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 Julia (0.5.0) (judge verdict: Wrong Answer)

function reader(pos::Int)
    global membuff
    val = 0
    sign = 1
    @inbounds r = membuff[pos]
    pos += 1
    while r < 0x30 || 0x39 < r
        sign = r == '-' ? -1 : sign
        @inbounds r = membuff[pos]
        pos += 1
    end
    while 0x30 <= r <= 0x39
        val = val * 10 + r - 0x30 
        @inbounds r = membuff[pos]
        pos += 1
    end
    return val*sign, pos
end

const io = VERSION > v"1.0" ? stdin : STDIN
const membuff = read(io,1145141919)

#using LinearAlgebra: rank # 1.0 なら必要
function main()
    pos = 1
    N, pos = reader(pos)
    M, pos = reader(pos)
    a = zeros(Int,(N,M))
    for j=1:M,i=1:N # j が先に回る
        a[i,j], pos = reader(pos)
    end
    r = rank(a)
    mod = 998244353
    ans = powermod(2, N+M-1, mod) - powermod(2, N+M-r-1, mod)
    println( (ans+mod) % mod )
end

main()