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: Time Limit Exceeded)

from fractions import gcd
from functools import reduce

def lcm_pair(a, b):
    return int((a * b) // gcd(a, b))

def lcm(nums):
    if len(nums) > 1:
        l = lcm_pair(nums[0], nums[1])
        for num in nums[2:]:
            l = lcm_pair(l, num)
        return l
    else:
        return nums[0]

def gcd_list(nums):
    g = gcd(nums[0], nums[1])
    for num in nums[2:]:
        g = gcd(g, num)
    return g

def solve(n, a):
    if n == 1:
        return [1]
    elif n == 2:
        return a
    elif len(set(a)) == 1:
        return [1] * n
    else:
        b = [a[1]] + [lcm_pair(a[i-1], a[i+1]) for i in range(1, n-1)] + [a[-2]]
        gcd_b = gcd_list(b)
        b = [int(x // gcd_b) for x in b]
        c = lcm(list(map(lambda x, y: x * y, a, b)))
        b = [int(c // x) for x in a]
        gcd_b = gcd_list(b)
        return [int(x // gcd_b) for x in b]

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

print(sum(solve(n, a)) % (10 ** 9 + 7))