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)

n=int(input())
edge=[[]for i in range(n+1)]
for i in range(1,n+1):
    s=list(input())
    for j in range(i,n+1):
        if s[j-1]=="1":
            edge[i].append(j)
            edge[j].append(i)



ans=0
for i in range(1,n+1):
    bubun=[[] for iii in range(n+1)]
    bubun[0].append(i)
    check=0
    for j in range(n):
        for k in bubun[j]:
            for y in edge[k]:
                if y in bubun[j-1]:
                    continue
                elif y in bubun[j]:
                    break
                elif y in bubun[j+1]:
                    continue
                else:
                    bubun[j+1].append(y)
            else:
                continue
            break
        else:
            continue
        break
    else:
        for ii in bubun:
            if ii:
                check+=1
        ans=max(ans,check)
if ans==0:
    print(-1)
else:
    print(ans)