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 (3.8.2) (judge verdict: Time Limit Exceeded)

from sys import setrecursionlimit, exit
setrecursionlimit(1000000000)

def main():
    MOD = 10 ** 9 + 7
    n = int(input())
    a = list(map(int, input().split()))
    a.sort()
    prime = [True] * (a[-1] + 1)
    prime[0] = False
    prime[1] = False
    for i in range(len(prime)):
        if prime[i] == False:
            continue
        j = i * 2
        while j <= a[-1]:
            prime[j] = False
            j += i
    lst = []
    for i, v in enumerate(prime):
        if v:
            lst.append([i, 0])
    for i in a:
        for j, v in enumerate(lst):
            c = 0
            while i >= v[0]:
                if i % v[0] != 0:
                    break
                i //= v[0]
                c += 1
            if lst[j][1] < c:
                lst[j][1] = c
    ans = 0
    for i in a:
        d = 1
        for j, v in enumerate(lst):
            c = 0
            while i >= v[0]:
                if i % v[0] != 0:
                    break
                i //= v[0]
                c += 1
            d *= v[0] ** (v[1] - c) % MOD
        ans = (ans + d) % MOD
    print(ans)

main()