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 Go (1.6) (judge verdict: Accepted)

// Package main provides
//
// File:  main.go
// Author: ymiyamoto
//
// Created on Sun Feb  2 11:20:26 2020
//
package main

import (
	"fmt"
	"math/big"
)

const MOD = 1e9 + 7

var N int
var A []*big.Int

func solve() int64 {
	mod := big.NewInt(MOD)

	lcm := big.NewInt(A[0].Int64())
	for _, a := range A {
		g := big.NewInt(0).GCD(nil, nil, lcm, a)
		lcm.Mul(lcm, a)
		lcm.Div(lcm, g)
	}

	ans := big.NewInt(0)
	for _, a := range A {
		x := big.NewInt(0).Div(lcm, a)
		ans.Add(ans, x)
	}
	return ans.Mod(ans, mod).Int64()
}

func main() {
	fmt.Scan(&N)
	A = make([]*big.Int, N)
	for i := range A {
		var a int64
		fmt.Scan(&a)
		A[i] = big.NewInt(a)
	}

	fmt.Println(solve())
}