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.

Examples

Input

2
01
10

Output

2

Input

3
011
101
110

Output

-1

Input

6
010110
101001
010100
101000
100000
010000

Output

4

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