Boboniu Walks on Graph

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.

For the third example, there's only one tuple: (1,2,2,2).

The out-degree of vertex u means the number of edges outgoing from u.

inputFormat

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.

outputFormat

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.

For the third example, there's only one tuple: (1,2,2,2).

The out-degree of vertex u means the number of edges outgoing from u.

样例

5 5 1
1 4 1
5 1 2
2 5 3
4 3 4
3 2 5

1

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