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 C (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>
long mod(long x){
    long tmp=1;
    for(int i=0;i<9;i++)tmp=tmp*10;
    return x%(tmp+7);
}

long uci(long x,long y){
    if(x<y){
        long tmp=x;
        x=y;
        y=tmp;
    }
    if(x%y ==0){
        return y;
    }else{
        return uci(y,x%y);
    }
}

int main(){
    int n;
    scanf("%d",&n);
    long a[n];
    long b[n];
    long tmp;
    for(int i=0;i<n;i++){
        scanf("%ld",&a[i]);
        b[i]=1;
    }
    for(int i=0;i<n;i++){
        long gcd=uci(a[i],b[i]);
        long point=a[i]/gcd;
        b[i]=b[i]/gcd;
        for(int j=0;j<n;j++){
            if(j!=i)b[j]=mod(b[j])*mod(point);
        }
    }
    long ans=0;
    for(int i=0;i<n;i++){
        ans=mod(ans+b[i]);
    }
    printf("%ld",ans);
    return 0;
}