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.

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.

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.

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

见题面 Input 部分

见题面 Output 部分