D. Divide and Equalizetime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given an array a consisting of n positive integers. You can perform the following operation on it:   Choose a pair of elements a_i and a_j (1 \le i, j \le n and i \neq j);  Choose one of the divisors of the integer a_i, i.e., an integer x such that a_i \bmod x = 0;  Replace a_i with \frac{a_i}{x} and a_j with a_j \cdot x.  Determine whether it is possible to make all elements in the array the same by applying the operation a certain number of times (possibly zero).For example, let's consider the array a = [100, 2, 50, 10, 1] with 5 elements. Perform two operations on it:   Choose a_3 = 50 and a_2 = 2, x = 5. Replace a_3 with \frac{a_3}{x} = \frac{50}{5} = 10, and a_2 with a_2 \cdot x = 2 \cdot 5 = 10. The resulting array is a = [100, 10, 10, 10, 1];  Choose a_1 = 100 and a_5 = 1, x = 10. Replace a_1 with \frac{a_1}{x} = \frac{100}{10} = 10, and a_5 with a_5 \cdot x = 1 \cdot 10 = 10. The resulting array is a = [10, 10, 10, 10, 10].  After performing these operations, all elements in the array a become equal to 10.InputThe first line of the input contains a single integer t (1 \le t \le 2000) — the number of test cases.Then follows the description of each test case.The first line of each test case contains a single integer n (1 \le n \le 10^4) — the number of elements in the array a.The second line of each test case contains exactly n integers a_i (1 \le a_i \le 10^6) — the elements of the array a.It is guaranteed that the sum of n over all test cases does not exceed 10^4.OutputFor each test case, output a single line:   "YES" if it is possible to make all elements in the array equal by applying the operation a certain (possibly zero) number of times;  "NO" otherwise. You can output the answer in any case (for example, the strings "yEs", "yes", "Yes", and "YES" will all be recognized as a positive answer).ExampleInput
75100 2 50 10 131 1 148 2 4 2430 50 27 20275 4024 432 3 1Output
YES
YES
NO
YES
NO
YES
NO
NoteThe first test case is explained in the problem statement.
75100 2 50 10 131 1 148 2 4 2430 50 27 20275 4024 432 3 1
YES YES NO YES NO YES NO 
['math', 'number theory', '*1300']