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.
from sys import stdin, stdout
import random as r


def dfs(l, v_a, k, wk, rnd):

    if l > k:
        return 1 if wk == rnd else 0

    res = 0
    for i in range(1, l+1):
        res += dfs(l+1, v_a, k, wk + v_a[l][i], rnd)

    return res


def boboniu_walks_on_graph(n, m, k, e_a):
    MAX = 2 ** 31 - 1
    n_a = [0] * (n + 1)
    rnd = 0
    v_a = [[0 for _ in range(10)] for _ in range(10)]

    for i in range(1, n + 1):
        n_a[i] = r.randint(0, MAX)
        rnd += n_a[i]

    for i in range(1, n + 1):
        for j in range(1, len(e_a[i]) + 1):
            v_a[len(e_a[i])][j] += n_a[e_a[i][j-1]]

    return dfs(1, v_a, k, 0, rnd)


n, m, k = map(int, stdin.readline().split())
e_a = [[] for _ in range(n+1)]
for _ in range(m):
    u, v, w = map(int, stdin.readline().split())
    e_a[u].append(v)

ans = boboniu_walks_on_graph(n, m, k, e_a)
stdout.write(str(ans) + '\n')
