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>
int main(){
    int n;
    scanf("%d",&n);
    if(n==0){
        puts("0");
        return 0;
    }
    int k=(n>0)?-1:1;
    long long ans=0;
    int d=0;
    if(n<0)n=-n;
    while(1){
        //printf("n=%d\n",n);
        if(n==-k*(1<<d)){
            ans+=(1<<d);
            break;
        }
        if((n%(1<<(d+1)))!=0){
            ans+=(1<<d);
            n+=k*(1<<d);
        }
        k=-k;
        d++;
    }
    long long anstmp=ans;
    int digit=0;
    while(anstmp){
        //printf("anstmp=%d\n",anstmp);
        digit++;
        anstmp/=2;
    }
    while(digit){
        printf("%d",(ans>>(digit-1))%2);
        digit--;
    }
    return 0;
}