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: Runtime Error)

import java.util.Scanner;

public class Main{
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
   int N = sc.nextInt();
    StringBuilder sb = new StringBuilder();
    sb.append("");
//System.out.println(N);
    if(N!=0){
      do{
        switch (N%4){
          case 2:
          sb.insert(0, "10");
          N+=2;
          break;
          case 3:
          sb.insert(0, "11");
          N+=1;
          break;
          case 0:
          sb.insert(0, "00");
          break;
          case 1:
          sb.insert(0, "01");
          N-=1;
        }
        N=N/4;
      }while(N!=0);

      while(sb.charAt(0)=='0'){
        sb = sb.deleteCharAt(0);
      }
      System.out.println(sb);
    }else{
      System.out.println(0);
    }
  }
}