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>
using namespace std;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
typedef pair<int, int> P;
typedef long long ll;
int main(){
    ll n;
    cin >> n;
    vector<int> ans;
    for(int i=1;i<60;i+=2){
        if(n&(1LL<<i)){
            n+=(1LL<<(i+1));
        }
    }
    rep(i,60){
        if (n & (1LL << i))
        {
            ans.push_back(1);
        }
        else
        {
            ans.push_back(0);
        }
    }
    reverse(ans.begin(),ans.end());
    int i = 0;
    while(i<ans.size()&&ans[i]==0){
        i++;
    }
    if(i==ans.size()){
        cout << 0 << endl;
    }
    else{
        while(i<ans.size()){
            cout << ans[i];
            i++;
        }
        cout << endl;
    }
    return 0;
}