Problem Statement

You are given a simple undirected graph with $N$ vertices numbered $1$ to $N$ and $M$ edges numbered $1$ to $M$. Edge $i$ connects vertex $u_i$ and vertex $v_i$.

Find the number, modulo $998244353$, of ways to write an integer between $1$ and $K$, inclusive, on each vertex of this graph to satisfy the following condition:

• two vertices connected by an edge always have different numbers written on them.

Constraints

• $1 \leq N \leq 30$
• $0 \leq M \leq \min \left(30, \frac{N(N-1)}{2} \right)$
• $1 \leq K \leq 10^9$
• $1 \leq u_i \lt v_i \leq N$
• The given graph is simple.

Input

The input is given from Standard Input in the following format:

N M K
u_1 v_1
u_2 v_2
\vdots
u_M v_M

Output

Print the number, modulo $998244353$, of ways to write integers between $1$ and $K$, inclusive, on the vertices to satisfy the condition.