You are given an array A of size N . Generate an array B of size N . Find the sum of array B.

Array B has a definite property. For every i where 1<=i<=n

1. \(B[i]=A[i]/X\) 

2. \(A[i]%X==0\)%X==0

2. X is a perfect square.

X can be varied.

Find the minimum possible sum of array B.

INPUT

First line of input contains a single integer N denoting size of array A.

Next line contains N seperated integers of array A.

OUTPUT

Output the sum of new array B.

CONSTRAINTS

1<=N<=1000000

1<=A[i]<=1000000