Problem:
Score : 500 points

Problem Statement

Snuke received a positive integer N from Takahashi.
A positive integer m is called a favorite number when the following condition is satisfied:

The quotient and remainder of N divided by m are equal, that is, \lfloor \frac{N}{m} \rfloor = N \bmod m holds.

Find all favorite numbers and print the sum of those.

Constraints

All values in input are integers.

1 \leq N \leq 10^{12}

Input

Input is given from Standard Input in the following format:

N

Output

Print the answer.

Sample Input 1

8

Sample Output 1

10

There are two favorite numbers: 3 and 7. Print the sum of these, 10.

Sample Input 2

1000000000000

Sample Output 2

2499686339916

Watch out for overflow.

Solution in Ruby (2.3.3) (judge verdict: Accepted)

##templete

n = gets.chomp.to_i

res = 0
list = []

for i in 1..10**6 + 1 do
  if n % i == 0
    list.push(i)
    list.push(n/i)
  end
end

list = list.uniq
for x in list do
  if x != 1 && (n / (x-1) == n % (x-1)) 
    res += x - 1
  end
end

puts res