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 C (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>
#define SIZE 1000
int main(){
  int n,a=1,i=0,j=0;
  int b[SIZE];
  scanf("%d", &n);
  while(n!=0){
    if(n>0){
      a=n%2;
      b[i]=a;
      n=-(n/2);
      i++;
    }
    else{
      a=(-n)%2;
      b[i]=a;
      if(a==1) n=-(n/2)+1;
      else n=-(n/2);
      i++;
    }
    j++;
  }
  for(i=j-1;i>=0;i--){
    printf("%d", b[i]);
  }
  printf("\n");
  return 0;
}