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: Accepted)

#include<math.h>
#include<stdio.h>
int zettaiti(int n){
  if(n<0){n=-n;}
  return n;
}


int main (){
  int n,i,j;
  int S[100];
  for(i=0;i<100;i++){S[i]=0;}
  scanf("%d", &n);

  if(n==0){printf("0");return 0;}

  i=0;
  while(n!=0){
    if((zettaiti(n))%2==0){
      S[i]=0;}else{S[i]=1;}
    n=n-S[i]*pow(-1,i);
    n=n/2;
    i++;
  }

  for(j=i-1;j>=0;j--){
    printf("%d",S[j]);
  }
  return 0;
}