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)

#二部グラフ化できるか
#最大深さ

import sys
readline = sys.stdin.readline
write = sys.stdout.write
from collections import deque

n = int(input())
s = []

for i in range(n):
    sij = input()
    s.append(sij)
    
d = [-1]*n

Q = deque()

d[0] = 0

Q.append(0)

while Q:
    v = Q.popleft()
    for i in range(n):
        if int(s[v][i]):
            if d[i]<0:
                d[i] = d[v] + 1
                Q.append(i)
            elif (d[i]-d[v])%2==0:
                #print(d)
                print(-1)
                exit()

mxd = max(d)
mxd_id = d.index(mxd)

    
d2 = [-1]*n

d2[mxd_id] = 0

Q.append(mxd_id)

while Q:
    v = Q.popleft()
    for i in range(n):
        if int(s[v][i]):
            if d2[i]<0:
                d2[i] = d2[v] + 1
                Q.append(i)
#print(d)
#print(d2)
print(max(d2)+1)