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: Wrong Answer)

# -*- coding: utf-8 -*-
#グローバル変数
pn_list = {2:0,3:0}

def next_pn(pn):
    npn = pn + 2
    pn_flg = 0
    while pn_flg == 0:
        for i in sorted(list(pn_list.keys())):
            if npn % i == 0:
                break
            if (i ** 2) > npn:
                pn_flg = 1
                break
        if pn_flg == 1:
            break # 素数が見つかったらbreak
        else:
            npn += 2
    pn_list[npn] = 0
    return npn

def check_a(n,a):
    res = "ok"
    for i in range(n):
        if a[i] > 1:
            res = "notyet"
    return res

# 整数の入力
n = int(input())
s = input()
a = [int(x) for x in s.split()]
aa = [int(x) for x in s.split()]

#素数作成
sqr_max_a = int((1.0 * 10**6) ** 0.5) + 1
pn = 3
while pn < sqr_max_a:
    pn = next_pn(pn)

# a を素因数分解する
pn_lcm = []
for i in pn_list.keys():
    wareta = 1
    while wareta == 1:
        wareta = 0
        for j in range(len(a)):
            if a[j] % i == 0:
                a[j] = a[j] / i
                wareta = 1
        if wareta == 1:
            pn_list[i] += 1
            pn_lcm.append(i)
    if check_a(n,a) == "ok":
        break

for i in a:
    if i > 1:
        pn_lcm.append(i)

min_bsum = int(0)

for i in aa:
    b = int(1)
    aaa = int(i)
    for j in pn_lcm:
        if aaa % j == 0:
            aaa = aaa / j
        else:
            b = (b * j) % (10**9+7)
    min_bsum = (min_bsum + b) % (10**9+7)

print(min_bsum)