A16188 | Divide and Equalize

You are given an array $a$ consisting of $n$ positive integers. You can perform the following operation on it:

1. Choose a pair of elements $a_i$ and $a_j$ ( $1 \le i, j \le n$ and $i \neq j$ );
2. Choose one of the divisors of the integer $a_i$ , i.e., an integer $x$ such that $a_i \bmod x = 0$ ;
3. 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:

1. 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 $a$ = \[ $100, 10, 10, 10, 1$ \];
2. 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 $10$ .

The 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 $10^4$ .

For 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).