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 'prime'
n = gets.to_i
a = gets.split.map{|e| e.to_i.prime_division.to_h}

h = Hash.new(0)
a.each do |e|
    e.each do |arr|
        h[arr[0]] = arr[1] if h[arr[0]] < arr[1]
    end
end

ans = 0
mod = 10 ** 9 + 7
n.times do |i|
    x = 1
    h.keys.each do |key|
        x = x * key ** (h[key] - (a[i][key] ? a[i][key] : 0)) % mod
    end
    ans = (ans + x) % mod
end

puts ans