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: Wrong Answer)

N = int(input())
A = []
for i in range(N):
    A.append([])
    for j in input():
        A[-1].append(int(j))


def confirm(index):
    R = [ind for ind in range(N)]
    R.remove(index)
    res = dict()
    depth = 1
    res[index] = depth
    box = [index]
    while True:
        depth += 1
        app = []
        for l in box:
            for k in range(N):
                if A[l][k] == 1:

                    if k in res.keys() and not(abs(res[k] - depth) != 1 or abs(res[k] - depth) != 0):
                        return False
                    elif k not in res.keys():
                        R.remove(k)
                        res[k] = depth
                        app.append(k)
        box = app

        if len(R) == 0:
            return depth


result = -1
for i in range(len(A)):
    J = confirm(i)
    if not J:
        continue
    if result < J:
        result = J
print(result)