B. Boboniu Walks on Graphtime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputBoboniu 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,\ldots,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\le c_i\le i) smallest weight among all edges outgoing from u.Now Boboniu asks you to calculate the number of tuples (c_1,c_2,\ldots,c_k) such that  1\le c_i\le i for all i (1\le i\le 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. InputThe first line contains three integers n, m and k (2\le n\le 2\cdot 10^5, 2\le m\le \min(2\cdot 10^5,n(n-1) ), 1\le k\le 9).Each of the next m lines contains three integers u, v and w (1\le u,v\le n,u\ne v,1\le w\le 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.OutputPrint one integer: the number of tuples.ExamplesInput
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
NoteFor 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.
4 6 3
4 2 1
1 2 2
2 4 3
4 1 4
4 3 5
3 1 6

2 
['brute force', 'dfs and similar', 'graphs', 'hashing', '*2300']