For the given positive integers a_1, a_2, ..., a_n, find the sum of the GCD (greatest common divisor) of all possible pairs of these numbers.
The first line contains the number of test cases t~(1 < t < 100). Each test consists of one line containing the number n~(1 < n < 100), followed by positive integers. All input integers do not exceed 10^6.
For each test, print the sum of the GCDs of all possible pairs on a separate line.
Örnek 1
The answer for the third example is