You are given $n$ integer numbers $a_1, a_2, \dots, a_n$. Consider graph on $n$ nodes, in which nodes $i$, $j$ ($i\neq j$) are connected if and only if, $a_i$ AND $a_j\neq 0$, where AND denotes the [bitwise AND operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND).

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

The first line contains one integer $n$ $(1 \le n \le 10^5)$ — number of numbers.

The second line contains $n$ integer numbers $a_1, a_2, \dots, a_n$ ($0 \le a_i \le 10^{18}$).

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

4

the shortest cycle is $(9, 3, 6, 28)$.

3

the shortest cycle is $(5, 12, 9)$.

-1

The graph has no cycles