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)


def gcd(a,b):
    x = max([a,b])
    y = min([a,b])
    while y:
        x, y = y, x % y
    return x

# x * y = lcm(x, y) // gcd(x, y)より
def lcm(x, y):
    return x * y // gcd(x, y)

def main():
    N = int(input())
    A = tuple(map(int, input().split()))
    MOD = 10**9+7


    tmp = A[0]
    for a in A[1:]:
        tmp = lcm(tmp, a)

    B = [0] * N
    for i in range(N):
        B[i] = tmp // A[i]

    ans = 0
    for b in B:
        ans += b
        ans %= MOD
        

    print(ans)

if __name__ == "__main__":
    main()