Problem Statement

Given is an undirected graph with $N$ vertices and $M$ edges. The $i$-th edge connects Vertices $A_i$ and $B_i$ and has a weight of $C_i$.

Initially, all vertices are painted black. You can do the following operation at most $K$ times.

• Operation: choose any vertex $v$ and any integer $x$. Paint red all vertices reachable from the vertex $v$ by traversing edges whose weights are at most $x$, including $v$ itself.

How many sets can be the set of vertices painted red after the operations?
Find the count modulo $998244353$.

Constraints

• $2 \\leq N \\leq 10^5$
• $0 \\leq M \\leq 10^5$
• $1 \\leq K \\leq 500$
• $1 \\leq A_i,B_i \\leq N$
• $1 \\leq C_i \\leq 10^9$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $M$ $K$ $A_1$ $B_1$ $C_1$ $\\vdots$ $A_M$ $B_M$ $C_M$

Output

Print the answer.

Sample Input 1

3 2 1
1 2 1
2 3 2

Sample Output 1

6

For example, an operation with $(v,x)=(2,1)$ paints Vertices $1,2$ red, and an operation with $(v,x)=(1,0)$ paints Vertex $1$.

After at most one operation, the set of vertices painted red can be one of the following six: $\\{\\},\\{1\\},\\{2\\},\\{3\\},\\{1,2\\},\\{1,2,3\\}$.

Sample Input 2

5 0 2

Sample Output 2

16

The given graph may not be connected.

Sample Input 3

6 8 2
1 2 1
2 3 2
3 4 3
4 5 1
5 6 2
6 1 3
1 2 10
1 1 100

Sample Output 3

40

The given graph may have multi-edges and self-loops.