Problem:
Score : 400 points

Problem Statement

Caracal is fighting with a monster.

The health of the monster is H.

Caracal can attack by choosing one monster. When a monster is attacked, depending on that monster's health, the following happens:

If the monster's health is 1, it drops to 0.

If the monster's health, X, is greater than 1, that monster disappears. Then, two new monsters appear, each with the health of \lfloor X/2 \rfloor.

(\lfloor r \rfloor denotes the greatest integer not exceeding r.)

Caracal wins when the healths of all existing monsters become 0 or below.

Find the minimum number of attacks Caracal needs to make before winning.

Constraints

1 \leq H \leq 10^{12}

All values in input are integers.

Input

Input is given from Standard Input in the following format:

H

Output

Find the minimum number of attacks Caracal needs to make before winning.

Sample Input 1

2

Sample Output 1

3

When Caracal attacks the initial monster, it disappears, and two monsters appear, each with the health of 1.

Then, Caracal can attack each of these new monsters once and win with a total of three attacks.

Sample Input 2

4

Sample Output 2

7

Sample Input 3

1000000000000

Sample Output 3

1099511627775

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.*;
import java.util.*;

public class Main {
    public static HashMap<Long, Long> map;

    public static void main(String args[]) {
        InputOutput io = new InputOutput(System.in, System.out);
        long h = io.l();
        map = new HashMap<>();
        io.pln(hit(h));
        io.flush();
    }
    
    public static long hit(long h) {
        if (h == 1)
            return 1;
        if (map.containsKey(h))
            return map.get(h);
        long ans = hit((long) Math.floor(h / 2)) + hit((long) Math.floor(h / 2)) + 1;
        map.put(h, ans);
        return ans;
    }

    public static class InputOutput {
        private BufferedReader br;
        private StringTokenizer tok;
        private PrintWriter pw;

        InputOutput(InputStream inputStream, OutputStream outputStream) {
            br = new BufferedReader(new InputStreamReader(inputStream));
            pw = new PrintWriter(new OutputStreamWriter(outputStream));
        }

        public String s() {
            while (tok == null || !tok.hasMoreElements()) {
                try {
                    tok = new StringTokenizer(br.readLine());
                } catch (IOException exc) {
                    exc.printStackTrace();
                }
            }
            return tok.nextToken();
        }

        public int i() {
            return Integer.parseInt(this.s());
        }

        public long l() {
            return Long.parseLong(this.s());
        }

        public void p(Object... out) {
            for (Object e : out)
                pw.print(e.toString());
        }

        public <T> void pln(T out) {
            pw.println(out);
        }

        public void pln() {
            pw.println();
        }

        public void flush() {
            pw.flush();
        }
    }
}