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)

#!/usr/bin/env python3
import sys
sys.setrecursionlimit(10**8)
import functools
INF = float("inf")

MOD = 1000000007  # type: int


def GCD(a, b):
    if a == 0:
        return b
    else:
        return GCD(b % a, a)


def LCM(a, b):
    return a*b//GCD(a, b)


def solve(N: int, A: "List[int]"):

    # 最小公倍数
    lcm = 1
    for a in A:
        lcm = LCM(lcm, a)
    tot = 0

    @functools.lru_cache(maxsize=None)
    def f(a):
        return (lcm//a) % MOD
    tot = 0
    for a in A:
        tot += f(a)
    print(tot % MOD)

    return


def main():

    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    A = [int(next(tokens)) for _ in range(N)]  # type: "List[int]"
    solve(N, A)


if __name__ == '__main__':
    main()