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: Accepted)

import sys
input = sys.stdin.readline

n = int(input())
s = [input() for _ in range(n)]

ans = -1

for i in range(n):
    edges = [[] for _ in range(n)]
    for j in range(n):
        for k in range(j,n):
            if s[j][k] == '1':
                edges[j].append(k)
                edges[k].append(j)

    tmp = 0
    stack = [i]
    visit = [False]*n
    visit[i] = True
    flag = True
    while True:
        li = []
        while stack:
            li2 = []
            l = stack.pop(-1)
            for j in edges[l]:
                li2.append(j)
            for j in li2:
                edges[j].remove(l)
            li += li2
        li = list(set(li))
        for j in li:
            if visit[j]:
                flag = False
        if flag:
            stack = li
            for j in li:
                visit[j] = True
            tmp += 1
        else:
            break
        if not stack:
            ans = max(ans,tmp)
            break

print(ans)