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 (7.3.0) (judge verdict: Accepted)

from itertools import count
def max_dist(adj,v):

    q = [v]
    visited = [False]*len(adj)
    visited[v] = True
    last = None
    for d in count():
        if not q:
            return d,last
        nq = []
        last = q[0]
        for v in q:
            for u in adj[v]:
                if not visited[u]:
                    visited[u] = True
                    nq.append(u)
        q = nq


def solve(S):

    N = len(S)

    adj = [[] for _ in range(N)]
    for i,l in enumerate(S):
        for j,f in enumerate(l):
            if f:
                adj[i].append(j)

    stack = [0]
    color = [None]*N
    color[0] = True

    while stack:
        v = stack.pop()
        nc = not color[v]
        for u in adj[v]:
            if color[u] is None:
                color[u] = nc
                stack.append(u)
            elif color[u] != nc:
                return -1

    return max(max_dist(adj,v)[0] for v in range(N))

if __name__ == '__main__':
    N = int(input())
    S = [[c=='1' for c in input()] for _ in range(N)]
    print(solve(S))