#P1325E. Ehab's REAL Number Theory Problem
Ehab's REAL Number Theory Problem
Description
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.
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 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".
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".
Samples
3
1 4 6
1
4
2 3 6 6
2
3
6 15 10
3
4
2 3 5 7
-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.