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: Time Limit Exceeded)

from collections import defaultdict


N = int(input())
A = list(map(int, input().split())) 
MOD = 10**9 + 7
def gcd(a,b):
  x = max([a,b])
  y = min([a,b])
  while y:
    x, y = y, x % y
  return x

# x * y = lcm(x, y) // gcd(x, y)より
def lcm(x, y):
  return x * y // gcd(x, y)

l = 1
for a in A:
    l = lcm(l, a)

ans = 0
for i in range(N):
    ans += l // A[i]
    ans %= MOD

print(ans)


"""
def primes(num):
    if num == 1:
        d = defaultdict(int)
        d[1] = 1
        return d

    i = 2
    d = defaultdict(int)
    while i * i <= num:
        while num % i == 0:
            num //= i
            d[i] += 1
        i += 1
    if num > 1:
        d[num] += 1

    return d

d = primes(A[0])

for a in A[1:]:
    tmp_d = primes(a)
    dk = set(d.keys())
    tmp_dk = set(tmp_d.keys())
    dk = dk | tmp_dk
    for k in dk:
        d[k] = max(d[k], tmp_d[k])

lcm = 1

for k in d.keys():
    lcm *= k**d[k] % MOD


ans = 0
for i in range(N):
    ans += (lcm // A[i])
    ans %= MOD

print(ans)
"""