Problem:
Score : 500 points

Problem Statement

Given are N positive integers A_1,...,A_N.

Consider positive integers B_1, ..., B_N that satisfy the following condition.

Condition: For any i, j such that 1 \leq i < j \leq N, A_i B_i = A_j B_j holds.

Find the minimum possible value of B_1 + ... + B_N for such B_1,...,B_N.

Since the answer can be enormous, print the sum modulo (10^9 +7).

Constraints

1 \leq N \leq 10^4

1 \leq A_i \leq 10^6

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 ... A_N

Output

Print the minimum possible value of B_1 + ... + B_N for B_1,...,B_N that satisfy the condition, modulo (10^9 +7).

Sample Input 1

3
2 3 4

Sample Output 1

13

Let B_1=6, B_2=4, and B_3=3, and the condition will be satisfied.

Sample Input 2

5
12 12 12 12 12

Sample Output 2

5

We can let all B_i be 1.

Sample Input 3

3
1000000 999999 999998

Sample Output 3

996989508

Print the sum modulo (10^9+7).

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.util.*;
import java.math.*;
class Main
{
 public static BigInteger gcd(BigInteger x,BigInteger y)
{
 if(y.intValue()==0) 
 return x; 
 return gcd(y,x.remainder(y));
}
 public static void main(String args[])
 {
  Scanner sc=new Scanner(System.in);
  int i,n;
  n=sc.nextInt();
  int[] a=new int[n];
  for(i=0;i<n;i++)
  a[i]=sc.nextInt();
  BigInteger b=new BigInteger("0");
  BigInteger k=new BigInteger("0");
  BigInteger s=new BigInteger("0");
  b=BigInteger.valueOf(a[0]);
  for(i=1;i<n;i++)
  {
   k=BigInteger.valueOf(a[i]);
   b=(b.multiply(k)).divide(gcd(k,b));
  }
  for(i=0;i<n;i++)
  {
   k=BigInteger.valueOf(a[i]);
   s=s.add(b.divide(k));
  }
  s=s.remainder(new BigInteger("1000000007"));
  System.out.print(s);
 }
}