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 (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

func newScanner() *bufio.Scanner {
	scanner := bufio.NewScanner(os.Stdin)
	scanner.Split(bufio.ScanWords)
	// buf := make([]byte, 10000)
	// scanner.Buffer(buf, 1000000)
	return scanner
}

func scanInt(s *bufio.Scanner) int {
	if s.Scan() {
		t := s.Text()
		if v, err := strconv.Atoi(t); err == nil {
			return v
		}
		panic(fmt.Sprintln("Could't scan int from input", t))
	}
	panic(s.Err())
}

func pow(p, n, m int64) int64 {
	if n == 0 {
		return 1
	}
	r := pow(p, n/2, m) % m
	r *= r
	r %= m
	if n&1 == 1 {
		r *= p
		r %= m
	}
	return r
}

func main() {
	const m int64 = 1000000007
	sc := newScanner()
	n := scanInt(sc)
	a := make([]int, n)
	maxA := 0
	for i := 0; i < n; i++ {
		a[i] = scanInt(sc)
		if a[i] > maxA {
			maxA = a[i]
		}
	}

	if maxA > 1000 {
		// A <= 10^6
		maxA = 1000
	}

	p := []int{2}
	for i := 3; i <= maxA; i++ {
		isPrime := true
		for _, x := range p {
			if i%x == 0 {
				isPrime = false
				break
			}
		}
		if isPrime {
			p = append(p, i)
		}
	}

	lcm := make(map[int]int)
	l := make([]map[int]int, n)
	for i := 0; i < n; i++ {
		l[i] = make(map[int]int)

		for j := 0; j < len(p); j++ {
			r := a[i] % p[j]
			if r == 0 {
				x := a[i] / p[j]
				d := 1
				for x%p[j] == 0 {
					x /= p[j]
					d++
				}
				l[i][j] = d
				if lcm[j] < d {
					lcm[j] = d
				}
			}

		}
	}

	var res int64 = 0
	for i := 0; i < n; i++ {
		var b int64 = 1
		for j, v := range lcm {
			b *= pow(int64(p[j]), int64(v-l[i][j]), m)
			b %= m
		}
		res += b
	}

	res %= m
	fmt.Println(res)
}