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)

n=int(input())
l=[[] for i in range(n+1)]
for i in range(1,1+n):
  l1=list(input())
  for j in range(1,1+n):
    if l1[j-1]=="1":
      l[i].append(j)
color=[0 for i in range(n+1)]
b=True
def f(v,c):
    #頂点vに隣接する頂点全てを塗るあるいは判定する
    color[v] = c
    for i in range(len(l[v])):
        if color[ l[v][i] ] == c:
            return False
        elif color[ l[v][i] ] == 0 and not f(l[v][i],-c):
            #(g[v][i]がまだ塗られていない　かつ　そこを-cで塗っても問題ない) ではないなら
            return False
    return True
b=f(1,1)
if not b:
  print(-1)
else:
  inf=10**10
  d=[[inf for i in range(n+1)] for j in range(n+1)]
  for i in range(n+1):
    for j in l[i]:
      d[i][j]=1
  for k in range(n+1):
    for j in range(1,n+1):
      for i in range(1,n+1):
        d[i][j]=min(d[i][j],d[i][k]+d[k][j])
  max=0
  for i in range(1,n+1):
    for j in range(1,n+1):
      if d[i][j]>max:
        max=d[i][j]
  print(max+1)