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)

n = gets.chomp.to_i

ary = []
sqrt = (n**(1/2.0)).floor
for i in 1..sqrt
    if n % i == 0
        ary << i
    end
end
ary_reverse = ary.reverse()
ary_reverse.each do |item|
    ary << n/item
end

sum = 0
ary.each do |num|
    if num == 1
        next
    end
    okiniiri = num-1
    syo = n/okiniiri
    amari = n%okiniiri
    # p [syo, amari]
    if syo == amari
        sum += okiniiri
    end
end
puts sum
# ary.length.times do |i|
#     if i != 0
#         if ary[i] - ary[i-1] != 1
#             # p ary[i]
#             sum += ary[i] - 1
#         end
#     end
# end