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)

import sys
sys.setrecursionlimit(10000000)
# input = sys.stdin.readline
from bisect import *
from collections import *
from heapq import *
# import functools
# import itertools
# import math
INF = 500000
mod = 10**9+7

N = int(input())
A = [int(x) for x in input().split()]
dic = defaultdict(lambda : 0)
for a in A:
    for i in range(2, int(a**0.5)+1):
        if a % i == 0:
            c = 0
            while a % i == 0:
                c += 1
                a //= i
            if dic[i] < c:
                dic[i] = c
    if a > 1 and dic[a] == 0:
        dic[a] = 1
MAX = 1
for k in dic:
    MAX *= pow(k, dic[k])
ans = 0
for a in A:
    ans += MAX//a
    ans %= mod
print(ans)