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)

# 二部グラフかどうかの判定法
#二個だけTLEだった泣
import sys
n=int(input())
s=[list(input()) for _ in range(n)]
g=[[] for _ in range(n+1)]
for i in range(n):
    for j in range(i+1,n):
        if s[i][j]=="1":
            g[i+1].append(j+1)
            g[j+1].append(i+1)
#二部グラフかどうかの判定
flag=[-1]*(n+1)
forest=[]
for i in range(1,n+1):
    U=[]
    if flag[i]==-1:
        que=[[i]]
        j=1
        flag[i]=1
        while que:
            h=que.pop()
            H=[]
            for u in h:
                flag[u]=j%2
                U.append(u)
                for v in g[u]:
                    if flag[v]==-1:
                        H.append(v)
                        flag[v]=(j+1)%2
                    elif flag[v]==j%2:
                        print(-1)
                        sys.exit()
            if H:
                que.append(H)
            j+=1
    if U:
        forest.append(U)