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 mod_inv(a, m):
    return pow(a, m-2, m)


MOD = 10**9+7
MX = 10**6+5
N = int(input())
A = list(map(int, input().split()))


P = defaultdict(int)

for a in set(A):
    e = defaultdict(int)
    rest = a
    for i in range(2, a + 1):
        while rest % i == 0:
            e[i] += 1
            rest //= i
    for k, v in e.items():
        P[k] = max(P[k], v)

lcm = 1
for k, v in P.items():
    lcm *= k ** v
    lcm %= MOD

ans = 0
for a in A:
    ans += lcm * mod_inv(a, MOD)
    ans %= MOD

print(int(ans))