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)

from fractions import gcd #直して
n = int(input())
a = list(map(int, input().split()))
def primelist(N):
    prime = [2]
    for i in range(3, N+1):
        flag = 1
        for j in prime:
            if i % j == 0:
                flag = 0
                break
        if flag == 1:
            prime.append(i)
    return prime
prime = primelist(1001)

def factorization(n):
    arr = []
    temp = n
    for i in prime:
        if temp%i==0:
            cnt=0
            while temp%i==0:
                cnt+=1
                temp //= i
            arr.append([i, cnt])

    if temp!=1:
        arr.append([temp, 1])

    if arr==[]:
        arr.append([n, 1])

    return arr


mod = 10**9+7
def modinv(a, mod=10**9+7):
    return pow(a, mod-2, mod)

fact = [0] * (1000001)
pri = []
for i in range(n):
    f = factorization(a[i])
    for fac, c in f:
        fact[fac] = max(fact[fac], c)

fact_list = []
for i in range(1000001):
    if fact[i] > 0:
        fact_list.append((i, fact[i]))




ans = 0
for i in range(n):
    m = modinv(a[i])
    for fac, c in fact_list:
        m *= pow(fac, c, mod)
        m %= mod

    ans += m
    ans %= mod

print(ans)