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)

def x2(n)
  rn=(1+Math.sqrt(1+4*n)).floor/2
  divisors=[]
  factors=Hash.new(0)
  othersum=0
  n2=n
  (2..rn).each do |i|
    if n%i==0
      othersum+=i-1
      divisors << i
    end
    while n2%i==0
      n2/=i
      factors[i]+=1
    end
  end
  factors[n2]+=1 if n2!=1
  divisorssum=1
  divisorsnum=1
  factors.each do |f,m|
    divisorsnum*=m+1
    divisorssum*=(f**(m+1)-1)/(f-1)
  end
  return divisorssum-divisorsnum-othersum
end

puts x2(gets.to_i)