#include <bits/stdc++.h>
const long long HASHMAX = 5;
const int MAXN = 200005;
int numbers[MAXN];
long long hash[15][15][10];
long long tag_hash[15];
long long hash_tmp[15];
int select_index[15];
std::vector<long long> primes(HASHMAX);
long long MOD_MAX = 9999999999997;
int main(int argc, char* argv[]) {
  srand(time(0));
  for (auto i = 0; i < HASHMAX; i++) {
    primes[i] = rand() % 99997;
  }
  int t;
  long long n, m, k, z;
  scanf("%lld %lld %lld", &n, &m, &k);
  std::vector<std::vector<std::pair<long long, long long>>> out_edges(n + 5);
  long long u, v, w;
  for (auto i = 0; i < m; i++) {
    scanf("%lld %lld %lld", &u, &v, &w);
    out_edges[u].emplace_back(w, v);
  }
  for (auto i = 1; i <= n; i++) {
    sort(out_edges[i].begin(), out_edges[i].end());
    int degree = int(out_edges[i].size());
    for (long long j = 0; j < degree; j++) {
      for (long long ii = 0; ii < HASHMAX; ii++) {
        long long val = out_edges[i][j].second;
        hash[degree][j + 1][ii] += (val * (primes[ii] + val) +
                                    (val * val * (val + primes[ii])) % MOD_MAX);
      }
    }
  }
  for (long long j = 0; j < HASHMAX; j++)
    for (long long i = 1; i <= n; i++) {
      {
        tag_hash[j] +=
            (i * (primes[j] + i) + (i * i * (primes[j] + i)) % MOD_MAX);
      }
    }
  long long cnt_res = 0;
  for (auto i = 1; i <= k; i++) {
    select_index[i] = 1;
  }
  while (!select_index[k + 1]) {
    bool ok_tag = true;
    for (auto i = 0; i < HASHMAX; i++) {
      hash_tmp[i] = 0;
    }
    for (auto i = 1; i <= k; i++) {
      for (auto j = 0; j < HASHMAX; j++) {
        hash_tmp[j] += hash[i][select_index[i]][j];
      }
    }
    for (auto i = 0; i < HASHMAX; i++) {
      if (hash_tmp[i] != tag_hash[i]) {
        ok_tag = false;
        break;
      }
    }
    if (ok_tag) {
      cnt_res++;
    }
    select_index[1]++;
    int index_now = 1;
    while (select_index[index_now] > index_now) {
      select_index[index_now] = 1;
      select_index[index_now + 1]++;
      index_now++;
    }
  }
  printf("%lld\n", cnt_res);
  return 0;
}

### Prompt

In cpp, your task is to solve the following problem:

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.

### Response

```cpp
#include <bits/stdc++.h>
const long long HASHMAX = 5;
const int MAXN = 200005;
int numbers[MAXN];
long long hash[15][15][10];
long long tag_hash[15];
long long hash_tmp[15];
int select_index[15];
std::vector<long long> primes(HASHMAX);
long long MOD_MAX = 9999999999997;
int main(int argc, char* argv[]) {
  srand(time(0));
  for (auto i = 0; i < HASHMAX; i++) {
    primes[i] = rand() % 99997;
  }
  int t;
  long long n, m, k, z;
  scanf("%lld %lld %lld", &n, &m, &k);
  std::vector<std::vector<std::pair<long long, long long>>> out_edges(n + 5);
  long long u, v, w;
  for (auto i = 0; i < m; i++) {
    scanf("%lld %lld %lld", &u, &v, &w);
    out_edges[u].emplace_back(w, v);
  }
  for (auto i = 1; i <= n; i++) {
    sort(out_edges[i].begin(), out_edges[i].end());
    int degree = int(out_edges[i].size());
    for (long long j = 0; j < degree; j++) {
      for (long long ii = 0; ii < HASHMAX; ii++) {
        long long val = out_edges[i][j].second;
        hash[degree][j + 1][ii] += (val * (primes[ii] + val) +
                                    (val * val * (val + primes[ii])) % MOD_MAX);
      }
    }
  }
  for (long long j = 0; j < HASHMAX; j++)
    for (long long i = 1; i <= n; i++) {
      {
        tag_hash[j] +=
            (i * (primes[j] + i) + (i * i * (primes[j] + i)) % MOD_MAX);
      }
    }
  long long cnt_res = 0;
  for (auto i = 1; i <= k; i++) {
    select_index[i] = 1;
  }
  while (!select_index[k + 1]) {
    bool ok_tag = true;
    for (auto i = 0; i < HASHMAX; i++) {
      hash_tmp[i] = 0;
    }
    for (auto i = 1; i <= k; i++) {
      for (auto j = 0; j < HASHMAX; j++) {
        hash_tmp[j] += hash[i][select_index[i]][j];
      }
    }
    for (auto i = 0; i < HASHMAX; i++) {
      if (hash_tmp[i] != tag_hash[i]) {
        ok_tag = false;
        break;
      }
    }
    if (ok_tag) {
      cnt_res++;
    }
    select_index[1]++;
    int index_now = 1;
    while (select_index[index_now] > index_now) {
      select_index[index_now] = 1;
      select_index[index_now + 1]++;
      index_now++;
    }
  }
  printf("%lld\n", cnt_res);
  return 0;
}

```