#include <bits/stdc++.h>
using namespace std;
using lli = long long int;
const int MOD = 1000000007;
const int MOD1 = 998244353;
const int maxn = 100010;
const int lim = (int)1e9;
int n, m, k, x, y, w, res = 0;
vector<pair<int, int> > v[2 * maxn];
vector<int> aux[10];
bitset<2 * maxn> bset[10][10];
bitset<2 * maxn> nset;
int vis[2 * maxn];
int pick[10];
bool poss[10][10];
bool good[10][10][10][10];
void dfs(int node) {
  if (node == k + 1) {
    ++res;
    return;
  }
  if ((int)aux[node].size() == 0) {
    dfs(node + 1);
    return;
  }
  auto check = [&](int x, int y) {
    pick[x] = y;
    for (int i = 1; i < x; ++i)
      if (!aux[i].empty()) {
        if (!good[i][pick[i]][x][y]) return false;
      }
    return true;
  };
  for (int i = 1; i <= node; ++i) {
    if (poss[node][i]) {
      if (check(node, i)) dfs(node + 1);
    }
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cin >> n >> m >> k;
  for (int i = 0; i < m; ++i) {
    cin >> x >> y >> w;
    v[x].emplace_back(w, y);
  }
  for (int i = 1; i <= n; ++i) {
    sort(v[i].begin(), v[i].end());
    aux[(int)v[i].size()].push_back(i);
  }
  for (int i = 1; i <= k; ++i)
    for (int j = 1; j <= i; ++j) {
      bool flag = true;
      for (auto &l : aux[i]) {
        int t = v[l][j - 1].second;
        if (vis[t]) {
          flag = false;
          break;
        } else {
          vis[t] = l;
          bset[i][j][t] = 1;
        }
      }
      if (flag) poss[i][j] = true;
      for (auto &l : aux[i]) {
        int t = v[l][j - 1].second;
        if (vis[t] == l)
          vis[t] = 0;
        else
          break;
      }
    }
  for (int i = 1; i <= k; ++i)
    for (int j = i + 1; j <= k; ++j)
      for (int g = 1; g <= i; ++g) {
        if (poss[i][g]) {
          for (int h = 1; h <= j; ++h) {
            if (poss[j][h]) {
              if ((bset[i][g] & bset[j][h]) == nset) {
                good[i][g][j][h] = true;
                good[j][h][i][g] = true;
              }
            }
          }
        }
      }
  int p = 1;
  for (int i = 1; i <= k; ++i)
    if ((int)aux[i].size() == 0) p *= i;
  dfs(1);
  cout << (p * res);
}

### Prompt

Your task is to create a CPP solution to 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>
using namespace std;
using lli = long long int;
const int MOD = 1000000007;
const int MOD1 = 998244353;
const int maxn = 100010;
const int lim = (int)1e9;
int n, m, k, x, y, w, res = 0;
vector<pair<int, int> > v[2 * maxn];
vector<int> aux[10];
bitset<2 * maxn> bset[10][10];
bitset<2 * maxn> nset;
int vis[2 * maxn];
int pick[10];
bool poss[10][10];
bool good[10][10][10][10];
void dfs(int node) {
  if (node == k + 1) {
    ++res;
    return;
  }
  if ((int)aux[node].size() == 0) {
    dfs(node + 1);
    return;
  }
  auto check = [&](int x, int y) {
    pick[x] = y;
    for (int i = 1; i < x; ++i)
      if (!aux[i].empty()) {
        if (!good[i][pick[i]][x][y]) return false;
      }
    return true;
  };
  for (int i = 1; i <= node; ++i) {
    if (poss[node][i]) {
      if (check(node, i)) dfs(node + 1);
    }
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cin >> n >> m >> k;
  for (int i = 0; i < m; ++i) {
    cin >> x >> y >> w;
    v[x].emplace_back(w, y);
  }
  for (int i = 1; i <= n; ++i) {
    sort(v[i].begin(), v[i].end());
    aux[(int)v[i].size()].push_back(i);
  }
  for (int i = 1; i <= k; ++i)
    for (int j = 1; j <= i; ++j) {
      bool flag = true;
      for (auto &l : aux[i]) {
        int t = v[l][j - 1].second;
        if (vis[t]) {
          flag = false;
          break;
        } else {
          vis[t] = l;
          bset[i][j][t] = 1;
        }
      }
      if (flag) poss[i][j] = true;
      for (auto &l : aux[i]) {
        int t = v[l][j - 1].second;
        if (vis[t] == l)
          vis[t] = 0;
        else
          break;
      }
    }
  for (int i = 1; i <= k; ++i)
    for (int j = i + 1; j <= k; ++j)
      for (int g = 1; g <= i; ++g) {
        if (poss[i][g]) {
          for (int h = 1; h <= j; ++h) {
            if (poss[j][h]) {
              if ((bset[i][g] & bset[j][h]) == nset) {
                good[i][g][j][h] = true;
                good[j][h][i][g] = true;
              }
            }
          }
        }
      }
  int p = 1;
  for (int i = 1; i <= k; ++i)
    if ((int)aux[i].size() == 0) p *= i;
  dfs(1);
  cout << (p * res);
}

```