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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<bits/stdc++.h>
using namespace std;
int mod(int n, int k){
    if(n%k < 0)
        return n-(n/k+1)*k;
    else
        return n%k;
}
int main()
{
    int n;int flag = 0;
    cin>>n;
    string ans = "";
    while(n)
    {
        char a = mod(n,-2) + '0';
        //cout<<a<<endl;
        ans = ans + a;
        if(n%-2 < 0)
            n = n/-2+1;
        else
            n /= -2;
    }
    reverse(ans.begin(), ans.end());
    cout<<ans<<endl;
    return 0;
}