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 Lua (Lua 5.3.5) (judge verdict: Accepted)

local n=io.read("n")

local t={}
for i=1,math.sqrt(n) do
    if n%i==0 then
        if i>1 then
            table.insert(t,i)
        end
        if i~=n//i then
            table.insert(t,n//i)
        end
    end
end
table.sort(t)

local sum=0
for i=1,#t do
    local m=t[i]-1
    if (m+1)*(n//m)==n then
        sum=sum+m
    end
end
print(sum)