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 (2.4.0) (judge verdict: Accepted)

N = int(input())
graph = []
for _ in range(N):
	graph.append(list(map(int, input().strip())))

def check(graph):
	queue = [0]
	dists = [None] * N
	dists[0] = 0
	while queue:
		cur = queue.pop()
		dist = dists[cur] + 1
		col = graph[cur]
		for i in range(N):
			c = col[i]
			if c == 1:
				d = dists[i]
				if d == None:
					dists[i] = dist
					queue.append(i)
				else:
					if d % 2 != dist %2:
						return False
					elif d > dist:
						dists[i] = dist
						queue.append(i)
	return True

def search(graph, start):
	queue = [start]
	dists = [None] * N
	dists[start] = 0
	while queue:
		cur = queue.pop()
		dist = dists[cur] + 1
		col = graph[cur]
		for i in range(N):
			c = col[i]
			if c == 1:
				d = dists[i]
				if d == None or d > dist:
					dists[i] = dist
					queue.append(i)
	return max(dists)

if check(graph):
	diam = 0
	for i in range(N):
		d = search(graph, i)
		if d > diam:
			diam = d
	print(diam + 1)
else:
	print(-1)