F. Minimum Sum of Array
time limit per test
2.5 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given an array a consisting of n integers a1, ..., an. In one operation, you can choose 2 elements ai and aj in which ai is divisible by aj and transform ai to aj.

A number x is said to be divisible by a number y if x can be divided by y and the result is an exact whole number. For example, 15 is divisible by 3, because 15÷ 3 = 5 exactly, but 9 is not divisible by 2 because 9÷ 2 is 4 with 1 left over.

Your task is to find the minimum sum of the array a that can be obtained by making as many transform operations as you want. Can you?

Input

The first line contains an integer T (1 ≤ T ≤ 100) specifying the number of test cases.

The first line of each test case contains an integer n (1 ≤ n ≤ 105), in which n is the size of array a. Then a line follows containing n integers a1, ..., an (1 ≤ ai ≤ 106), giving array a.

The sum of n overall test cases does not exceed 3 × 106.

Output

For each test case, print a single line containing the minimum sum of the array a that can be obtained after making as many transform operations as you want.

Example
Input
1
5
2 2 3 6 6
Output
11