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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

def main():
  MOD=10**9+7
  import sys
  input = sys.stdin.readline
  N=int(input())
  A=list(map(int,input().split()))
  def lcm(a,N):
      from fractions import gcd
      x = a[0]
      y=  a[N//2]
      for i in range(1, N//2):
          x = (x * a[i]) // gcd(x, a[i])
          y = (y * a[i+N//2]) // gcd(y, a[i+N//2])
      y = (y * a[-1]) // gcd(y, a[-1])
      return (x*y)//gcd(x,y)
  z=lcm(A,N)
  ans=0
  import numpy as np
  A=np.array(A)
  ans=0
  for i in range(N):
    ans+=z//A[i]
  print(ans%MOD)
  
if __name__=='__main__':
  main()