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)
r = []
h.times do
	r << gets.split().map(&:to_i)
end

1.upto(h-1) do |i|
	1.upto(w-1) do |j|
		m = [r[i-1][j],r[i][j-1],r[i-1][j-1]].max
		if m == 1 || r[i][j] == 1
			next
		end
		r[i][j] = m-1
	end
end

puts (r.map(&:min).min-1)**2