Problem:
Score : 800 points

Problem Statement

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:

The sum of the |A||B| numbers contained in the intersection of the rows belonging to A and the columns belonging to B, is odd.

Constraints

1 \leq N,M \leq 300

0 \leq a_{i,j} \leq 1(1\leq i\leq N,1\leq j\leq M)

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M
a_{11} ... a_{1M}
:
a_{N1} ... a_{NM}

Output

Print the number of the pairs of a subset of the rows and a subset of the columns that satisfy the condition, modulo 998244353.

Sample Input 1

2 2
0 1
1 0

Sample Output 1

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.

Sample Input 2

2 3
0 0 0
0 1 0

Sample Output 2

8

Solution in Python (3.4.3) (judge verdict: Time Limit Exceeded)

import numpy as np
N, M = map(int, input().split())
aij = np.zeros((N,M),dtype=int)
for i in range(N):
  lst = list(map(int, input().split()))
  for j, aj in enumerate(lst):
    aij[i,j] = aj

total = 0
for i in range(N):
  for j in range(N+1):
    for k in range(M):
      for l in range(M+1):
        part = aij[i:j, k:l]
        if np.sum(part) % 2 != 0:
          total += np.sum(part)
print(total)