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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <iostream>
using namespace std;

int main() {
	// input
	int N, M;
	cin >> N >> M;

	bool A[300][300];
	
	for (int row = 0; row < N; row++) {
		for (int col = 0; col < M; col++) {
			int input;
			cin >> input;
			if (input == 1)A[row][col] = true;
			else A[row][col] = false;
		}
	}


	// calc
	int count = 0;
	


	for (int row = 0; row < N; row++) {
		for (int col = 0; col < M; col++) {



			//row,colを再左下とした部分集合を全探索
			for (int r = row; r >= 0; r--) {
				for (int c = col; c >= 0; c--) {

					bool flg = false;

					for (int rr = r; rr <= row; rr++) {
						for (int cc = c; cc <= col; cc++) {
							if(A[rr][cc]) flg = flg ^ A[rr][cc];
						}
					}

					if (flg) {
						count++;
						count %= 998244353;
					}


				}
			}


		}
	}




	cout << count;


	return 0;
}