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: Wrong Answer)

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

using ll = long long;
// #define int long long

#define REP(i, n) for (int i = 0; i < (n); ++i)
#define REPS(i, r, n) for (int i = (r); i < (n); ++i)
#define REPR(i, n) for(int i = (n); i >= 0; --i) // from n to 0
#define REPRS(i, r, n) for(int i = (n); i >= (r); --i) // from n to r
#define COUTB(x) cout << (x) << "\n"
#define COUTS(x) cout << (x) << " "
#define PB push_back
#define SORT(obj) sort((obj).begin(), (obj).end())
#define SORTR(obj) sort((obj).begin(), (obj).end(), greater<>())
#define ALL(obj) (obj).begin(), (obj).end()
#define MOD 1000000007
#define PI (acos(-1))
/***** MAIN *****/
signed main() {
  int n;
  cin >> n;
  string s = "";
  while(n) {
    if(n%2) {
      s += '1';
      --n;
    } else {
      s += '0';
    }
    n /= -2;
  }
  reverse(ALL(s));
  cout << s << endl;
  return 0;
}
/***** MAIN *****/