#include<bits/stdc++.h>
#define IL inline
#define _ 400005
#define ll long long
using namespace std ;

IL int gi(){
    int data = 0 , m = 1; char ch = 0;
    while(ch!='-' && (ch<'0'||ch>'9')) ch = getchar();
    if(ch == '-'){m = 0 ; ch = getchar() ; }
    while(ch >= '0' && ch <= '9'){data = (data<<1) + (data<<3) + (ch^48) ; ch = getchar(); }
    return (m) ? data : -data ; 
}

int n , m , N , A[305][305] , pw[100005] , ID[305] ;
#define mod 998244353

int main() {
	n = gi() ; m = gi() ;
	for(int i = 1; i <= n; i ++) for(int j = 1; j <= m; j ++) A[i][j] = gi() ;
	N = n * m ;
	pw[0] = 1 ; for(int j = 1; j <= N; j ++) pw[j] = 2ll * pw[j - 1] % mod ;
	for(int i = 1; i <= n; i ++)
		for(int j = 1; j <= m; j ++) {
			if(A[i][j]) {
				if(!ID[j]) {ID[j] = i ; break ; }
				else for(int k = 1; k <= m; k ++) A[i][k] = A[i][k] ^ A[ID[j]][k] ;
			}
		}
	int _cnt = 0 ;
	for(int j = 1; j <= m; j ++) if(ID[j] != 0) ++ _cnt ;
	cout << 1ll * pw[m - 1] * (pw[n] - pw[n - _cnt] + mod) % mod << endl ;
	return 0 ;
}

### Prompt

In Cpp, your task is to solve 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 IL inline
#define _ 400005
#define ll long long
using namespace std ;

IL int gi(){
    int data = 0 , m = 1; char ch = 0;
    while(ch!='-' && (ch<'0'||ch>'9')) ch = getchar();
    if(ch == '-'){m = 0 ; ch = getchar() ; }
    while(ch >= '0' && ch <= '9'){data = (data<<1) + (data<<3) + (ch^48) ; ch = getchar(); }
    return (m) ? data : -data ; 
}

int n , m , N , A[305][305] , pw[100005] , ID[305] ;
#define mod 998244353

int main() {
	n = gi() ; m = gi() ;
	for(int i = 1; i <= n; i ++) for(int j = 1; j <= m; j ++) A[i][j] = gi() ;
	N = n * m ;
	pw[0] = 1 ; for(int j = 1; j <= N; j ++) pw[j] = 2ll * pw[j - 1] % mod ;
	for(int i = 1; i <= n; i ++)
		for(int j = 1; j <= m; j ++) {
			if(A[i][j]) {
				if(!ID[j]) {ID[j] = i ; break ; }
				else for(int k = 1; k <= m; k ++) A[i][k] = A[i][k] ^ A[ID[j]][k] ;
			}
		}
	int _cnt = 0 ;
	for(int j = 1; j <= m; j ++) if(ID[j] != 0) ++ _cnt ;
	cout << 1ll * pw[m - 1] * (pw[n] - pw[n - _cnt] + mod) % mod << endl ;
	return 0 ;
}

```