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: Wrong Answer)

require 'prime'
M=10**9+7
ps=Prime.take_while{|e| e<=1000 }
ps2={1=>1}
gets
as=gets.split.map &:to_i
lexs=[0]*ps.size
s=0
as.each{|e|
  t=1
  ps.each_with_index{|q,i|
    r=0
    while e%q==0
      e/=q
      r+=1
    end
    if lexs[i]<r
      s=s*q**(r-lexs[i])%M
      lexs[i]=r
    elsif lexs[i]>r
      t=t*q**(lexs[i]-r)%M
    end
  }
  if !ps2[e]
    s=s*e%M
    ps2[e]=1
  end
  s=(s+t)%M
}
puts s