E. Ehab's REAL Number Theory Problem
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given an array $a$ of length $n$ that has a special condition: every element in this array has at most 7 divisors. Find the length of the shortest non-empty subsequence of this array product of whose elements is a perfect square.

A sequence $a$ is a subsequence of an array $b$ if $a$ can be obtained from $b$ by deletion of several (possibly, zero or all) elements.

Input

The first line contains an integer $n$ ($1 \le n \le 10^5$) — the length of $a$.

The second line contains $n$ integers $a_1$, $a_2$, $\ldots$, $a_{n}$ ($1 \le a_i \le 10^6$) — the elements of the array $a$.

Output

Output the length of the shortest non-empty subsequence of $a$ product of whose elements is a perfect square. If there are several shortest subsequences, you can find any of them. If there's no such subsequence, print "-1".

Examples
Input
3
1 4 6

Output
1
Input
4
2 3 6 6

Output
2
Input
3
6 15 10

Output
3
Input
4
2 3 5 7

Output
-1
Note

In the first sample, you can choose a subsequence $[1]$.

In the second sample, you can choose a subsequence $[6, 6]$.

In the third sample, you can choose a subsequence $[6, 15, 10]$.

In the fourth sample, there is no such subsequence.