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.
#include <bits/stdc++.h>
using namespace std;
int na[9][9] = {0};
long long ba[9][9] = {0};
long long ans = 0;
long long fun(long long x, long long y) { return x * (x + 1) / 2 + y; }
void fun2(int i, int k, long long store) {
  if (i >= k) {
    ans++;
    return;
  }
  for (int j = 0; j <= i; j++) {
    if (na[i][j] || ba[i][j] & store)
      continue;
    else {
      fun2(i + 1, k, store | (1LL << fun(i, j)));
    }
  }
}
int main() {
  int n, m, k;
  cin >> n >> m >> k;
  vector<pair<int, int>> out[n], in[n];
  for (int i = 0; i < m; i++) {
    int a, b, c;
    cin >> a >> b >> c;
    a--, b--;
    out[a].push_back({c, b});
  }
  for (int i = 0; i < n; i++) {
    sort(out[i].begin(), out[i].end());
    for (int j = 0; j < out[i].size(); j++) {
      int b = out[i][j].second;
      in[b].push_back({(int)out[i].size() - 1, j});
    }
  }
  for (int i = 0; i < n; i++) {
    sort(in[i].begin(), in[i].end());
    vector<pair<int, int>> p;
    long long store = 0;
    for (auto u : in[i]) {
      if (p.size() && p[p.size() - 1] == u)
        na[u.first][u.second] = 1;
      else {
        p.push_back(u);
      }
    }
    for (auto u : in[i]) {
      store |= (1LL << fun(u.first, u.second));
      ba[u.first][u.second] |= store;
    }
  }
  fun2(0, k, 0LL);
  cout << ans;
}
