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: Runtime Error)

import numpy as np

n = int(input())
a = np.array(input().split(), dtype=np.int)
mod = 10**9 + 7
max_a = a.max()
sieve = [True] * (max_a // 2)
prime = [2]
p = 3
while p * p <= max_a:
  if sieve[p // 2 - 1]:
    prime.append(p)
    for i in range(p * p, max_a + 1, 2 * p):
      sieve[i // 2 - 1] = False
  p += 2
prime.extend([i for i in range(p, max_a + 1, 2) if sieve[i // 2 - 1]])
prime_dict = {p: idx for idx, p in enumerate(prime)}

pf = np.zeros((n, len(prime)), dtype=np.int)
for i in range(n):
  for j, p in enumerate(prime):
    if p * p > a[i]:
      break
    while a[i] % p == 0:
      a[i] //= p
      pf[i, j] += 1
  if a[i] > 1:
    pf[i, prime_dict[a[i]]] += 1
    
b_pf = pf.max(axis=0) - pf
b_sum = 0
for i in range(n):
  b = 1
  for j, p in enumerate(prime):
    b = b * p ** b_pf[i, j] % mod
  b_sum = (b_sum + b) % mod
print(b_sum)