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)

# AGC039B - Graph Partition (153ms)
from collections import deque


def is_bipartite() -> bool:
    stack, color = [(1, 1)], [0] * (N + 1)
    color[1] = 1
    while stack:
        v, cur_color = stack.pop()
        next_color = -cur_color
        for u in E[v]:
            if color[u] == cur_color:
                return False
            if not color[u]:
                color[u] = next_color
                stack.append((u, next_color))
    return True


def bfs(source: int) -> int:
    queue = deque([source])
    dist = [0] * (N + 1)  # dist[i] := distance from V_source to V_i
    dist[source] = 1
    while queue:
        v = queue.popleft()
        cur = dist[v]
        for u in E[v]:
            if not dist[u]:
                dist[u] = cur + 1
                queue.append(u)
    return max(dist)


def main():
    # if bipartite graph -> diameter of the graph + 1
    global N, E
    N, *S = open(0)
    N = int(N)
    E = [0] + [[i for i, flg in enumerate(s, 1) if flg == "1"] for s in S]
    if is_bipartite():
        ans = max(bfs(i) for i in range(1, N + 1))
        print(ans)
    else:
        print(-1)


if __name__ == "__main__":
    main()