You are given nn integer numbers a1,a2,…,ana1,a2,…,an. Consider graph on nn nodes, in which nodes ii, jj (i≠ji≠j) are connected if and only if, aiaiAND aj≠0aj≠0, where AND denotes the .

Find the length of the shortest cycle in this graph or determine that it doesn't have cycles at all.

Input

The first line contains one integer nn (1≤n≤105)(1≤n≤105) — number of numbers.

The second line contains nn integer numbers a1,a2,…,ana1,a2,…,an (0≤ai≤10180≤ai≤1018).

Output

If the graph doesn't have any cycles, output −1−1. Else output the length of the shortest cycle.

Examples

input

Copy

43 6 28 9

output

Copy

4

input

Copy

55 12 9 16 48

output

Copy

3

input

Copy

41 2 4 8

output

Copy

-1

Note

In the first example, the shortest cycle is (9,3,6,28)(9,3,6,28).

In the second example, the shortest cycle is (5,12,9)(5,12,9).

The graph has no cycles in the third example.

 代码：

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