Problem:
Score : 500 points

Problem Statement

Given is a connected undirected graph with N vertices and M edges. The vertices are numbered 1 to N, and the edges are described by a grid of characters S.
If S_{i,j} is 1, there is an edge connecting Vertex i and j; otherwise, there is no such edge.

Determine whether it is possible to divide the vertices into non-empty sets V_1, \dots, V_k such that the following condition is satisfied. If the answer is yes, find the maximum possible number of sets, k, in such a division.

Every edge connects two vertices belonging to two "adjacent" sets. More formally, for every edge (i,j), there exists 1\leq t\leq k-1 such that i\in V_t,j\in V_{t+1} or i\in V_{t+1},j\in V_t holds.

Constraints

2 \leq N \leq 200

S_{i,j} is 0 or 1.

S_{i,i} is 0.

S_{i,j}=S_{j,i}

The given graph is connected.

N is an integer.

Input

Input is given from Standard Input in the following format:

N
S_{1,1}...S_{1,N}
:
S_{N,1}...S_{N,N}

Output

If it is impossible to divide the vertices into sets so that the condition is satisfied, print -1.
Otherwise, print the maximum possible number of sets, k, in a division that satisfies the condition.

Sample Input 1

2
01
10

Sample Output 1

2

We can put Vertex 1 in V_1 and Vertex 2 in V_2.

Sample Input 2

3
011
101
110

Sample Output 2

-1

Sample Input 3

6
010110
101001
010100
101000
100000
010000

Sample Output 3

4

Solution in Ruby (2.3.3) (judge verdict: Runtime Error)

require 'set'
N = gets.to_i
S = N.times.map{
	gets.strip.each_char.map{|c| c==?1 }
}

I = lambda{|i,j|
	return i < j ? (N-i-1)*(N-i-2)/2+(j-i-1) : (N-j-1)*(N-j-2)/2+(i-j-1)
}
Ds = [nil]*(N*(N-1)/2) # I[i,j]th element is for dist between i&j
U = Set.new 1...N # unreached
V = Set.new [0]   #   reached
until U.empty?
	i = U.each{|i| break V.each{|j| break i if S[i][j] } }
	U.delete(i); V << i

	uq = []
	V.each{|j|
		next unless S[i][j]
		uq << [i,j,2]
	}
	until uq.empty?
		x, y, d = uq.shift
		di = I[x,y]
		d0 = Ds[di]
		if d0
			if d0&1 != d&1
				p(-1)
				exit
			end
			next if d0 <= d
		end
		Ds[di] = d

		V.each{|z|
			uq << [z,x,d+1] if z != x && S[z][y]
			uq << [z,y,d+1] if z != y && S[z][x]
		}
	end
end

p Ds.max