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: Time Limit Exceeded)

import java.util.*;

public class Main {
  
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int N = sc.nextInt();
    for (int i = Integer.MIN_VALUE; i <= Integer.MAX_VALUE; i++) {
      if (calc(i) == N) {
        printAns(i);
        return;
      }
    }
  }
  private static int calc(int pattern) {
    int ret = 0;
    int i = 0;
    while (pattern != 0) {
      
      if (pattern % 2 == 1) {
        ret += pow(i);
      }
      
      pattern = pattern >>> 1;
      i++;
    }
    return ret;
  }
  
  private static int pow(int n) {
    if (n == 0) {
      return 1;
    }
    if (n % 2 == 1) {
      return -2 * pow(n-1);
    }
    int half = pow(n/2);
    return half*half;
  }
  
  private static void printAns(int pattern){
    StringBuilder builder = new StringBuilder();
    while (pattern != 0) {
      builder.append(pattern%2);
      pattern = pattern >>> 1;
    }
    
    System.out.println(builder.toString());
  }
}