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;
typedef long long ll;

#define EPS (1e-7)
#define INF (1e9)
#define PI (acos(-1))
//const ll mod = 1000000007;
ll N;

int main() {
    //cout.precision(10);
    cin >> N;
    if(N == 0) {
        cout << 0 << endl;
        return 0;
    }
    ll val = 1;
    vector<int> ans;
    while(N != 0) {
        //cerr << N << " " << val << endl;
        if((abs(N) % ((2 * abs(val))) != 0)) {
            ans.push_back(1);
            N -= val;
        } else {
            ans.push_back(0);
        }
        val *= -2;
    }
    for(int i = ans.size() - 1; i >= 0; i--) cout << ans[i];
    cout << endl;
    return 0;
}