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.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;

public class Main {

	public static void main(String[] args) throws Exception {
		// TODO Auto-generated method stub
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter out = new PrintWriter(System.out);
		StringTokenizer st;
		st = new StringTokenizer(br.readLine());
		int n = Integer.parseInt(st.nextToken());
		st = new StringTokenizer(br.readLine());
		int a[] = new int[n];
		long pre = Integer.parseInt(st.nextToken());
		n--;
		a[n] = (int) pre;
		while(n-->0) {
			a[n] = Integer.parseInt(st.nextToken());
			pre = lcm(a[n],pre);
		}
		int cnt = 0;
		for(int e:a) {
			cnt = (int) ((cnt+pre/e)%(1e9+7));
		}
		out.println(cnt);
		out.flush();
	}
	static long gcd(long n, long m) {
		if(n == 0)
			return m;
		return gcd(m % n, n);
	}
	static long lcm(long n, long m) {
		return (n*m)/gcd(n, m);
	}
}