Score : 800 points
There is a square grid with N rows and M columns. Each square contains an integer: 0 or 1. The square at the i-th row from the top and the j-th column from the left contains a_{ij}.
Among the 2^{N+M} possible pairs of a subset A of the rows and a subset B of the columns, find the number of the pairs that satisfy the following condition, modulo 998244353:
Input is given from Standard Input in the following format:
N M a_{11} ... a_{1M} : a_{N1} ... a_{NM}
Print the number of the pairs of a subset of the rows and a subset of the columns that satisfy the condition, modulo 998244353.
2 2 0 1 1 0
6
For example, if A consists of the first row and B consists of both columns, the sum of the numbers contained in the intersection is 0+1=1.
2 3 0 0 0 0 1 0
8