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: Runtime Error)

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

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


def main()
  n= gets.to_i
  a= gets.chomp.split(" ").map(&:to_i)
  mod=1e9+7
  lcmNum=1
  a.each do |i|
    lcmNum=lcm(lcmNum, i).to_i;
  end
  ans=0
  a.each do |i|
    ans+=lcmNum.to_i/i;
    ans%=mod; 
  end
  puts ans.to_i
end

main()