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)

def warshall_floyd(d):
    for k in range(n):
        for i in range(n):
            for j in range(n):
                d[i][j] = min(d[i][j],d[i][k] + d[k][j])
    return d
n = int(input())
d = [[float("inf") for i in range(n)] for i in range(n)] 
l=[]
#d[u][v] : 辺uvのコスト(存在しないときはinf)
for i in range(n):
    s=input()
    for j in range(n):
        if s[j]=="1":
            d[i][j] = 1
            l.append([i,j])
for i in range(n):
    d[i][i] = 0
wf=warshall_floyd(d)
visited = [1]+[0 for i in range(n-1)]
while 0 in visited:
    for i in l:
        if visited[i[0]]!=0:
            if visited[i[0]]==1:
                if visited[i[1]]==1:
                    print(-1)
                    exit()
                elif visited[i[1]]==0:
                    visited[i[1]]=-1
            else:
                if visited[i[1]]==-1:
                    print(-1)
                    exit()
                elif visited[i[1]]==0:
                    visited[i[1]]=1
ans=0
for i in wf:
    ans=max(ans,max(i)+1)
print(ans)