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)

import sys

sys.setrecursionlimit(10 ** 7)
f_inf = float('inf')
mod = 10 ** 9 + 7


def resolve():
    def dfs(v, c):
        for u in edge[v]:
            if color[u] is None:
                color[u] = c
                dfs(u, c ^ 1)
            else:
                if color[u] != c:
                    print(-1)
                    exit()

    n = int(input())
    S = [list(input()) for _ in range(n)]
    edge = [[] for _ in range(n)]
    for i in range(n):
        for j in range(n):
            if S[i][j] == "1":
                edge[i].append(j)
                edge[j].append(i)

    color = [None] * n
    dfs(0, 0)
    for i in range(n):
        for j in range(n):
            if i == j:
                S[i][j] = 0
            else:
                S[i][j] = f_inf if S[i][j] == "0" else 1

    for k in range(n):
        for i in range(n):
            for j in range(n):
                S[i][j] = min(S[i][j], S[i][k] + S[k][j])

    res = 0
    for s in S:
        res = max(res, max(s))
    print(res + 1)


if __name__ == '__main__':
    resolve()