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Given an array $$$a$$$ of length $$$n$$$, tell us whether it has a non-empty subsequence such that the product of its elements is not a perfect square.

A sequence $$$b$$$ is a subsequence of an array $$$a$$$ if $$$b$$$ can be obtained from $$$a$$$ by deleting some (possibly zero) elements.

Input

The first line contains an integer $$$t$$$ ($$$1 \le t \le 100$$$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains an integer $$$n$$$ ($$$1 \le n \le 100$$$) — the length of the array $$$a$$$.

The second line of each test case contains $$$n$$$ integers $$$a_1$$$, $$$a_2$$$, $$$\ldots$$$, $$$a_{n}$$$ ($$$1 \le a_i \le 10^4$$$) — the elements of the array $$$a$$$.

Output

If there's a subsequence of $$$a$$$ whose product isn't a perfect square, print "

Perfectly Imperfect Array

Examples