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: Runtime Error)

import collections
import math
import numpy as np
n = int(input())
ai = [int(i) for i in input().split()]

num = 10**6+1

mod = 10**9+7

if n == 1:
    print(1)
    exit()
    
    
# 素因数分解、辞書で返すやつ
# mathをimportする
def prime(n):
    factor = {}
    tmp = int(math.sqrt(n)) + 1
    for num in range(2, tmp):
        while n % num == 0:
            n //= num
            if not num in factor.keys():
                factor[num] = 1
            else:
                factor[num] += 1
        if num > n:
            break
    if n != 1:
        if not n in factor.keys():
            factor[n] = 1
        else:
            factor[n] += 1
    return factor


pri_li = []

for i in range(n):
    pri_li.append(collections.Counter(prime(ai[i])))
com_ab = [0]*(num)

dic = {}
for a in ai:
    pr = prime(a)
    for num, count in pr.items():
        if not num in dic.keys():
            dic[num] = count
        else:
            if dic[num] < count:
                dic[num] = count

kari = 1
for num,count in dic.items():
    kari *= pow(num,count,mod)

kari_old = kari
ans = 0

for i in range(n):
    kari = kari_old
    #com_ab_new = copy.deepcopy(com_ab)
    #print(com_ab,com_ab_new)
    keys = pri_li[i].keys()
    #kari = 1
    #for j in range(kosu):
    #    kari *= pow(sosu_li[j][0],com_ab[sosu_li[j][0]],mod)
    for j in keys:
        kari *= pow(pow(j,pri_li[i][j],mod),mod-2,mod)
    ans += kari
    ans %= mod
    #print(ans)
        
print(ans)