For the given $n$ positive integers $a_1, a_2, ..., a_n$, find the sum of the GCD (greatest common divisor) of all possible pairs of these numbers. $$ \sum_{\mathclap{1 \le i < j\le n}} GCD(a_i,a_j) $$ \InputFile 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 $n$ positive integers. All input integers do not exceed $10^6$. \OutputFile For each test, print the sum of the \textbf{GCDs} of all possible pairs on a separate line. \Note The answer for the third example is $$ GCD(125,15) + GCD(125,25) + GCD(15,25) = 5 + 25 + 5 = 35 $$