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>
//#include <stdlib.h>
//#include <string.h>
//#include <stdbool.h>
//#include <limits.h>
//#include <math.h>

#define MOD 1000000007

long gcd(long a, long b) {
  if (b == 0) return a;
  return gcd(b, a%b);
}

long lcm(long a, long b) {
  long g = gcd(a, b);
  return a*b/g;
}

int main() {
  int n;
  scanf("%d", &n);
  long a[n], ans = 0;
  for (int i=0; i<n; i++)
    scanf("%ld", a+i);
  long l = a[0];
  for (int i=1; i<n; i++)
    l = lcm(a[i], l);
  for (int i=0; i<n; i++) {
    ans += l/a[i];
    ans %= MOD;
  }
  printf("%ld\n", ans);
  return 0;
}