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<stdio.h>

int main(){
  long int N;
  long int q;
  long int r;
  scanf("%li",&N);
  int ans[1000],tail=0;
  if(N==0) printf("0");
  else{
  while(1){
    if(N<0 && (-N)%2!=0 ){
      q=((-N+1)/2);
      r=1;
    }
    else {
      q=N/(-2);
      r=N%(-2);
    }
    ans[tail]=r;
    tail++;
    N=q;
    if(N==1) break;
  }
  printf("1");
  tail--;
  for (; tail >= 0; tail--) {
    printf("%d",ans[tail] );
  }
}
  return 0;
}