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: Wrong Answer)




#N=gets.to_i
#S=gets.chomp
#A=(0...N).map{gets.to_i}
#sum=A.inject(&:+)
#B=gets.split.map(&:to_i)
N=gets.to_i

rn=Math.sqrt(N).ceil

divisors=[]

othersum=0

(2..rn).each do |i|
  if N%i==0
    othersum+=i-1
    divisors << i
  end
end

n=N

factors=Hash.new(0)

divisors.each do |d|
  if n%d==0
    factors[d]+=1
    n/=d
    redo
  end
end

divisorssum=1
divisorsnum=1
factors.each do |f,m|
  divisorsnum*=m+1
  divisorssum*=(f**(m+1)-1)/(f-1)
end

puts divisorssum-divisorsnum-othersum