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>
#include<cstdio>
#include<cstring>
#include<algorithm>
#define ll long long
#define mod 998244353
#define maxn 330
using namespace std;
inline int getint(){
    char c=getchar();int x=0;bool p=0;
    while((c>'9'||c<'0')&&c!='-')c=getchar();
    if(c=='-')p=1,c=getchar();
    while(c>='0'&&c<='9')x=x*10+c-'0',c=getchar();
    if(p)x=-x;return x;
}
inline int qpower(int x,int k){
	int ans=1;
	for(;k;k>>=1,x=1ll*x*x)if(k&1)ans=1ll*ans*x%mod;
	return ans;
}
int n,m,cnt,a[maxn][maxn],b[maxn][maxn];
int main(){
	memset(b,0,sizeof(b));
	n=getint(),m=getint();
	for(int i=1;i<=n;++i)
	for(int j=1;j<=m;++j)
	a[i][j]=getint();
	cnt=0;
	for(int i=1;i<=n;++i)
	for(int j=1;j<=m;++j)
	if(a[i][j]){
		if(!b[j][j]){
			++cnt;
			for(int k=j;k<=m;++k)b[j][k]=a[i][k];
			break;
		}
		else for(int k=j;k<=m;++k)a[i][k]^=b[j][k];
	}
	int ans=qpower(2,n)-qpower(2,n-cnt);
	if(ans<0)ans+=mod;
	ans=1ll*ans*qpower(2,m-1)%mod;
	cout<<ans<<endl;
	return 0;
}