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 (5.3.2) (judge verdict: Accepted)

local DBG = false
local function dbgpr(...)
    if DBG then
        io.write("[dbg]")
        print(...)
    end
end

local N = io.read("n")
local lim = math.ceil(N^0.5)
local ans = 0
dbgpr(lim)
for k=lim,1,-1 do
    dbgpr(k)
    if N % k == 0 then
        local d = N // k
        local m = d - 1
        if m > 0 and (N // m == N % m) then
            dbgpr("OK", k, d, m)
            ans = ans + m
        end
    end
end
print(ans)