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;
typedef vector<int> VI;
typedef vector<ll> VL;
typedef vector<VI> VVI;
typedef vector<VL> VVL;
typedef pair<int, int> P;
typedef pair<ll, ll> PL;
#define FOR(i, a, b) for(int i = (a); i < (b); ++i)
#define rep(i, n) for (int i = 0; i < (n); ++i)
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define debug(x) cout << #x << ": " << x << endl
#define out(x) cout << x << endl
//#define int long long int
const int MOD = 1000000007;
const ll LINF = (ll)1e18 - 1;
const int INF = 1e9 - 1;
const double EPS = 0.000000001;
int dx[4] = {1, 0, -1, 0};
int dy[4] = {0, 1, 0, -1};

void print(const vector<int> &v) {
  for(auto x : v) {
    cout << x << " ";
  }
  cout << endl;
}

signed main()
{
  cin.tie(0);
  ios::sync_with_stdio(false);
  ll n;
  cin >> n;
  string s = "";
  if(n == 0) out('0');
  while(n != 0) {
    if(n % 2 != 0) {
      s = '1' + s;
      n -= 1LL;
    }
    else s = '0' + s;
    n /= -2LL;
  }
  out(s);
  return 0;
}