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 (7.3.0) (judge verdict: Time Limit Exceeded)

import sys
input = sys.stdin.readline
sys.setrecursionlimit(10 ** 7)

n = int(input())
a = list(map(int, input().split()))
MOD = 10 ** 9 + 7

import collections

lcm_pf = collections.defaultdict(int)
for i, v in enumerate(a):
    j = 2
    pf = {}
    while j ** 2 <= v:
        ext = 0
        while v % j == 0:
            ext += 1
            v //= j
        if ext:
            pf[j] = ext
            lcm_pf[j] = max(lcm_pf[j], ext)
        j += 1
    if v != 1:
        pf[v] = 1
        lcm_pf[v] = max(lcm_pf[v], 1)

lcm = 1
for p in lcm_pf:
    lcm = lcm * (p ** lcm_pf[p])

ans = 0
for v in a:
    ans = (ans + (lcm // v)) % MOD
print(ans)