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 fractions import gcd
import time
n = int(input())
a = list(map(int, input().split()))
t1 = time.time()
mod = 10**9+7
def modinv(a, mod=10**9+7):
    return pow(a, mod-2, mod)
g = 1
flag = 1
for i in range(n):
    g = a[i] * g // gcd(a[i], g)
    #g %= mod
    t2 = time.time()
    if t2 - t1 > 0.8:
        flag = 0
        break

if flag == 1:
    ans = 0
    for i in range(n):
        ans += g * modinv(a[i])
        ans %= mod
    print(ans)

else:
    ans = 0

    for i in range(n):
        g = 1
        for j in range(n):
            if i == j:
                continue
            else:
                g *= a[j]
                g %= mod
        ans += g
    print(ans%mod)