Problem:
Score : 300 points

Problem Statement

Given an integer N, find the base -2 representation of N.

Here, S is the base -2 representation of N when the following are all satisfied:

S is a string consisting of 0 and 1.

Unless S = 0, the initial character of S is 1.

Let S = S_k S_{k-1} ... S_0, then S_0 \times (-2)^0 + S_1 \times (-2)^1 + ... + S_k \times (-2)^k = N.

It can be proved that, for any integer M, the base -2 representation of M is uniquely determined.

Constraints

Every value in input is integer.

-10^9 \leq N \leq 10^9

Input

Input is given from Standard Input in the following format:

N

Output

Print the base -2 representation of N.

Sample Input 1

-9

Sample Output 1

1011

As (-2)^0 + (-2)^1 + (-2)^3 = 1 + (-2) + (-8) = -9, 1011 is the base -2 representation of -9.

Sample Input 2

123456789

Sample Output 2

11000101011001101110100010101

Sample Input 3

0

Sample Output 3

0

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

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

public class Main {
  public static void main(String args[]) {
    Scanner sc = new Scanner(System.in);

    long n = sc.nextLong();
    long tmp = 1;
    String ans = "";

    while (true) {
      if ((n-tmp) % (tmp*(-2)) == 0) {
        ans += "1";
        n -= tmp;
      } else {
        ans += "0";
      }

      if (n == 0) break;
      tmp *= -2;
    }

    StringBuffer sb = new StringBuffer(ans);
		String dst = sb.reverse().toString();
		System.out.println(""+dst);
  }
}