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.*;

public class Main {
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    long MOD = (long)Math.pow(10, 9) + 7;
    long[] a = new long[n];
    HashMap[] map = new HashMap[n];
    HashMap<Long, Long> map0 = new HashMap<Long, Long>();
    for(int i = 0; i < n; i++) {
      long t = sc.nextLong();
      a[i] = t;
      HashMap<Long, Long> m = new HashMap<Long, Long>();
      for(long j = 2; (j * j) <= t; j++) {
        long k = 0;
        while((t % j) == 0) {
          k++;
          t /= j;         
        }
        if(k > 0) {
          m.put(j, k);
          if(map0.containsKey(j)) {
            map0.put(j, Math.max(map0.get(j), k));
          } else {
            map0.put(j, k);
          }
        }
      }
      if(t > 0) {
        m.put(t, (long)1);
        if(map0.containsKey(t)) {
          map0.put(t, Math.max(map0.get(t), 1));
        } else {
          map0.put(t, (long)1);
        }        
      }
      map[i] = m;
    }

    long ans = 0;
/**    for(int i = 0; i < n; i++) {
      HashMap<Long, Long> m = map[i];
      long t = 1;
      for(long key : map0.keySet()) {
        long p1 = map0.get(key);
        long p2 = 0;
        if(m.containsKey(key)) p2 = m.get(key);
        t = (t * (long)Math.pow(key, p1 - p2)) % MOD;
      }
      ans = (ans + t) % MOD;
    } */

    for(int i = 0; i < n; i++) {
      long t = 1;
      for(long key : map0.keySet()) {
        long p1 = map0.get(key);
        long p2 = 0;
        while((a[i] % key) == 0) {
          p2++;
          a[i] /= key;
        }
        t = (t * (long)Math.pow(key, p1 - p2)) % MOD;
      }
      ans = (ans + t) % MOD;
    }

    System.out.println(ans);
  }
}