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: Runtime Error)

#include <iostream>
#include <string.h>
#include <vector>
#include <algorithm>
#include <cmath>
#include <map>
#include <functional>
#include <cassert>
#include <utility>
#include <stack>
#include <queue>
using namespace std;
#define min(a,b) ((a)<(b)?(a):(b))
#define max(a,b) ((a)>(b)?(a):(b))
#define REP(i,n) for(int i=0;i<n;i++)
#define FOR(i,n1,n2) for(int i=n1;i<n2;i++)
#define speed_up    ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
typedef pair<int,int> Pi;
typedef long long int ll;
const int INF=(ll)(1<<30)-1;
const ll INFl=(ll)9223372036854775807;
const int MAX=10000;
const ll MOD=(ll)1e9+7;
int gcd(int a,int b){return b?gcd(b,a%b):a;}
int lcm(int a,int b){return a/gcd(a, b)*b;}

int n;

int main(){
	cin>>n;
	string s;
	int i=-2;
	while(n!=0){
		if(n%i!=0){
			n-=i/(-2);
			s='1'+s;
		}
		else s='0'+s;
		i*=(-2);
	}
	cout<<s<<endl;
	return 0;
}