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C. Hossam and Trainees

time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputHossam has $$$n$$$ trainees. He assigned a number $$$a_i$$$ for the $$$i$$$-th trainee.

A pair of the $$$i$$$-th and $$$j$$$-th ($$$i \neq j$$$) trainees is called successful if there is an integer $$$x$$$ ($$$x \geq 2$$$), such that $$$x$$$ divides $$$a_i$$$, and $$$x$$$ divides $$$a_j$$$.

Hossam wants to know if there is a successful pair of trainees.

Hossam is very tired now, so he asks you for your help!

Input

The input consists of multiple test cases. The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^5$$$), the number of test cases. A description of the test cases follows.

The first line of each test case contains an integer number $$$n$$$ ($$$2 \le n \le 10^5$$$).

The second line of each test case contains $$$n$$$ integers, the number of each trainee $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10^9$$$).

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^5$$$.

Output

Print the answer — "YES" (without quotes) if there is a successful pair of trainees and "NO" otherwise. You can print each letter in any case.

Example

Input

2332 48 7314 5 9

Output

YES NO

Note

In the first example, the first trainee and the second trainee make up a successful pair:

$$$a_1 = 32, a_2 = 48$$$, you can choose $$$x = 4$$$.

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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