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## SUMGCD - Sum of GCD

Given “n” positive integers, you have to find the summation of GCD (greatest common divisor) of every possible pair of these integers.

### Input

The first line of the input contains an integer denoting the number of test cases. The description of Ttest cases follows. Each test case, described in a single line, contains “n+1” space-separated integers: The first one is the number “n” (1 < n < 100) indicating the number of input integers, the remaining ones includes “n” positive integers. Note that each input integer do not exceed 106.

### Output

For each test case, output the sum of the GCDs of every possible pair.

### Example

```Input:
34 10 20 30 403 7 5 123 125 15 25

Output:
70335```

 Added by: mbk_live Date: 2019-01-09 Time limit: 1s Source limit: 50000B Memory limit: 1536MB Cluster: Cube (Intel G860) Languages: C-CLANG C C++ 4.3.2 CPP CPP14 CPP14-CLANG C99 JAVA PYTHON PYTHON3 SWIFT