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 PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

def main():
    import fractions
    import sys
    input = sys.stdin.readline
    N = int(input())
    a = list(map(int,input().split()))
    MOD = 10**9+7
    g1 = 1
    for t in a[:N//2]:
        g1 = divmod(g1*t,fractions.gcd(g1,t))[0]

    g2 = 1
    for t in a[N//2:]:
        g2 = divmod(g2*t,fractions.gcd(g2,t))[0]
    res = 0
    g = fractions.gcd(g1,g2)

    r1 = (g2//g)%MOD
    for t in a[:N//2]:
        res += divmod(g1,t)[0]
    res = res*r1%MOD

    res2 = 0
    r2 = (g1//g)%MOD
    for t in a[N//2:]:
        res2 += divmod(g2,t)[0]
    res2 = res2*r2%MOD
    print((res+res2)%MOD)
if __name__ == '__main__':
    main()