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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

#require 'pp'
require 'prime'

MOD = 10 ** 9 + 7
n = gets.chomp!.to_i
a_n = gets.chomp!.split.map(&:to_i)

max = Hash.new(0)

primes = []
a_n.each do |a|
    prime = Prime.prime_division(a)
    prime.each do |n, cnt|
        max[n] = max[n] > cnt ? max[n] : cnt
    end
    primes << prime.to_h
end

memo = {}
max.each do |x, y|
    memo[x] = []
    memo[x][0] = 1
    1.upto(y) do |i|
        memo[x][i] = memo[x][i - 1] * x 
    end
end

#pp memo

total = 0
primes.each do |prime|
    sum = 1
    max.each do |n, cnt|
        sum = sum * memo[n][cnt - (prime[n] || 0)] % MOD
    end

    total = (total + sum) % MOD
end

puts total