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 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define rep(i,n) for (int i = 0; i < (n); ++i)
#define INF (1LL<<50)
#define MOD 1000000007

int main(){
    ll N;
    cin >> N;
    if(N==0){
        cout << 0 << endl;
        return 0;
    }
    string S = "";
    while(N!=0){
        if(N%2==0){
            if(N<0){
                N*=(-1);
                N/=2;
            }else{
                N/=2;
                N*=(-1);
            }
            S+='0';
            continue;
        }
        if(N<0){
            N*=(-1);
            N+=1;
            N/=2;
        }else{
            N/=2;
            N*=(-1);
        }
        S+='1';
    }
    reverse(S.begin(),S.end());
    cout << S << endl;
    return 0;
}