Ehab's REAL Number Theory Problem

给一些数，每个的因数个数不超过 $7$，求最少选出多少个，使得乘积为完全平方。无解输出 $-1$。

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".

3
1 4 6

1

4
2 3 6 6

2

3
6 15 10

3

4
2 3 5 7

-1

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.