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.