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: Accepted)

from fractions import gcd
from functools import reduce
N = int(input())
A = list(map(int, input().split()))
MOD = 10 ** 9 + 7

def lcm(a,b):
    return (a * b // gcd(a, b))

def modpow(a, n, mod): # a^n mod
    result = 1
    while n > 0:
        if n & 1: result = result * a % mod
        a = a * a % mod
        n >>= 1
    return result

h = reduce(lcm, A)
B = [h * modpow(A[i], MOD-2, MOD) for i in range(N)]
print(sum(B) % MOD)