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

combi = []
count = 0
(1..(2 ** n - 1)).each do |i|
  i = i.to_s(2)
  x_len = i.length - 1
  x_array = i.split("").map.with_index{|e,i| e == "1" ? x_len - i : nil}.compact
    (1..(2 ** m - 1)).each do |j|
      j = j.to_s(2)
      y_len = j.length - 1
      y_array = j.split("").map.with_index{|e,i| e == "1" ? y_len - i : nil}.compact
      combi.push([x_array,y_array])
    end
end

combi.each do |pair|
  sum = 0
  pair[0].each do |x|
    pair[1].each do |y|
      sum += table[x][y].to_i
    end
  end
  count += 1 if sum % 2 == 1
end

puts count % 998244353