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 Pascal (FPC 2.6.2) (judge verdict: Wrong Answer)

Var a:Array[1 .. 100000] of Longint;
    ans,sum:Int64;
    n,i:Longint;
Function gcd(a,b:Int64):Int64;
    Begin
        If b = 0 then exit(a); 
        Exit(gcd(b, a mod b)); 
    End;
Begin
    Readln(n);
    For i:=1 to n do read(a[i]);
    ans:=a[1];
    For i:=2 to n do ans:=(((a[i] * ans)) div (gcd(a[i], ans)));
    For i:=1 to n do sum:=(sum+ans div a[i]) mod 1000000007;
    Writeln(sum);
End.