We call a positive number $X$ P-number if there is not a positive number that is less than $X$ and the greatest common divisor of these two numbers is bigger than 1.
Now you are given a sequence of integers. You task is to calculate the sum of P-numbers of the sequence.
Input
There are several test cases.
In each test case:
The first line contains a integer $N(1\leq N\leq 1000)$. The second line contains $N$ integers. Each integer is between 1 and 1000.
Output
For each test case, output the sum of P-numbers of the sequence.
