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: Accepted)

# import 周り
from fractions import gcd

# 定数関係
mod = 10 ** 9 + 7

# 補助関数
def inv(a):
    b, u, v = mod, 1, 0
    while b != 0:
        t = a // b
        a, b = b, a - t * b
        u, v = v, u - t * v
        if u < 0: u += mod
    return u

if __name__ == '__main__':
    #入力関係
    n = int(input())
    A = list(map(int, input().split()))

    V = 1
    U = 0
    for ele in A:
      V = V * ele // gcd(V, ele) # LCMを計算
      U += inv(ele)
    V %= mod
    print(U * V % mod)