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 fractions
import collections

mp = 1000###max prime
mod = 10 ** 9 + 7
def prime_factorize(n):
    a = [0] * mp
    while n % 2 == 0:
        a[2] += 1
        n //= 2
    f = 3
    while f * f <= n:
        if n % f == 0:
            a[f] += 1
            n //= f
        else:
            f += 2
    if n != 1:
        a[n] += 1
    return a

def lcm(x,y):
    return x * y // fractions.gcd(x,y)

def fact_mul(x,y):
    ret = [0] * mp
    for i in range(mp):
        ret[i] = x[i] + y[i]
    return ret

def fact_div(x,y):
    ret = [0] * mp
    for i in range(mp):
        ret[i] = x[i] - y[i]
    return ret

def cal_mod(x):
    ret = 1
    for i in range(mp):
        ret *= (i**x[i]) % mod
        ret %= mod
    return ret


N = int(input())
A = list(map(int,input().split()))


l = A[0]###A全体の最大公約数

for i in range(1,N):
    l = lcm(l,A[i])

B0_fact = [0] * mp
l_fact = prime_factorize(l)

A_fact = [0] * N
for i in range(N):
    A_fact[i] = prime_factorize(A[i])

for i in range(mp):
    B0_fact[i] = max(0,l_fact[i]-A_fact[0][i])

ans = cal_mod(B0_fact)

#print(A_fact)
#print(B0_fact)
for i in range(1,N):
    Bi = fact_div(fact_mul(A_fact[0],B0_fact),A_fact[i])
    ans += cal_mod(Bi)
    ans %= mod

print(ans)