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)

#ふるい
def primes(max_number):
    pr = list(range(3, max_number + 1,2))
    npr = len(pr)
    for i, n in enumerate(pr):
        if n:
            if n*n > max_number:
                break
            for j in range(i+n, npr,n):
                pr[j] = 0
    if max_number >= 2:
        yield 2
    yield from [i for i in pr if i]

#ある素因数が何個含まれるか
def get_coef_num(a,pr):
    num = 0
    while True:
        if((a%pr)==0):
            a = a//pr
            num+=1
        else:
            break
    return num


N = int(input())
A = list(map(int, input().split()))
B = A.copy()
pr_list = list(primes(10**6))
#print(f'#ofPR:{len(pr_list)}')

coef_list = [[0]*N for i in range(len(pr_list))]

for i,a in enumerate(A):
    for j,pr in enumerate(pr_list):
        coef_list[j][i] = get_coef_num(a,pr)
#print(coef_list)

LCM = 1
for i,pr in enumerate(pr_list):
        LCM*=(pr**max(coef_list[i]))
#print(LCM)

for i,a in enumerate(A):
    B[i] = (LCM//a)
#print(B)

print(sum(B)%(10**9+7))