write a go solution for Description:
Yura is a mathematician, and his cognition of the world is so absolute as if he have been solving formal problems a hundred of trillions of billions of years. This problem is just that!

Consider all non-negative integers from the interval [0,10^n). For convenience we complement all numbers with leading zeros in such way that each number from the given interval consists of exactly n decimal digits.

You are given a set of pairs (u_i,v_i), where u_i and v_i are distinct decimal digits from 0 to 9.

Consider a number x consisting of n digits. We will enumerate all digits from left to right and denote them as d_1,d_2,ldots,d_n. In one operation you can swap digits d_i and d_i+1 if and only if there is a pair (u_j,v_j) in the set such that at least one of the following conditions is satisfied:

1. d_i=u_j and d_i+1=v_j,
2. d_i=v_j and d_i+1=u_j.

We will call the numbers x and y, consisting of n digits, equivalent if the number x can be transformed into the number y using some number of operations described above. In particular, every number is considered equivalent to itself.

You are given an integer n and a set of m pairs of digits (u_i,v_i). You have to find the maximum integer k such that there exists a set of integers x_1,x_2,ldots,x_k (0<=x_i<10^n) such that for each 1<=i<j<=k the number x_i is not equivalent to the number x_j.

Input Format:
The first line contains an integer n (1<=n<=50,000) — the number of digits in considered numbers.

The second line contains an integer m (0<=m<=45) — the number of pairs of digits in the set.

Each of the following m lines contains two digits u_i and v_i, separated with a space (0<=u_i<v_i<=9).

It's guaranteed that all described pairs are pairwise distinct.

Output Format:
Print one integer — the maximum value k such that there exists a set of integers x_1,x_2,ldots,x_k (0<=x_i<10^n) such that for each 1<=i<j<=k the number x_i is not equivalent to the number x_j.

As the answer can be big enough, print the number k modulo 998,244,353.

Note:
In the first example we can construct a set that contains all integers from 0 to 9. It's easy to see that there are no two equivalent numbers in the set.

In the second example there exists a unique pair of equivalent numbers: 01 and 10. We can construct a set that contains all integers from 0 to 99 despite number 1.. Output only the code with no comments, explanation, or additional text.