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: Runtime Error)

import fractions


def lcm(x, y):
    return (x * y) // fractions.gcd(x, y)


n = int(input())
a = list(map(int, input().split()))
mod = 1000000007

lcm_pre = lcm(a[0], a[1])
lcm_current = lcm_pre
ans = lcm_current // a[0]
ans += lcm_current // a[1]

if n == 1:
    print(a[0] % mod)
    exit()
elif n == 2:
    print(ans % mod)
    exit()

for i in range(2, n):
    lcm_current = lcm(lcm_pre, a[i])
    if lcm_current != lcm_pre:
        ans *= lcm_current // lcm_pre
        lcm_pre = lcm_current % mod
    ans += lcm_current // a[i]
    ans %= mod
print(ans % mod)