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 (3.4.3) (judge verdict: Time Limit Exceeded)

def prime(x):
    y = list(range(1, x + 1))
    y[0] = 0
    x_sqrt = x ** 0.5
    for i in y:
        if i > x_sqrt:
            break
        elif i == 0:
            continue
        for not_prime in range(2 * i, x + 1, i):
            y[not_prime - 1] = 0
    return [i for i in y if i > 0]

def prime_factrize(a, prime):
    x = []
    for p in prime:
        n = 0
        while a % p == 0:
            a = a // p
            n += 1
        x.append(n)
    return x

def lcm_prime(a, b):
    return list(map(max, zip(a, b)))

MOD = 10 ** 9 + 7
n = int(input())
a = list(map(int, input().split()))
prime_list = prime(max(a))
a_prime = []
l_prime = [0 for _ in range(len(prime_list))]

for ai in a:
    a_prime.append(prime_factrize(ai, prime_list))
    l_prime = lcm_prime(l_prime, a_prime[-1])

ans = 0
for ai in a_prime:
    x = 1
    for ap, lp, p in zip(ai, l_prime, prime_list):
        x *= pow(p, lp - ap, MOD)
        x %= MOD
    ans += x
    ans %= MOD
print(ans)