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GCD operations SOLUTION GCDOPS
Consider a sequence [Math Processing Error], where initially, [Math Processing Error] for each valid [Math Processing Error]. You may perform any number of operations on this sequence (including zero). In one operation, you should choose two valid indices [Math Processing Error] and [Math Processing Error], compute the greatest common divisor of [Math Processing Error] and [Math Processing Error] (let’s denote it by [Math Processing Error]), and change both [Math Processing Error] and [Math Processing Error] to [Math Processing Error].
You are given a sequence [Math Processing Error]. Is it possible to obtain this sequence, i.e. change [Math Processing Error] to [Math Processing Error], using the given operations?
Input
The first line of the input contains a single integer [Math Processing Error] denoting the number of test cases. The description of [Math Processing Error] test cases follows.
The first line of each test case contains a single integer [Math Processing Error].
The second line contains [Math Processing Error] space-separated integers [Math Processing Error].
Output
For each test case, print a single line containing the string “YES” if it is possible to obtain [Math Processing Error] or “NO” if it is impossible.
Constraints
[Math Processing Error]
[Math Processing Error] for each valid [Math Processing Error]
the sum of [Math Processing Error] over all test cases does not exceed [Math Processing Error]
Subtasks
Subtask #1 (10 points): [Math Processing Error]
Subtask #2 (20 points): there is at most one valid index [Math Processing Error] such that [Math Processing Error]
Subtask #3 (70 points): original constraints
Example Input
2
3
1 2 2
4
1 2 3 2
Example Output
NO
YES
Explanation
Example case 1: We cannot make the third element of the sequence [Math Processing Error] become [Math Processing Error].
Example case 2: We can perform one operation with [Math Processing Error], which changes the sequence [Math Processing Error] to [Math Processing Error].
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