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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
class Program{
	const int mod=998244353;
	const long o=1;
	static int[][] h;
	static int[] s;
	static long ans=0,r=1;
	static void Main(){
		Sc sc=new Sc();
		s=sc.Ia;
		h=new int[s[0]][];
		for(int i=0;i<s[0];i++){
			h[i]=sc.Ia;
		}
		for(int i=0;i<s[1]-1;i++){
			r*=2;
			r%=mod;
		}
		for(int i=0;i<s[0];i++){
			int[] q=new int[s[1]];
			for(int j = 0;j<s[1];j++) {
				q[j]=h[i][j];
			}
			Fu(i-1,q);
		}
		Console.WriteLine("{0}",ans);
	}
	static void Fu(int a,int[] q){
		if(a==-1){
			bool b=false;
			for(int j = 0;j<s[1];j++) {
				if(q[j]%2==1){b=true;break;}
			}
			if(b){ans+=r;}
			return;
		}
		else{
			int[] p=new int[s[1]];
			for(int j = 0;j<s[1];j++) {p[j]=q[j];}
			Fu(a-1,p);
			for(int j = 0;j<s[1];j++) {
				p[j]+=h[a][j];
			}
			Fu(a-1,p);
		}
	}
}

public class Sc{
	public int I{get{return int.Parse(Console.ReadLine());}}
	public long L{get{return long.Parse(Console.ReadLine());}}
	public double D{get{return double.Parse(Console.ReadLine());}}
	public string S{get{return Console.ReadLine();}}
	public int[] Ia{get{return Array.ConvertAll(Console.ReadLine().Split(),int.Parse);}}
	public long[] La{get{return Array.ConvertAll(Console.ReadLine().Split(),long.Parse);}}
	public double[] Da{get{return Array.ConvertAll(Console.ReadLine().Split(),double.Parse);}}
	public string[] Sa{get{return Console.ReadLine().Split();}}
}