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: Accepted)

#include <bits/stdc++.h>
#include <cmath>
using namespace std;

int main(){
    int n;
    int bef=0;
    cin >> n;
    string ans="";
    while(n!=1 and n!= 0){
        bef=n%-2;
        if(bef==1){
            n--;
            ans.insert(0,"1");
        //    cout<<"   "<<1<<endl;
        }else if(bef==-1){
            n--;
            ans.insert(0, "1");
          //  cout << "   " << 1 << endl;
        }else{
            ans.insert(0, "0");
           // cout << "   " << 0 << endl;
        }
      //  cout<<n<<"->  ";
        n/=-2;
     //   cout<<n<<endl;
    }
    ans.insert(0, "1");
    if(n==1){
    //cout << "   " << 1 << endl;
    cout<<ans;}
    else{
        cout<<"0";
    }
}