Question
Make the array Equal
You are given an array A of length N. Determine if it is possible to make all the elements of A equal by performing the following operation any number of times (possibly, zero):
- Choose two distinct indices i and j (1 ≤ i, j ≤ N, i ≠ j); and
- Update the value at index i by setting Ai to Ai + Aj
- Choosing i = 5 and j = 3 would result in the array [1, 5, 3, 5, 9], since we replace A5 with A5 + A3 = 9.
- Choosing i = 2 and j = 4 would instead result in the array [1, 10, 3, 5, 6].
"Yes" if it is possible to make all elements of the array equal after performing several (possibly, zero) of these operations, otherwise output "No" (without quotes).Input
The first line of input will contain a single integer T, denoting the number of test cases.
Each test case consists of two lines of input.
- The first line of each test case contains a single integer N, denoting the length of an array.
- The second line of each test case contains N space-separated integers, denoting the initial array.
Constraints
1 ≤ T ≤ 105
1 ≤ N ≤ 2 * 105
0 ≤ Ai ≤ 109
The sum of N over all test cases won't exceed 4 * 105.
Each test case consists of two lines of input.
- The first line of each test case contains a single integer N, denoting the length of an array.
- The second line of each test case contains N space-separated integers, denoting the initial array.
Constraints
1 ≤ T ≤ 105
1 ≤ N ≤ 2 * 105
0 ≤ Ai ≤ 109
The sum of N over all test cases won't exceed 4 * 105.
Output
For each test case, output on a new line, print "Yes" if it is possible to make all elements of array equal using any number of operations, otherwise print "No" (without quotes).
Example
Sample Input
2
3
1 1 1
2
1 2
Sample Output
Yes
No
Explanation
Test case 1: All the elements of A are already equal.
Test case 2: It can be shown that no matter how many operations are performed, it's not possible to make A1 = A2.
2
3
1 1 1
2
1 2
Sample Output
Yes
No
Explanation
Test case 1: All the elements of A are already equal.
Test case 2: It can be shown that no matter how many operations are performed, it's not possible to make A1 = A2.