write a go solution for Description:
Monocarp is playing a game "Assimilation IV". In this game he manages a great empire: builds cities and conquers new lands.

Monocarp's empire has n cities. In order to conquer new lands he plans to build one Monument in each city. The game is turn-based and, since Monocarp is still amateur, he builds exactly one Monument per turn.

Monocarp has m points on the map he'd like to control using the constructed Monuments. For each point he knows the distance between it and each city. Monuments work in the following way: when built in some city, a Monument controls all points at distance at most 1 to this city. Next turn, the Monument controls all points at distance at most 2, the turn after — at distance at most 3, and so on. Monocarp will build n Monuments in n turns and his empire will conquer all points that are controlled by at least one Monument.

Monocarp can't figure out any strategy, so during each turn he will choose a city for a Monument randomly among all remaining cities (cities without Monuments). Monocarp wants to know how many points (among m of them) he will conquer at the end of turn number n. Help him to calculate the expected number of conquered points!

Input Format:
The first line contains two integers n and m (1<=n<=20; 1<=m<=5*10^4) — the number of cities and the number of points.

Next n lines contains m integers each: the j-th integer of the i-th line d_i,j (1<=d_i,j<=n+1) is the distance between the i-th city and the j-th point.

Output Format:
It can be shown that the expected number of points Monocarp conquers at the end of the n-th turn can be represented as an irreducible fraction x/y. Print this fraction modulo 998,244,353, i. e. value x*y^-1bmod998244353 where y^-1 is such number that y*y^-1bmod998244353=1.

Note:
Let's look at all possible orders of cities Monuments will be build in:

- [1,2,3]:   the first city controls all points at distance at most 3, in other words, points 1 and 4;  the second city controls all points at distance at most 2, or points 1, 3 and 5;  the third city controls all points at distance at most 1, or point 1.  In total, 4 points are controlled.
- [1,3,2]: the first city controls points 1 and 4; the second city — points 1 and 3; the third city — point 1. In total, 3 points.
- [2,1,3]: the first city controls point 1; the second city — points 1, 3 and 5; the third city — point 1. In total, 3 points.
- [2,3,1]: the first city controls point 1; the second city — points 1, 3 and 5; the third city — point 1. In total, 3 points.
- [3,1,2]: the first city controls point 1; the second city — points 1 and 3; the third city — points 1 and 5. In total, 3 points.
- [3,2,1]: the first city controls point 1; the second city — points 1, 3 and 5; the third city — points 1 and 5. In total, 3 points.. Output only the code with no comments, explanation, or additional text.