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>
#include <string>
using namespace std;

int main() {
	long n;
	cin>>n;
	int count;
	vector<int> d(100);
	if (n==0) cout << 0 << endl;
	else if(n==1) cout << 1 << endl;
	else {
		for(int i=0;i<100;i++) {
			if(n%(-2)==0){
				d[i]=0;
				n/=(-2);
			}
			else {
				d[i] = 1;
				if(n>0)n = -1*(n/2);
				else n = n/(-2)+1;
			}
			if(n==1){
				count = i;
				break;
			}
		}
		cout << "1";
		for (int i=count;i>=0;i--){
			cout << d[i];
		}
		cout << endl;
	}
}