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: Wrong Answer)

n = int(input())
A = list(map(int, input().split()))
from collections import *
cmn = defaultdict(int)

def get_primes(n):
    erat = [False, False] + [True for i in range(n - 1)]
    for i in range(n + 1):
        if erat[i]:
            for j in range(i * 2, n + 1, i):
                erat[j] = False
    return [i for i in range(n + 1) if erat[i]]

primes = get_primes(1000)


def prime_factorization(n):
    d = defaultdict(int)
    def check(k):
        nonlocal d, n
        while n % k == 0:
            d[k] += 1
            n //= k
    for p in primes:
        check(p)
        if n == 1:
            break
    return d

P = [prime_factorization(a) for a in A]

for p in P:
    for k in p.keys():
        cmn[k] = max(cmn[k], p[k])

ans = 0

for p in P:
    t = 1
    for k in cmn.keys():
        t *= pow(k, max(cmn[k] - p[k], 0), 10 ** 9 + 7)

    ans += t
    ans %= 10 ** 9 + 7

print(ans)