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)

import sys
 
input = sys.stdin.readline
 
ri = lambda: int(input())
rs = lambda: input().rstrip()
ril = lambda: list(map(int, input().split()))
rsl = lambda: input().rstrip().split()
ris = lambda n: [ri() for _ in range(n)]
rss = lambda n: [rs() for _ in range(n)]
rils = lambda n: [ril() for _ in range(n)]
rsls = lambda n: [rsl() for _ in range(n)]
 
import sys
import numpy as np
import fractions
 
from functools import reduce
 
def lcm_base(x, y):
    return (x * y) // fractions.gcd(x, y)
 
def lcm(*numbers):
    return reduce(lcm_base, numbers, 1)
 
def lcm_list(numbers):
    ans = 1
    for num in numbers:
        ans = ans * num // fractions.gcd(ans,num)
    return ans
 
def LI():
  return [int(s) for s in input().split()]
 
input = sys.stdin.readline
ri = lambda: int(input())
ril = lambda: list(map(int, input().split()))
 
N = ri()
A_s = ril()
mod = 10**9 + 7
 
#l = lcm_list(A_s)
l = 1
for num in A_s:
    l = l * num // fractions.gcd(l,num)

print(sum(map(lambda x : l//x, A_s)) % mod)