#include<bits/stdc++.h>
#define ll long long
#define inf 1000000000
#define infll 1000000000000000000ll
#define vi vector<int>
#define vll vector<ll>
#define pb push_back
#define pii pair<int,int>
#define pll pair<ll,ll>
#define pdd pair<double,double>
#define mpr make_pair
#define fi first
#define se second
#define pq priority_queue<int>
#define pqll priority_queue<ll>
#define up(x,y) (x<(y)?x=(y):0)
#define dn(x,y) (x>(y)?x=(y):0)
#define ad(x,y) (x=(x+(y))%mod)
#define mod 998244353
#define N 309
using namespace std;

int m,n,b[N]; bitset<N> a[N];
int read(){
	int x=0; char ch=getchar(); bool flag=0;
	while (ch<'0' || ch>'9'){ if (ch=='-') flag=1; ch=getchar(); }
	while (ch>='0' && ch<='9'){ x=x*10+ch-'0'; ch=getchar(); }
	return flag?-x:x;
}
ll readll(){
	ll x=0; char ch=getchar(); bool flag=0;
	while (ch<'0' || ch>'9'){ if (ch=='-') flag=1; ch=getchar(); }
	while (ch>='0' && ch<='9'){ x=x*10+ch-'0'; ch=getchar(); }
	return flag?-x:x;
}
int ksm(int x,int y){
	int ans=1;
	for (; y; y>>=1,x=(ll)x*x%mod) if (y&1) ans=(ll)ans*x%mod;
	return ans;
}
int main(){
	scanf("%d%d",&m,&n);
	int i,j,cnt=0;
	for (i=1; i<=m; i++)
		for (j=0; j<n; j++) a[i][j]=(read()>0);
	for (i=1; i<=m; i++){
		for (j=0; j<n; j++) if (a[i][j])
			if (b[j]) a[i]^=a[b[j]]; else{
				b[j]=i; cnt++; break;
			}
	}
	int t=(ksm(2,m)-ksm(2,m-cnt)+mod)%mod;
	printf("%lld\n",(ll)t*ksm(2,n-1)%mod);
	return 0;
}

### Prompt

Please create a solution in Cpp to 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>
#define ll long long
#define inf 1000000000
#define infll 1000000000000000000ll
#define vi vector<int>
#define vll vector<ll>
#define pb push_back
#define pii pair<int,int>
#define pll pair<ll,ll>
#define pdd pair<double,double>
#define mpr make_pair
#define fi first
#define se second
#define pq priority_queue<int>
#define pqll priority_queue<ll>
#define up(x,y) (x<(y)?x=(y):0)
#define dn(x,y) (x>(y)?x=(y):0)
#define ad(x,y) (x=(x+(y))%mod)
#define mod 998244353
#define N 309
using namespace std;

int m,n,b[N]; bitset<N> a[N];
int read(){
	int x=0; char ch=getchar(); bool flag=0;
	while (ch<'0' || ch>'9'){ if (ch=='-') flag=1; ch=getchar(); }
	while (ch>='0' && ch<='9'){ x=x*10+ch-'0'; ch=getchar(); }
	return flag?-x:x;
}
ll readll(){
	ll x=0; char ch=getchar(); bool flag=0;
	while (ch<'0' || ch>'9'){ if (ch=='-') flag=1; ch=getchar(); }
	while (ch>='0' && ch<='9'){ x=x*10+ch-'0'; ch=getchar(); }
	return flag?-x:x;
}
int ksm(int x,int y){
	int ans=1;
	for (; y; y>>=1,x=(ll)x*x%mod) if (y&1) ans=(ll)ans*x%mod;
	return ans;
}
int main(){
	scanf("%d%d",&m,&n);
	int i,j,cnt=0;
	for (i=1; i<=m; i++)
		for (j=0; j<n; j++) a[i][j]=(read()>0);
	for (i=1; i<=m; i++){
		for (j=0; j<n; j++) if (a[i][j])
			if (b[j]) a[i]^=a[b[j]]; else{
				b[j]=i; cnt++; break;
			}
	}
	int t=(ksm(2,m)-ksm(2,m-cnt)+mod)%mod;
	printf("%lld\n",(ll)t*ksm(2,n-1)%mod);
	return 0;
}

```