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: Accepted)

def powmod(b,r,mod)
  a = 1
  while r > 0
    if r%2 == 1
      a = a * b % mod
    end
    b = b * b % mod
    r /= 2
  end
  a
end

def invmod(f, mod)
  powmod(f, mod-2, mod)
end

require "prime"
N,*A = `dd`.split.map &:to_i
Mod = 10**9 + 7
qs = {}
PD = A.map{ |a|
  pd = a.prime_division
  pd.each{ |q,d| qs[q] = [qs[q] || 0, d].max }
  pd
}
LCM = qs.map{ |q,d| powmod(q,d,Mod) }.reduce(1){ |a,b| a * b % Mod }
p PD.reduce(0){ |a,pd|
  divisor = pd.map{ |q,d| powmod(q,d,Mod) }.reduce(1){ |a,b| a * b % Mod }
  (a + (LCM * invmod(divisor,Mod))) % Mod
}