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>
#pragma comment(linker, "/stack:512000000")
#pragma GCC optimize("Ofast")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,tune=native")
#pragma GCC optimize("unroll-loops")
using namespace std;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
mt19937_64 gen(time(nullptr));
struct custom_hash {
  static uint64_t splitmix64(uint64_t x) {
    x += 0x9e3779b97f4a7c15;
    x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
    x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
    return x ^ (x >> 31);
  }
  size_t operator()(uint64_t x) const {
    static const uint64_t FIXED_RANDOM =
        chrono::steady_clock::now().time_since_epoch().count();
    return splitmix64(x + FIXED_RANDOM);
  }
};
ll mod = 1e9 + 7;
namespace {
ll mul(ll a, ll b) {
  ll val = a * b - (ll)((ld)a * b / mod) * mod;
  if (val < 0) val += mod;
  if (val >= mod) val -= mod;
  return val;
}
ll poww(ll a, ll b) {
  ll val = 1;
  a %= mod;
  while (b > 0) {
    if (b % 2) val = mul(a, val);
    a = mul(a, a);
    b >>= 1;
  }
  return val % mod;
}
ll inv(ll a) { return poww(a, mod - 2); }
}  // namespace
ll const maxn = 3e5 + 5;
struct edge {
  ll to, w;
};
vector<edge> g[maxn], gg[maxn];
ll type[maxn];
vector<ll> rofl[maxn];
bool f[10][10][10][10];
ll k, ans = 0;
vector<ll> kek;
void dfs(ll i, ll j) {
  kek.push_back(j);
  if (i == k - 1) {
    bool good = true;
    for (ll ii = 0; ii < k; ii++) {
      if (!good) break;
      for (ll jj = ii; jj < k; jj++) {
        if (f[ii][kek[ii]][jj][kek[jj]]) {
          good = false;
          break;
        }
      }
    }
    if (good) {
      ans++;
    }
  } else {
    for (ll jj = 0; jj <= i + 1; jj++) {
      dfs(i + 1, jj);
    }
  }
  kek.pop_back();
}
void ggg() {
  cout << 0 << endl;
  exit(0);
}
signed main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  ll n, m;
  cin >> n >> m >> k;
  for (ll i = 0; i < m; i++) {
    ll u, v, w;
    cin >> u >> v >> w;
    g[u].push_back({v, w});
    rofl[u].push_back(w);
  }
  for (ll i = 1; i <= n; i++) {
    type[i] = (ll)g[i].size() - 1;
    for (auto& e : g[i]) {
      e = {e.to,
           lower_bound(rofl[i].begin(), rofl[i].end(), e.w) - begin(rofl[i])};
    }
    for (auto e : g[i]) {
      ll v = e.to;
      gg[v].push_back({i, e.w});
    }
  }
  for (ll v = 1; v <= n; v++) {
    for (auto& e : gg[v]) {
      e = {type[e.to], e.w};
    }
    set<pair<ll, ll>> st;
    for (auto e : gg[v]) {
      if (st.count({e.to, e.w})) {
        f[e.to][e.w][e.to][e.w] = 1;
      }
      st.insert({e.to, e.w});
    }
    vector<edge> tmp;
    for (auto e : st) {
      tmp.push_back({e.first, e.second});
    }
    gg[v] = tmp;
    for (ll i = 0; i < gg[v].size(); i++) {
      for (ll j = i + 1; j < gg[v].size(); j++) {
        f[gg[v][i].to][gg[v][i].w][gg[v][j].to][gg[v][j].w] = 1;
        f[gg[v][j].to][gg[v][j].w][gg[v][i].to][gg[v][i].w] = 1;
      }
    }
  }
  dfs(0, 0);
  cout << ans << endl;
  return 0;
}
