CF1881D 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).

The first test case is explained in the problem statement.