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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

n,m = gets.split.map(&:to_i)
table = []
(1..n).each do |i|
  table.push(gets.split.map(&:to_i))
end

x_array = [0,1].repeated_permutation(n).to_a.map{|ele| ele.size.times.select{|i| 1 == ele[i]}}
y_array = [0,1].repeated_permutation(m).to_a.map{|ele| ele.size.times.select{|i| 1 == ele[i]}}
combi = x_array.product(y_array)
count = 0
combi.each do |pair|
  judge = false
  pair[0].each do |x|
    pair[1].each do |y|
     judge =  judge == true ? false : true if table[x][y] == 1
    end
  end
  count += 1 if judge == true
end

puts count % 998244353