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 (Clang 3.8.0) (judge verdict: Time Limit Exceeded)

#include <stdio.h>
#define ABS(a) ((a)<0?(-(a)):(a))


int main()
{
    long long i,j,memo=-1,n;
    scanf("%lld", &n);
    if(n==0){
        printf("0\n");
        return 0;
    }
    while(n!=0){
        if(n>0){
            for(i=1,j=0;i<n;i|=i<<2,j+=2);
            n-=1<<j;
        }else{
            for(i=2,j=1;i<ABS(n);i|=i<<2,j+=2);
            n+=1<<j;
        }
        if(memo!=-1)for(i=memo-1;i>j;i--)printf("0");
        printf("1");
        memo=j;
    }
    for(i=memo-1;i>=0;i--)printf("0");
    printf("\n");
    return 0;
}