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: Runtime Error)

import numpy as np
MOD = 998244353
n, m = map(int, input().split())
a = np.array([list(map(int, input().split())) for _ in [0]*n])
#a[:, [0, 1]] = a[:, [1, 0]]
#print(a)
r = 0
for i in range(n):
	if a[i][i] != 1:
		for j in range(i+1, m):
			if a[i][j] == 1:
				a[:, [i, j]] = a[:, [j, i]]
				break
		else:
			for j in range(i+1, n):
				if a[j][i] == 1:
					a[[i, j]] = a[[j, i]]
				break
			else:
				break
	if a[i][i] == 0:
		continue

	r += 1
	for j in range(i+1, m):
		a[:, j] += a[i][j] * a[:, i]
		a[:, j] %= 2
	for j in range(i+1, n):
		a[j] += a[j][i] * a[i]
		a[j] %= 2
#print(r)
print((pow(2, n+m-1, MOD) - pow(2, n+m-r-1, MOD)) % MOD)