Problem Statement

There are $N$ squares numbered $1$ to $N$. Initially, all squares are painted white.

Additionally, there are $M$ balls numbered $1$ to $M$ in a box.

We repeat the procedure below until all squares are painted black.

1. Pick up a ball from a box uniformly at random.
2. Let $x$ be the index of the ball. Paint Squares $L_x, L_x+1, \ldots, R_x$ black.
3. Return the ball to the box.

Find the expected value of the number of times the procedure is done, modulo $998244353$ (see Notes).

Note

It can be proved that the sought expected value is always a rational number. Additionally, under the Constraints of this problem, when that value is represented as $\frac{P}{Q}$ using two coprime integers $P$ and $Q$, it can be proved that there uniquely exists an integer $R$ such that $R \times Q \equiv P\pmod{998244353}$ and $0 \leq R \lt 998244353$. You should find this $R$.

Constraints

• $1 \leq N,M \leq 400$
• $1 \leq L_i \leq R_i \leq N$
• For every square $i$, there is an integer $j$ such that $L_j \leq i \leq R_j$.
• 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
\hspace{0.5cm}\vdots
L_M R_M

Output

Print the sought expected value modulo $998244353$.