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)

from collections import deque
import sys
input = sys.stdin.readline
sys.setrecursionlimit(10**7)
n = int(input())
edges = [[]for _ in range(n)]
for i in range(n):
    s = list(map(int, list(input().rstrip())))
    for j in range(n):
        if s[j]:
            edges[i].append(j)


def dfs(v, parent, d):
    visited[v] = 1
    depth[v] = d
    for v2 in edges[v]:
        if v2 == parent:
            continue
        if visited[v2]:
            d2 = depth[v2]
            n_cycle = d-d2+1
            if 0 < n_cycle:
                cycle.append(n_cycle)
            continue
        dfs(v2, v, d+1)


cycle = []
depth = [0]*n
visited = [0]*n
dfs(0, -1, 0)


def bfs(init_v):
    next_v = deque([init_v])
    INF = 10**18
    dist = [INF]*n
    dist[init_v] = 0
    while next_v:
        v = next_v.popleft()
        for v2 in edges[v]:
            if dist[v2] <= dist[v]+1:
                continue
            dist[v2] = dist[v]+1
            next_v.append(v2)
    return dist


if all(c % 2 == 0 for c in cycle):
    ans = 0
    for i in range(n):
        dist = bfs(i)
        x = max(dist)
        if ans < x:
            ans = x
    print(ans+1)
else:
    print(-1)