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)

"""
the condition is quite simple actually.
each element of A and B must multiply to the same value.
to minimise the total of B, simply make that value as small
as possible (since A is fixed).

lcm(2, 3, 4) = 12
therefore B is
12/2, 12/3, 12/4
and the sum of B is
12/2 + 12/3 + 12/4

lcd of a list is loop: lcd(partial, new_value)
lcd(a, b) = ab / gcd(a, b)
"""

def gcd(x, y):
  return 1


def lcm(list_ints):
    lcm_ongoing = 1
    for val in list_ints:
        lcm_ongoing = int(round(val*lcm_ongoing/gcd(val, lcm_ongoing)))
    return lcm_ongoing


def flatten(N, A):
    # get lcm
    lcm_of_A = lcm(A)
    # get sum of lcm/values
    ans = sum(int(round(lcm_of_A/value)) for value in A)
    modulo_value = int(int(10e9)+7)
    return ans % modulo_value


if __name__ == "__main__":
    test1 = \
"""3
2 3 4"""
    test2 = \
"""5
12 12 12 12 12"""
    test3 = \
"""3
1000000 999999 999998"""
    test = test3
    # N = int(test.split("\n")[0])
    # A = list(map(int, test.split("\n")[1].split()))
    N = int(input())
    A = list(map(int, input().split()))
    print(flatten(N, A))