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 (7.3.0) (judge verdict: Accepted)

import sys
from collections import defaultdict, Counter

read = sys.stdin.read
readline = sys.stdin.readline
readlines = sys.stdin.readlines
sys.setrecursionlimit(10 ** 9)
INF = 1 << 60
MOD = 1000000007

def main():
    N, *A = map(int, read().split())
    
    N_MAX = 10 ** 6

    min_factor = [0] * (N_MAX + 1)
    min_factor[1] = 1
    for i in range(2, N_MAX + 1):
        if min_factor[i]:
            continue
        for j in range(i, N_MAX + 1, i):
            if not min_factor[j]:
                min_factor[j] = i


    def prime_factorize_fast(n):
        a = Counter()
        while n != 1:
            f = min_factor[n]
            p = 0
            while min_factor[n] == f:
                p += 1
                n //= f
            a[f] = p

        return a

    lcm_prime = Counter()
    for a in A:
        for p, n in prime_factorize_fast(a).items():
            if lcm_prime[p] < n:
                lcm_prime[p] = n

    l = 1
    for p, n in lcm_prime.items():
        l = l * pow(p, n, MOD) % MOD

    ans = 0
    for a in A:
        ans = (ans + pow(a, MOD - 2, MOD)) % MOD

    ans = ans * l % MOD

    print(ans)
    return


if __name__ == '__main__':
    main()