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 PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

import fractions
from functools import reduce

def lcm_base(x, y):
  return (x*y) // fractions.gcd(x,y)
def lcm_list(numbers):
  return reduce(lcm_base,numbers,1)

N=int(input())
alist=list(map(int,input().split()))

if N==1:
  print(1)
else:
  alist.sort()
  lcm_alist=lcm_list(alist)
  
  answer=0
  last_a=-1
  last_b=-1
  for a in alist:
    b=last_b
    if a!=last_a:
      b=lcm_alist//a
      last_b=b

    answer=(answer+b)%(10**9+7)
    
  #print(blist)
  print(answer)