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: Time Limit Exceeded)

from collections import defaultdict


def factorize(n: int) -> dict:
    f = defaultdict(int)
    while n % 2 == 0:
        f[2] += 1
        n //= 2
    p = 3
    while p * p <= n:
        while n % p == 0:
            f[p] += 1
            n //= p
        p += 2
    if n != 1:
        f[n] += 1
    return f


def _pow(b, p, mod):
    ret = 1
    while p:
        if p % 2 == 1:
            ret *= b
            ret %= mod
        b **= 2
        p //= 2
    return ret


MOD = 10**9 + 7
n = int(input())
a = tuple(map(int, input().split()))

a_fac = []
lcm_fac = defaultdict(int)
for a_i in a:
    a_fac_i = factorize(a_i)
    a_fac.append(a_fac_i)
    for k, v in a_fac_i.items():
        lcm_fac[k] = max(lcm_fac[k], v)

# print(lcm_fac)
ans = 0
for a_fac_i in a_fac:
    b_i = 1
    for k, v in lcm_fac.items():
        b_i *= _pow(k, v - a_fac_i[k], MOD)
        b_i %= MOD
    # print(i, a[i], b_i)
    ans += b_i
    ans %= MOD

print(ans)