Graph Partition

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

inputFormat

Input

Input is given from Standard Input in the following format:

N S_{1,1}...S_{1,N} : S_{N,1}...S_{N,N}

outputFormat

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

样例

2
01
10

2