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 Python (3.4.3) (judge verdict: Accepted)

import sys
from scipy.sparse.csgraph import floyd_warshall
import numpy as np
from collections import deque

read = sys.stdin.read
readline = sys.stdin.readline

N = int(readline())
S = np.array([list(i) for i in read().split()], np.int64)
edges = np.where(S == 1)

# 二部グラフかを判定する。隣り合う頂点の色が被らないように白黒で塗り分ける
graph = [[] for _ in range(N)]

for i, j in zip(edges[0].tolist(), edges[1].tolist()):
    graph[i].append(j)
    graph[j].append(i)


def judge(start):
    colors = [-1] * N
    colors[start] = 0
    queue = deque([(start, 0)])
    while queue:
        V, c = queue.popleft()
        c ^= 1
        for v in graph[V]:
            if colors[v] == -1:
                colors[v] = c
                queue.append((v, c))
            else:
                if colors[v] != c:
                    return False
    return True


start = edges[0][0]
if judge(start):
    d = floyd_warshall(S)
    print(int(np.max(d)) + 1)
else:
    print(-1)