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)

from collections import deque

N = int(input())

S = []

for i in range(N):

    s = input()
    S.append(s)

lis = [float("inf")] * N
lis[0] = 0
q = deque([])

q.append(0)

#print (S,lis)

while len(q) > 0:

    now = q.pop()

    for i in range(N):

        #print (i,now)
        if S[now][i] == "1" and lis[i] > lis[now] + 1:
            lis[i] = lis[now] + 1
            q.append(i)

mind = 0
#print (lis)

for i in lis:
    if lis[mind] < lis[i]:
        mind = i


lis = [float("inf")] * N
lis[mind] = 0
q = deque([])
q.append(mind)

#print (q,len(q),lis)

while len(q) > 0:

    now = q.pop()
    #print (now)
    

    for i in range(N):

        if S[now][i] == "1" and lis[i] > lis[now] + 1:

            lis[i] = lis[now] + 1
            q.append(i)


nlis = [None] * N
nlis[mind] = 0
q = deque([])
q.append(mind)
flag = True

while len(q) > 0:

    now = q.pop()  

    for i in range(N):

        if S[now][i] == "1" and nlis[i] == None:
   
            nlis[i] = nlis[now] ^ 1
            q.append(i)

        elif S[now][i] == "1" and nlis[now] == nlis[i]:
            flag = False
            break

    if not flag:
        break

if flag:
    print (max(lis) + 1)

else:
    print (-1)