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 int llint;
typedef unsigned long long int ullint;
std::string YesNo[] = {"No","Yes"};
#define loop(i,N) for(int i=0; i<(N); i++)
template<typename T>
auto sort_all(T& v) { return std::sort(v.begin(),v.end()); }
template<typename T>
auto sum_all(const T& v) { auto z = v[0]; z = 0;
    return std::accumulate(v.begin(),v.end(),z); }
template<typename T>
auto input(int N) {
    std::vector<T> v(N);
    loop(i,N) std::cin >> v[i];
    return std::move(v);
}

typedef llint Int;

int main(void)
{
    int N;
    cin >> N;
    vector<int> ans;
    int k, i = 0;
    for (int s=1; N!=0; s*=-1, N/=2, i++) {
        if (k = N & 1) {
            N -= s;
        }
        ans.push_back(k);
    }
    if (i==0) {
        cout << 0 << endl;
    } else {
        for(i--;i>=0;i--)
            cout << ans[i];
        cout << endl;
    }

    return 0;
}