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 (2.7.1) (judge verdict: Time Limit Exceeded)

def prime_factor(n)
  prime = []
  2.upto(n) do |i|
    break unless i <= n / i
    while (n % i).zero?
      prime << i
      n /= i
    end
  end
  prime << n unless n == 1
  prime
end

M=10**9+7
N=gets.to_i
A=gets.split.map(&:to_i)

lcm=Hash.new{|h,k|h[k]=0}
m=Array.new(N){Hash.new{|h,k|h[k]=0}}
A.each.with_index do |a,i|
  prime_factor(a).each do |x|
    m[i][x]+=1
  end
  m[i].each do |k,v|
    lcm[k]=[lcm[k],v].max
  end
end

ans=0
m.each do |h|
  b=1
  lcm.each do |k,v|
    b*=k**(v-h[k])
    b%=M
  end
  ans+=b
  ans%=M
end
p ans