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: Time Limit Exceeded)

n = gets.chomp.to_i
INF = 1_000_000
dp = Array.new(n){ Array.new(n){ INF } }

n.times do |i|
  dp[i][i] = 0
end

edges = Array.new(n){ [] }

n.times do |i|
  s = gets.chomp
  s.chars.each_with_index do |j, index|
    if j == "1"
      dp[i][index] = 1
      edges[i] << index
    end
  end
end

# 三角形の頂点かどうかを調べる
edges.each do |edge|
  # [1,2,3] 同士が直接つながっていたらNG
  edge.each do |i|
    if (edges[i] & edge).size > 0
      puts -1
      exit
    end
  end
end

n.times do |i|
  n.times do |j|
    n.times do |k|
      dp[i][j] = [dp[i][j], dp[i][k] + dp[k][j]].min
    end
  end
end

max = 0
dp.each do |i|
  max = [max, i.max].max
end

puts max+1