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'

MOD=1000000007

def gcd(a,b)
    return a if b == 0
    gcd(b,a%b)
end

def lcm(a,b)
    a * b / gcd(a,b)
end

n=gets.to_i
a=gets.chomp.split.map(&:to_i)
h = Hash.new(0)
a.each do |i|
  tt = i.prime_division
  tt.each do |s,t|
    if h[s] < t
      h[s] = t
    end
  end
end

ans=0
a.each do |i|
  tt = i.prime_division
  hh = Hash.new(0)
  tt.each do |s,t|
    hh[s] = t
  end
  tmp=1
  h.each do |k,v|
    if h[k] > hh[k]
      (h[k]-hh[k]).times do
        tmp *= k
        tmp %= MOD
      end
    end
  end
  ans += tmp
  ans %= MOD
end


puts ans