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: Wrong Answer)

package main

import (
	"fmt"
	"math"
	"math/big"
)

func main() {
	solve()
}

func solve() {
	BBB := 1000000007
	var n int
	fmt.Scan(&n)
	a := make([]int, n)
	lcm := 1
	for i := 0; i < n; i++ {
		fmt.Scan(&a[i])
		lcm = (lcm * a[i] / gcd(lcm, a[i])) // % BBB
	}
	sum := 0
	for i := 0; i < n; i++ {
		sum = (sum + lcm/a[i]) % BBB
	}
	fmt.Print(sum)
}

func max(x int, y ...int) int {
	res := float64(x)
	for _, z := range y {
		res = math.Max(res, float64(z))
	}
	return int(res)
}

func min(x int, y ...int) int {
	res := float64(x)
	for _, z := range y {
		res = math.Min(res, float64(z))
	}
	return int(res)
}

func abs(x int) int {
	return int(math.Abs(float64(x)))
}

func sqrt(x int) int {
	return int(math.Sqrt(float64(x)))
}

func int2Int(x int) big.Int {
	var res big.Int
	res.SetInt64(int64(x))
	return res
}

func gcd(x, y int) int {
	var m, n int
	if x > y {
		m = x
		n = y
	} else {
		m = y
		n = x
	}
	for m%n != 0 {
		var tmp int
		tmp = m % n
		m = n
		n = tmp
	}
	return n
}