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 C (GCC 5.4.1) (judge verdict: Accepted)

#include<stdio.h>
#include<stdlib.h>
#include<stdint.h>
#include<inttypes.h>
#include<string.h>
#include<math.h>

typedef int32_t i32;
typedef int64_t i64;

#define MAX(a,b) ((a) > (b) ? (a) : (b))
#define MIN(a,b) ((a) < (b) ? (a) : (b))
#define ABS(a) ((a) > (0) ? (a) : -(a))

void run (void) {
  i64 n;
  scanf ("%" SCNi64, &n);
  i64 ans = 0;
  for (i64 i = 1;i <= n && (n - i) / i > i;++i) {
    if ((n - i) % i == 0) {
      ans += (n - i) / i;
    }
  }
  printf ("%" PRIi64 "\n", ans);
}

void test (void) {
  i64 n;
  scanf ("%" SCNi64, &n);
  for (i32 i = 1 ;i <= n; ++i) {
    printf ("%" PRIi32 " : ", i);
    for (i32 j = 1; j <= i; ++j) {
      if (i / j == i % j) {
	printf ("%" PRIi32 " ", j);
      }
    }
    puts ("");
  }
}

int main (void) {
  run();
  return 0;
}