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"
	"fmt"
	"math/big"
	"os"
	"strconv"
)

func main() {
	bigIntP := big.NewInt(1000000007)

	N := readInt()
	A := make([]*big.Int, N)
	for i := 0; i < N; i++ {
		A[i] = big.NewInt(int64(readInt()))
	}

	v := big.NewInt(1)
	for i := 0; i < N; i++ {
		gcd := new(big.Int).GCD(nil, nil, v, A[i])
		v.Mul(v, A[i])
		v.Div(v, gcd)
	}

	result := big.NewInt(0)
	for i := 0; i < N; i++ {
		t := new(big.Int).Div(v, A[i])
		result.Add(result, t)
	}
	result.Rem(result, bigIntP)

	fmt.Println(result)
}

const (
	ioBufferSize = 1 * 1024 * 1024 // 1 MB
)

var stdinScanner = func() *bufio.Scanner {
	result := bufio.NewScanner(os.Stdin)
	result.Buffer(make([]byte, ioBufferSize), ioBufferSize)
	result.Split(bufio.ScanWords)
	return result
}()

func readString() string {
	stdinScanner.Scan()
	return stdinScanner.Text()
}

func readInt() int {
	result, err := strconv.Atoi(readString())
	if err != nil {
		panic(err)
	}
	return result
}