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$, \max(p_{L_i},p_{L_i+1},\cdots,p_{R_i})=p_{x_i}$.

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.

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.

Sample Input 1

3 2
1 2
1 3

Sample Output 1

4

For example, for p=(2,1,3), we will have x=(1,3).
The four sequences that meet the requirement are x=(1,1),(1,3),(2,2),(2,3).

Sample Input 2

6 3
1 2
3 4
5 6

Sample Output 2

8

Sample Input 3

10 10
8 10
5 8
5 7
2 5
1 7
4 5
5 9
2 8
7 8
3 9

Sample Output 3

1060

见题面 Input 部分

见题面 Output 部分