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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)


public class Main {

    private static void solve() {
        long n = nl();

        long ret = 0;
        for (int p = 1; p <= (int) 1e6 + 10; p++) {
            if (n % p == 0) {
                long m = n / p - 1;
                if (m <= p)
                    continue;
                ret += m;
            }
        }
        System.out.println(ret);
    }

    public static void main(String[] args) {
        new Thread(null, new Runnable() {
            @Override
            public void run() {
                long start = System.currentTimeMillis();
                String debug = args.length > 0 ? args[0] : null;
                if (debug != null) {
                    try {
                        is = java.nio.file.Files.newInputStream(java.nio.file.Paths.get(debug));
                    } catch (Exception e) {
                        throw new RuntimeException(e);
                    }
                }
                reader = new java.io.BufferedReader(new java.io.InputStreamReader(is), 32768);
                solve();
                out.flush();
                tr((System.currentTimeMillis() - start) + "ms");
            }
        }, "", 64000000).start();
    }

    private static java.io.InputStream is = System.in;
    private static java.io.PrintWriter out = new java.io.PrintWriter(System.out);
    private static java.util.StringTokenizer tokenizer = null;
    private static java.io.BufferedReader reader;

    public static String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new java.util.StringTokenizer(reader.readLine());
            } catch (Exception e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

    private static double nd() {
        return Double.parseDouble(next());
    }

    private static long nl() {
        return Long.parseLong(next());
    }

    private static int[] na(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++)
            a[i] = ni();
        return a;
    }

    private static char[] ns() {
        return next().toCharArray();
    }

    private static long[] nal(int n) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++)
            a[i] = nl();
        return a;
    }

    private static int[][] ntable(int n, int m) {
        int[][] table = new int[n][m];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                table[i][j] = ni();
            }
        }
        return table;
    }

    private static int[][] nlist(int n, int m) {
        int[][] table = new int[m][n];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                table[j][i] = ni();
            }
        }
        return table;
    }

    private static int ni() {
        return Integer.parseInt(next());
    }

    private static void tr(Object... o) {
        if (is != System.in)
            System.out.println(java.util.Arrays.deepToString(o));
    }
}