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())
S = [input() for _ in range(N)]

E = [set() for _ in range(N)]
for i in range(N):
  for j in range(N):
    if S[i][j] == '1':
      E[i].add(j)

C = [0 for _ in range(N)]
def dfs(v,c):
  C[v] = c
  for u in E[v]:
    if C[u] == c:
      return False
    if C[u] == 0 and not dfs(u,-c):
      return False
  return True

if not dfs(0,1):
  print(-1)
  exit()

G = [[float('inf') for _ in range(N)] for _ in range(N)]
for i in range(N):
  G[i][i] = 0
for i in range(N):
  for j in range(N):
    if S[i][j] == '1':
      G[i][j] = 1

for k in range(N):
  for i in range(N):
    for j in range(N):
      G[i][j] = min(G[i][k]+G[k][j],G[i][j])
ans = 0
for g in G:
  mx = max(g)
  ans = max(ans,mx)
print(ans+1)