#include <bits/stdc++.h>
typedef long long ll;
#define FOR(i,a,b) for(int i=(a);i<(b);i++)
#define REP(i,a) FOR(i,0,a)
	
using namespace std;
const int MAX_N=300,MAX_M=300;
const  ll MOD=998244353;
int N,M;
typedef vector<int> vec;
typedef vector<vec> mat;
mat mt;
ll mpw(ll n,ll m){
	ll ret=1;
	while(m){
		if(m&1){
			ret*=n;
			ret%=MOD;
		}
		n*=n;
		n%=MOD;
		m>>=1;
	}
	return ret;
}
int main(){
	cin>>N>>M;
	mt.resize(N);
	REP(i,N){
		mt[i].resize(M);
	}
	REP(i,N){
		REP(j,M){
			cin>>mt[i][j];
		}
	}
	int c=0,i=0;
	while(i<N && c<M){
		int pvt=i;
		FOR(j,i+1,N){
			if(mt[j][c]>mt[pvt][c])pvt=j;
		}
		swap(mt[i],mt[pvt]);
		if(mt[i][c]==0){
			c++;
			continue;
		}
		FOR(j,i+1,N){
			if(mt[j][c]==1){
				FOR(k,c,M){
					mt[j][k]-=mt[i][k];
					mt[j][k]+=2;
					mt[j][k]%=2;
				}
			}
		}
		i++;
	}
	int r=-1;
	REP(i,N)REP(j,M){
		if(mt[i][j]==1)
			r=i;
	}
	r++;
	cout<<mpw(2,N-r)*(mpw(2,r)+MOD-1)%MOD*mpw(2,M-1)%MOD<<endl;
}
### Prompt

Create a solution in Cpp for the following problem:

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.

Examples

Input

2 2
0 1
1 0


Output

6


Input

2 3
0 0 0
0 1 0


Output

8

### Response

```cpp
#include <bits/stdc++.h>
typedef long long ll;
#define FOR(i,a,b) for(int i=(a);i<(b);i++)
#define REP(i,a) FOR(i,0,a)
	
using namespace std;
const int MAX_N=300,MAX_M=300;
const  ll MOD=998244353;
int N,M;
typedef vector<int> vec;
typedef vector<vec> mat;
mat mt;
ll mpw(ll n,ll m){
	ll ret=1;
	while(m){
		if(m&1){
			ret*=n;
			ret%=MOD;
		}
		n*=n;
		n%=MOD;
		m>>=1;
	}
	return ret;
}
int main(){
	cin>>N>>M;
	mt.resize(N);
	REP(i,N){
		mt[i].resize(M);
	}
	REP(i,N){
		REP(j,M){
			cin>>mt[i][j];
		}
	}
	int c=0,i=0;
	while(i<N && c<M){
		int pvt=i;
		FOR(j,i+1,N){
			if(mt[j][c]>mt[pvt][c])pvt=j;
		}
		swap(mt[i],mt[pvt]);
		if(mt[i][c]==0){
			c++;
			continue;
		}
		FOR(j,i+1,N){
			if(mt[j][c]==1){
				FOR(k,c,M){
					mt[j][k]-=mt[i][k];
					mt[j][k]+=2;
					mt[j][k]%=2;
				}
			}
		}
		i++;
	}
	int r=-1;
	REP(i,N)REP(j,M){
		if(mt[i][j]==1)
			r=i;
	}
	r++;
	cout<<mpw(2,N-r)*(mpw(2,r)+MOD-1)%MOD*mpw(2,M-1)%MOD<<endl;
}
```