Problem Statement

Given are an integer $N$ and $M$ pairs of integers. The $i$-th pair is $(L_i,R_i)$.

Find the number of integer sequences $x=(x_1,x_2,\cdots,x_M)$ that can be generated as follows, modulo $998244353$.

• Provide a permutation $p=(p_1,p_2,\cdots,p_N)$ of $(1,2,\cdots,N)$.
• For each $i$ ($1 \leq i \leq M$), let $x_i$ be the index of the largest element among $p_{L_i},p_{L_i+1},\cdots,p_{R_i}$. That is, $\max(p_{L_i},p_{L_i+1},\cdots,p_{R_i})=p_{x_i}$.

Constraints

• $2 \leq N \leq 300$
• $1 \leq M \leq N(N-1)/2$
• $1 \leq L_i < R_i \leq N$
• $(L_i,R_i) \neq (L_j,R_j)$ ($i \neq j$)
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M
L_1 R_1
L_2 R_2
\vdots
L_M R_M

Output

Print the answer.