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.util.ArrayList;
import java.io.UncheckedIOException;
import java.util.List;
import java.io.Closeable;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.Comparator;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) throws Exception {
        Thread thread = new Thread(null, new TaskAdapter(), "", 1 << 29);
        thread.start();
        thread.join();
    }

    static class TaskAdapter implements Runnable {
        @Override
        public void run() {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            FastInput in = new FastInput(inputStream);
            FastOutput out = new FastOutput(outputStream);
            BBoboniuWalksOnGraph solver = new BBoboniuWalksOnGraph();
            solver.solve(1, in, out);
            out.close();
        }
    }

    static class BBoboniuWalksOnGraph {
        boolean[] invalid;
        boolean[][] disallow;
        int[][] groups;

        public void solve(int testNumber, FastInput in, FastOutput out) {
            int n = in.readInt();
            int m = in.readInt();
            int k = in.readInt();
            Node[] nodes = new Node[n];
            Edge[] edges = new Edge[m];
            for (int i = 0; i < n; i++) {
                nodes[i] = new Node();
                nodes[i].id = i;
            }
            for (int i = 0; i < m; i++) {
                Edge e = new Edge();
                Node u = nodes[in.readInt() - 1];
                Node v = nodes[in.readInt() - 1];
                e.to = v;
                e.w = in.readInt();
                u.adj.add(e);
            }

            groups = new int[k + 1][];
            int order = 0;
            for (int i = 1; i <= k; i++) {
                groups[i] = new int[i];
                for (int j = 0; j < i; j++) {
                    groups[i][j] = order++;
                }
            }

            disallow = new boolean[order][order];
            invalid = new boolean[order];

            long[] added = new long[n];
            for (Node node : nodes) {
                node.adj.sort(Edge.sortByW);
                int size = node.adj.size();
                for (int j = 0; j < size; j++) {
                    int id = groups[size][j];
                    int to = node.adj.get(j).to.id;
                    if (Bits.get(added[to], id) == 1) {
                        invalid[id] = true;
                    }
                    added[to] = Bits.set(added[to], id);
                    for (int t = 0; t < order; t++) {
                        if (Bits.get(added[to], t) == 1) {
                            disallow[t][id] = disallow[id][t] = true;
                        }
                    }
                }
            }

            int ans = dfs(1, new int[k + 1]);
            out.println(ans);
        }

        public int dfs(int i, int[] picked) {
            if (i == groups.length) {
                return 1;
            }
            int ans = 0;
            for (int j = 0; j < i; j++) {
                int id = groups[i][j];
                if (invalid[id]) {
                    continue;
                }

                boolean allow = true;
                for (int k = 1; k < i; k++) {
                    if (disallow[picked[k]][id]) {
                        allow = false;
                        break;
                    }
                }
                if (allow) {
                    picked[i] = id;
                    ans += dfs(i + 1, picked);
                }
            }
            return ans;
        }

    }

    static class FastInput {
        private final InputStream is;
        private byte[] buf = new byte[1 << 13];
        private int bufLen;
        private int bufOffset;
        private int next;

        public FastInput(InputStream is) {
            this.is = is;
        }

        private int read() {
            while (bufLen == bufOffset) {
                bufOffset = 0;
                try {
                    bufLen = is.read(buf);
                } catch (IOException e) {
                    bufLen = -1;
                }
                if (bufLen == -1) {
                    return -1;
                }
            }
            return buf[bufOffset++];
        }

        public void skipBlank() {
            while (next >= 0 && next <= 32) {
                next = read();
            }
        }

        public int readInt() {
            int sign = 1;

            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+' ? 1 : -1;
                next = read();
            }

            int val = 0;
            if (sign == 1) {
                while (next >= '0' && next <= '9') {
                    val = val * 10 + next - '0';
                    next = read();
                }
            } else {
                while (next >= '0' && next <= '9') {
                    val = val * 10 - next + '0';
                    next = read();
                }
            }

            return val;
        }

    }

    static class Edge {
        Node to;
        int w;
        static Comparator<Edge> sortByW = (a, b) -> Integer.compare(a.w, b.w);

    }

    static class Bits {
        private Bits() {
        }

        public static int get(long x, int i) {
            return (int) ((x >>> i) & 1);
        }

        public static long set(long x, int i) {
            return x | (1L << i);
        }

    }

    static class FastOutput implements AutoCloseable, Closeable, Appendable {
        private StringBuilder cache = new StringBuilder(10 << 20);
        private final Writer os;

        public FastOutput append(CharSequence csq) {
            cache.append(csq);
            return this;
        }

        public FastOutput append(CharSequence csq, int start, int end) {
            cache.append(csq, start, end);
            return this;
        }

        public FastOutput(Writer os) {
            this.os = os;
        }

        public FastOutput(OutputStream os) {
            this(new OutputStreamWriter(os));
        }

        public FastOutput append(char c) {
            cache.append(c);
            return this;
        }

        public FastOutput append(int c) {
            cache.append(c);
            return this;
        }

        public FastOutput println(int c) {
            return append(c).println();
        }

        public FastOutput println() {
            cache.append(System.lineSeparator());
            return this;
        }

        public FastOutput flush() {
            try {
                os.append(cache);
                os.flush();
                cache.setLength(0);
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
            return this;
        }

        public void close() {
            flush();
            try {
                os.close();
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
        }

        public String toString() {
            return cache.toString();
        }

    }

    static class Node {
        List<Edge> adj = new ArrayList<>();
        int id;

    }
}

