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.*;
import java.io.*;
import java.math.BigInteger;

public class Main{
    public static void main(String[] args) {
    	InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        Solve solver = new Solve();
        solver.solve(1, in, out);
        out.close();
    }
    static class Solve {
    	static BigInteger un = new BigInteger("0");
    	static BigInteger gcd(BigInteger a, BigInteger b) { 
        if (a.equals(un)) 
            return b;  
        return gcd(b.mod(a), a);  
        } 
        static BigInteger lcm(BigInteger a, BigInteger b) { 
            return (a.multiply(b)).divide(gcd(a, b)); 
        } 
          
    	public void solve(int testNumber, InputReader in, OutputWriter out) {
    		int n = in.nextInt();
    		BigInteger ans = new BigInteger("0");
    		BigInteger lcm1 = new BigInteger("1");
    		BigInteger[] mem = new BigInteger[n];
    		for(int i = 0;i<n;i++) {
    			BigInteger num = new BigInteger(in.next());
    			lcm1 = lcm(lcm1,num);
    			mem[i] = num;
    		}
    		for(int i = 0;i<n;i++) {
    			ans = ans.add((lcm1.divide(mem[i])));
    		}
    		System.out.println(ans.mod(new BigInteger("1000000007")));
    	}
    }
    	
    
    static class OutputWriter {
	    private final PrintWriter writer;
	
	    public OutputWriter(OutputStream outputStream) {
	        writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
	    }
	
	    public OutputWriter(Writer writer) {
	        this.writer = new PrintWriter(writer);
	    }
	
	    public void close() {
	        writer.close();
	    }
	
	    public void println(String string) {
	        writer.println(string);
	    }
	    
	    public void println(int number) {
	        writer.println(number);
	    }
	    
	    public void println(long number) {
	        writer.println(number);
	    }
	    
	    public void println(double number) {
	    	writer.println(number);
	    }
	    
	    public void print(long number) {
	        writer.print(number);
	    }
	    
	    public void print(int number) {
	        writer.print(number);
	    }
	    
	    public void print(String string) {
	        writer.print(string);
	    }
	    
	    public void print(double number) {
	    	writer.print(number);
	    }
	}
    
	static class InputReader { 
		private InputStream in;
		private byte[] buffer = new byte[1024];
		private int curbuf;
		private int lenbuf;
		
		public InputReader(InputStream in) {
			this.in = in;
			this.curbuf = this.lenbuf = 0;
		}
		
		public String nextLine() {
			StringBuilder sb = new StringBuilder();
			int b = readByte();
			while (b!=10) {
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}
		
		public boolean hasNextByte() {
			if (curbuf >= lenbuf) {
				curbuf = 0;
				try {
					lenbuf = in.read(buffer);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (lenbuf <= 0)
					return false;
			}
			return true;
		}
 
		private int readByte() {
			if (hasNextByte())
				return buffer[curbuf++];
			else
				return -1;
		}
 
		private boolean isSpaceChar(int c) {
			return !(c >= 33 && c <= 126);
		}
 
		private void skip() {
			while (hasNextByte() && isSpaceChar(buffer[curbuf]))
				curbuf++;
		}
 
		public boolean hasNext() {
			skip();
			return hasNextByte();
		}
 
		public String next() {
			if (!hasNext())
				throw new NoSuchElementException();
			StringBuilder sb = new StringBuilder();
			int b = readByte();
			while (!isSpaceChar(b)) {
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}
 
		public int nextInt() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}
 
		public long nextLong() {
			if (!hasNext())
				throw new NoSuchElementException();
			int c = readByte();
			while (isSpaceChar(c))
				c = readByte();
			boolean minus = false;
			if (c == '-') {
				minus = true;
				c = readByte();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res = res * 10 + c - '0';
				c = readByte();
			} while (!isSpaceChar(c));
			return (minus) ? -res : res;
		}
		
		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;
		}
 
		public char[][] nextCharMap(int n, int m) {
			char[][] map = new char[n][m];
			for (int i = 0; i < n; i++)
				map[i] = next().toCharArray();
			return map;
		}
	}
}