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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php
$N = intval(fgets(STDIN));
for($i = 0; $i < $N; $i++)$map[] = array_map("boolval", str_split(trim(fgets(STDIN))));

$max = -1;
for($i = 0; $i < $N; $i++){
    $distance = array_fill(0, $N, 300);
    $current = [$i];
    $d = 0;
    $distance[$i] = $d;
    while($current){
        $d++;
        $next = [];
        foreach($current as $c){
            for($j = 0; $j < $N; $j++){
                if($map[$c][$j]){
                    if($distance[$j]==300){
                        $distance[$j] = $d;
                        $next[] = $j;
                    }elseif($distance[$j] == $d-2 || $distance[$j] == $d){
                    }else{
                        continue 4;
                    }
                }
            }
        }
        $current = $next;
    }
    if($d > $max){
        $max = $d;
    }
}
echo $max,"\n";