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(){
  int N,n;
  int odd=0;
  int exp[200],index=0;
   scanf("%d",&N);

   if(N==0)printf("0");
   while(N!=0){
     if(N<0)
       n=N-N/4*4+4;
     else
       n=N;
     exp[index++]=n%4;
     N=(N-n%4)/4+(n%4/2);
   }
   
   if(index){
     if(exp[--index]/2)
       printf("1");
     printf("%d",exp[index]%2);
   }
   while(index--)
     printf("%d%d",exp[index]/2,exp[index]%2);
     printf("\n");
   return 0;
}