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

import (
	"bufio"
	_ "container/heap"
	"fmt"
	"os"
	_ "sort"
	"strconv"
)

// I/O
type Scanner struct {
	sc *bufio.Scanner
}

func NewScanner() *Scanner {
	sc := bufio.NewScanner(os.Stdin)
	sc.Split(bufio.ScanWords)
	sc.Buffer(make([]byte, 1024), int(1e+9))
	return &Scanner{sc}
}

func (s *Scanner) nextStr() string {
	s.sc.Scan()
	return s.sc.Text()
}

func (s *Scanner) nextInt() int {
	i, e := strconv.Atoi(s.nextStr())
	if e != nil {
		panic(e)
	}
	return i
}

func (s *Scanner) nextFloat() float64 {
	f, e := strconv.ParseFloat(s.nextStr(), 64)
	if e != nil {
		panic(e)
	}
	return f
}

func (s *Scanner) nextRuneSlice() []rune {
	return []rune(s.nextStr())
}

func (s *Scanner) nextIntSlice(n int) []int {
	res := make([]int, n)
	for i := 0; i < n; i++ {
		res[i] = s.nextInt()
	}
	return res
}

func (s *Scanner) nextFloatSlice(n int) []float64 {
	res := make([]float64, n)
	for i := 0; i < n; i++ {
		res[i] = s.nextFloat()
	}
	return res
}

// Arithmetic
func max(nums ...int) int {
	m := nums[0]
	for _, i := range nums {
		if m < i {
			m = i
		}
	}
	return m
}

func min(nums ...int) int {
	m := nums[0]
	for _, i := range nums {
		if m > i {
			m = i
		}
	}
	return m
}

func abs(x int) int {
	if x > 0 {
		return x
	}
	return -x
}

func pow(x, y int) int {
	res := 1
	for i := 0; i < y; i++ {
		res *= x
	}
	return res
}

func ceil(a, b int) int {
	if a%b == 0 {
		return a / b
	} else {
		return a/b + 1
	}
}

func gcd(a, b int) int {
	if b == 0 {
		return a
	}
	return gcd(b, a%b)
}

func lcm(a, b int) int {
	return a / gcd(a, b) * b
}

// Sort
type RuneSlice []rune

func (a RuneSlice) Len() int           { return len(a) }
func (a RuneSlice) Less(i, j int) bool { return a[i] < a[j] }
func (a RuneSlice) Swap(i, j int)      { a[i], a[j] = a[j], a[i] }

// Main
const MOD = int(1e+9) + 7
const INF = 1 << 60

func main() {
	sc := NewScanner()
	wtr := bufio.NewWriter(os.Stdout)
	defer wtr.Flush()
	N := sc.nextInt()
	A := make([]map[int]int, N)
	AA := make([]int, N)
	for i := 0; i < N; i++ {
		a := sc.nextInt()
		A[i] = primeFactors(a)
		AA[i] = a
	}
	G := make(map[int]int)
	for i := 0; i < N; i++ {
		for k, v := range A[i] {
			if G[k] < v {
				G[k] = v
			}
		}
	}
	gcd := 1
	for k, v := range G {
		gcd *= modPow(k, v, MOD)
		gcd %= MOD
	}
	ans := 0
	for i := 0; i < N; i++ {
		res := 1
		res *= gcd * modInv(AA[i], MOD) % MOD
		res %= MOD
		ans += res
		ans %= MOD
	}

	fmt.Fprintln(wtr, ans)
}

func primeFactors(n int) map[int]int {
	pfs := make(map[int]int)
	for n%2 == 0 {
		pfs[2]++
		n = n / 2
	}
	for i := 3; i*i <= n; i = i + 2 {
		for n%i == 0 {
			pfs[i]++
			n = n / i
		}
	}
	if n > 2 {
		pfs[n]++
	}

	return pfs
}

func modPow(a, n, mod int) int {
	res := 1
	for n > 0 {
		if (n & 1) > 0 {
			res = res * a % mod
		}
		a = a * a % mod
		n >>= 1
	}
	return res
}

func modInv(a, mod int) int {
	b := mod
	u := 1
	v := 0
	for b > 0 {
		t := a / b
		a -= t * b
		a, b = b, a
		u -= t * v
		u, v = v, u
	}
	u %= mod
	if u < 0 {
		u += mod
	}
	return u
}