {
                this.x = x;
                this.y = y;
            }

            public boolean equals(Object o) {
                if (this == o) return true;
                if (o == null || getClass() != o.getClass()) return false;

                BBoboniuWalksOnGraph.Constraint that = (BBoboniuWalksOnGraph.Constraint) o;

                if (x != that.x) return false;
                return y == that.y;
            }

            public int hashCode() {
                int result = x;
                result = 31 * result + y;
                return result;
            }

        }

    }

    static class LightWriter implements AutoCloseable {
        private final Writer out;
        private boolean autoflush = false;
        private boolean breaked = true;

        public LightWriter(Writer out) {
            this.out = out;
        }

        public LightWriter(OutputStream out) {
            this(new OutputStreamWriter(new BufferedOutputStream(out), Charset.defaultCharset()));
        }

        public LightWriter print(char c) {
            try {
                out.write(c);
                breaked = false;
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
            return this;
        }

        public LightWriter print(String s) {
            try {
                out.write(s, 0, s.length());
                breaked = false;
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
            return this;
        }

        public LightWriter ans(String s) {
            if (!breaked) {
                print(' ');
            }
            return print(s);
        }

        public LightWriter ans(int i) {
            return ans(Integer.toString(i));
        }

        public LightWriter ln() {
            print(System.lineSeparator());
            breaked = true;
            if (autoflush) {
                try {
                    out.flush();
                } catch (IOException ex) {
                    throw new UncheckedIOException(ex);
                }
            }
            return this;
        }

        public void close() {
            try {
                out.close();
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
        }

    }

    static class LightScanner implements AutoCloseable {
        private BufferedReader reader = null;
        private StringTokenizer tokenizer = null;

        public LightScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
        }

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

        public int ints() {
            return Integer.parseInt(string());
        }

        public void close() {
            try {
                this.reader.close();
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
        }

    }
}

