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;
long long gcd(long long a, long long b) {
  if (!b) return a;
  return gcd(b, a % b);
}
long long mod = 1e9 + 7;
long long pw(long long a, long long k) {
  if (k == 0) return 1;
  if (k % 2) {
    return (pw(a, k - 1) * a) % mod;
  }
  long long t = pw(a, k / 2);
  return (t * t) % mod;
}
string yy = "YES\n", nn = "NO\n";
string imp = "IMPOSSIBLE\n";
vector<vector<long long>> all;
vector<long long> cc;
long long k;
void gen() {
  if (cc.size() == k) {
    all.push_back(cc);
    return;
  }
  for (long long j = 0; j <= cc.size(); j++) {
    cc.push_back(j);
    gen();
    cc.pop_back();
  }
}
int32_t main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long n, m;
  cin >> n >> m >> k;
  vector<vector<pair<long long, long long>>> g(n);
  for (long long i = 0; i < m; i++) {
    long long a, b, c;
    cin >> a >> b >> c;
    a--;
    b--;
    g[a].push_back(make_pair(c, b));
  }
  for (long long i = 0; i < n; i++) {
    sort(g[i].begin(), g[i].end());
  }
  vector<vector<pair<long long, long long>>> fl(n);
  for (long long i = 0; i < n; i++) {
    long long sz = g[i].size();
    for (long long j = 0; j < sz; j++) {
      long long p = g[i][j].second;
      fl[p].push_back(make_pair(sz - 1, j));
    }
  }
  map<pair<long long, long long>, long long> ind;
  vector<pair<long long, long long>> name;
  long long cnt = 0;
  for (long long i = 0; i < k; i++) {
    for (long long j = 0; j <= i; j++) {
      ind[make_pair(i, j)] = cnt;
      name.push_back(make_pair(i, j));
      cnt++;
    }
  }
  const long long maxn = 2e5;
  vector<bitset<maxn>> bs(cnt);
  vector<vector<bool>> good(cnt, vector<bool>(cnt));
  vector<bool> ww(cnt);
  for (long long i = 0; i < n; i++) {
    vector<bool> w(cnt);
    for (auto to : fl[i]) {
      long long id = ind[to];
      if (w[id]) continue;
      if (bs[id][i]) {
        bs[id][i] = false;
        w[id] = true;
        ww[id] = true;
      } else {
        bs[id][i] = true;
      }
    }
  }
  for (long long i = 0; i < cnt; i++) {
    for (long long j = 0; j < cnt; j++) {
      bitset<maxn> b = bs[i];
      b &= bs[j];
      if (b.count()) good[i][j] = true;
    }
  }
  gen();
  long long ans = 0;
  for (auto el : all) {
    vector<long long> pos;
    for (long long i = 0; i < k; i++) {
      pos.push_back(ind[make_pair(i, el[i])]);
    }
    bool fl = true;
    for (long long i = 0; i < k; i++) {
      for (long long j = 0; j < k; j++) {
        if (i == j) continue;
        if (good[pos[i]][pos[j]]) fl = false;
      }
    }
    bitset<maxn> b;
    if (fl) {
      for (auto e : pos) {
        if (ww[e]) fl = false;
      }
    }
    if (fl) ans++;
  }
  cout << ans << '\n';
}
