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: Wrong Answer)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

public class Main {
  private static class FastScanner {
    private BufferedReader reader = null;
    private StringTokenizer tokenizer = null;

    public FastScanner(InputStream in) {
      reader = new BufferedReader(new InputStreamReader(in));
      tokenizer = null;
    }

    public String next() {
      if (tokenizer == null || !tokenizer.hasMoreTokens()) {
        try {
          tokenizer = new StringTokenizer(reader.readLine());
        } catch (IOException e) {
          throw new RuntimeException(e);
        }
      }
      return tokenizer.nextToken();
    }

    public String nextLine() {
      if (tokenizer == null || !tokenizer.hasMoreTokens()) {
        try {
          return reader.readLine();
        } catch (IOException e) {
          throw new RuntimeException(e);
        }
      }

      return tokenizer.nextToken("\n");
    }

    public long nextLong() {
      return Long.parseLong(next());
    }

    public int nextInt() {
      return Integer.parseInt(next());
    }

    public double nextDouble() {
      return Double.parseDouble(next());
    }

    public int[] nextIntArray(int n) {
      int[] a = new int[n];
      for (int i = 0; i < n; i++)
        a[i] = nextInt();
      return a;
    }

    public long[] nextLongArray(int n) {
      long[] a = new long[n];
      for (int i = 0; i < n; i++)
        a[i] = nextLong();
      return a;
    }
  }

  private static final long mod = 1000_000_007L;

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

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

  private static long modinv(long a) {
    long b = mod;
    long u = 1L;
    long v = 0L;
    while (b > 0) {
      long t = a / b;
      a -= t * b;
      long temp = a;
      a = b;
      b = temp;
      u -= t * v;
      temp = u;
      u = v;
      v = temp;
    }
    u %= mod;
    if (u < 0) u += mod;
    return u;
  }

  public static void main(String[] args) {
    FastScanner sc = new FastScanner(System.in);
    int n = sc.nextInt();
    long[] a = sc.nextLongArray(n);
    long g = 1;
    for (int i = 0; i < n; i++) g = lcm(g, a[i]);
    g %= mod;
    long sum = 0;
    for (int i = 0; i < n; i++) {
      sum += g * modinv(a[i]) % mod;
      sum %= mod;
    }
    System.out.println(sum < 0 ? sum + mod : sum);
  }
}