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;
using VI = vector<long>;

int main() {
  long n;
  cin >> n;
  string ans = "";
  if (n == 0) {
    cout << "0" << endl;
    return 0;
  }
  while (n) {
    if (n % 2 == 0) {
      ans += "0";
    } else {
      ans += "1";
      n -= 1;
    }
    n /= -2;
  }

  reverse(ans.begin(), ans.end());
  int flag = false;
  for (int i = 0; i < ans.size() - 1; i++) {
    if (ans[i] == '1') {
      flag = true;
    }
    if (true) {
      cout << ans[i];
    }
  }
  cout << ans.back() << endl;
}