Problem:
Largest Square

Given a matrix (H × W) which contains only 1 and 0, find the area of the largest square matrix which only contains 0s.

Input

H W
c1,1 c1,2 ... c1,W
c2,1 c2,2 ... c2,W
:
cH,1 cH,2 ... cH,W

In the first line, two integers H and W separated by a space character are given. In the following H lines, ci,j, elements of the H × W matrix, are given.

Output

Print the area (the number of 0s) of the largest square.

Constraints

1 ≤ H, W ≤ 1,400

Sample Input

4 5
0 0 1 0 0
1 0 0 0 0
0 0 0 1 0
0 0 0 1 0

Sample Output

4

Solution in Ruby (judge verdict: Wrong Answer)

h, w = STDIN.gets.split.map(&:to_i)
c = h.times.map { STDIN.gets.split.map { |v| 1-v.to_i } }

h.times.each do |i|
  w.times.each do |j|
    if c[i][j] >= 1 && (i > 0 || j > 0)
      c[i][j] = 1_000_000
      c[i][j] = [c[i-1][j], c[i][j]].min if i > 0
      c[i][j] = [c[i][j-1], c[i][j]].min if j > 0
      c[i][j] = [c[i-1][j-1], c[i][j]].min if i > 0 && j > 0
      c[i][j] += 1
    end
  end
end

puts c.flatten.max**2