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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

import sys
input = sys.stdin.readline
from collections import deque
def main():
    N = int( input())
    S = [ list( map( int, list( input())[:-1])) for _ in range(N)]
    E = [[] for _ in range(N)]
    for i in range(N):
        for j in range(N):
            if S[i][j] == 1:
                E[i].append(j)
    
    d = deque([0])
    V = [-1]*N
    V[0] = 1
    
    while d:
        v = d.pop()
        now = V[v]
        for w in E[v]:
            if V[w] == -1:
                V[w] = now+1
                d.append(w)
                continue

            if (now + V[w])%2 == 1:
                continue
            print(-1)
            return
    ans = 2
    for i in range(N):
        d = deque([i])
        V = [-1]*N
        V[i] = 1
        while d:
            v = d.pop()
            now = V[v]
            for w in E[v]:
                if V[w] == -1:
                    V[w] = now+1
                    d.append(w)
        if max(V) > ans:
            ans = max(V)
    print(ans)
    
            
                
if __name__ == '__main__':
    main()