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.
import sys
from collections import deque

input=sys.stdin.buffer.readline

n,m,k=map(int,input().split())
OUT=[[] for i in range(n)]
for i in range(m):
    u,v,w=map(int,input().split())
    OUT[u-1].append((w,v-1))

mod=10**9+7

for u in range(n):
    OUT[u].sort()

def _solve(b,mod=10**9+7):
    res=[[0 for j in range(10)] for i in range(10)]
    for u in range(n):
        L=len(OUT[u])
        for j in range(len(OUT[u])):
            res[L][j]+=pow(b,OUT[u][j][1],mod)
            res[L][j]%=mod
    ans=0
    for i in range(n):
        ans+=pow(b,i,mod)
        ans%=mod

    return res,ans


table1,ans1=_solve(1001)
table2,ans2=_solve(29388)

deq=deque([(1,0,0)])
while deq and deq[0][0]<k+1:
    p,cond1,cond2=deq.popleft()
    for i in range(p):
        tmp1=(cond1+table1[p][i])%mod
        tmp2=(cond2+table2[p][i])%mod
        deq.append((p+1,tmp1,tmp2))

deq=list(deq)
ans=0
for p,cond1,cond2 in deq:
    if (cond1,cond2)==(ans1,ans2):
        ans+=1

print(ans)
