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 PHP7 (7.0.15) (judge verdict: Time Limit Exceeded)

<?php

const MOD = 10 ** 9 + 7;

list($n) = explode(' ', trim(fgets(STDIN)));
$a_list = explode(' ', trim(fgets(STDIN)));

$numbers = range(3, 10 ** 3, 2);
$prime_numbers = [2];
while (count($numbers) > 0) {
    $prime = array_shift($numbers);
    $prime_numbers[] = $prime;
    foreach ($numbers as $key => $number) {
        if ($number % $prime === 0) {
            unset($numbers[$key]);
        }
    }
}

$prime_factorized_a_list = array_map(function ($a) use ($prime_numbers) {
    $prime_factorized_a = [];

    foreach ($prime_numbers as $prime) {
        $expo = 0;
        while ($a % $prime === 0) {
            ++$expo;
            $a /= $prime;
        }
        $prime_factorized_a[$prime] = $expo;
        if ($a === 1) {
            break;
        }
    }

    if ($a > 1) {
        $prime_factorized_a[$a] = 1;
    }

    return $prime_factorized_a;
}, $a_list);

$prime_factorized_lcm = array_reduce($prime_factorized_a_list, function ($carry, $a) {
    $ret = [];
    foreach ($carry as $prime_number => $expo) {
        if (isset($a[$prime_number]) && $expo < $a[$prime_number]) {
            $ret[$prime_number] = $a[$prime_number];
        } else {
            $ret[$prime_number] = $expo;
        }
    }
    foreach ($a as $prime_number => $expo) {
        if (!isset($ret[$prime_number])) {
            $ret[$prime_number] = $expo;
        }
    }

    return $ret;
}, []);

$b_list = array_map(function ($a) use ($prime_factorized_lcm) {
    $b = 1;
    foreach ($prime_factorized_lcm as $prime_number => $expo) {
        $b_expo = isset($a[$prime_number]) ? $expo - $a[$prime_number] : $expo;
        $b = $b * ($prime_number ** $b_expo) % MOD;
    }
    return $b;
}, $prime_factorized_a_list);

$answer = array_reduce($b_list, function ($carry, $b) {
    return ($carry + $b) % MOD;
}, 0);

echo $answer;