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: Runtime Error)

import sys
def gcd(x, y):
    while y != 0:
        (x, y) = (y, x % y)
    return x
n=int(input())
if n==0:
  print(0)
  sys.exit()
else:
  c=list(map(int,input().split()))


v=[]


if len(c)==1:
  print(c[0] % (pow(10,9)+7))
elif len(c)==2:
  q=gcd(c[0],c[1])
  lcm=int(c[0]*c[1]/q)
  v=sum([int(lcm/c[0]),int(lcm/c[1])])
  print(v% (pow(10,9)+7))
else:
  q=gcd(c[0],c[1])
  lcm=int(c[0]*c[1]/q)
  for i in range(2,n):
    lcm=int(lcm*c[i]/(gcd(lcm,c[i])))
  
  for i in range(n):
    v.append(int(lcm/c[i]))
  g=sum(v)
  print(g % (pow(10,9)+7))