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)

import numpy as np
import fractions 
#from functools import reduce
import functools

MOD = 10**9+7


def main():
    N = int(input())
    A = list(map(int, input().split()))

    x = 1
    ans = 0
    # for a in A:
    #     tmp = gcd(x, a)
    #     # ans += (i) * A[i] // tmp + A[i] * x //tmp  
    #     x = (x * a) // tmp

    def lcm(x, y):
        return x * y // fractions.gcd(x, y)
        
    
    x = functools.reduce(lcm, A, 1)
        
    b = 0
    A = np.array(A)
    # for a in A:
    #     b += x // a
    b = np.sum(x//A, axis=0)
    print(b%MOD)
main()