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: Time Limit Exceeded)

n,*aa = map(int, open(0).read().split())
MOD = 10**9+7

from collections import Counter
from math import sqrt, ceil
def factors(x):
    c = Counter()
    while x % 2 == 0:
        c[2] += 1
        x //= 2
    for i in range(3, ceil(sqrt(x)) + 2, 2):
        while x % i == 0:
            c[i] += 1
            x //= i
    if x > 1:
        c[x] += 1
    return c

factors_of_aa = list(map(factors, aa))

lcm = Counter()
for factors_of_a in factors_of_aa:
    lcm |= factors_of_a

ans = 0
for factors_of_a in factors_of_aa:
    factors_to_add = lcm - factors_of_a
    to_add = 1
    for factor, cnt in factors_to_add.items():
        to_add *= pow(factor, cnt, MOD)
        to_add %= MOD
    ans += to_add
    ans %= MOD

print(ans)