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>
#include<stdlib.h>

int power(int m, int n);

int main(void)
{
    int n,kmax,i,ans[60]={0},k;

    scanf("%d",&n);

    for ( i = 0; 1; i++)
    {
        if(power(2,2*i)>=abs(n)) break;
    }
    kmax=2*i;
    
    if(n==0) ans[0]=0;
    else
    {
        for ( i = 0; i <= kmax; i++)
        {
            ans[i]=abs(n%power(2,i+1))/power(2,i);
            n-=power(-2,i)*ans[i];
        }
    }

    for ( i = 59; i >= 0; i--)
    {
        if(ans[i]==1)
        {
            k=i;
            break;
        }
    }

    for ( i = k; i >= 0; i--)
    {
        printf("%d",ans[i]);
    }
    

    return 0;
}

int power(int m, int n)
{
    int p=1;
    for (int i = 0; i < n; i++) p*=m;
    return p;
}