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: Accepted)

h, w = gets.split.map(&:to_i)
a = (1..h).map { gets.split.map(&:to_i) }
b = (1..h).map { Array.new(w) }
(0..h-1).each {|i| b[i][0] = 1 - a[i][0] }
(0..w-1).each {|j| b[0][j] = 1 - a[0][j] }
(1..h-1).each do |i|
  (1..w-1).each do |j|
    if a[i][j] == 1
      b[i][j] = 0
    else
      b[i][j] = [b[i-1][j-1], b[i-1][j], b[i][j-1]].min + 1
    end
  end
end
p b.map {|row| row.max }.max ** 2