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 (GCC 5.4.1) (judge verdict: Runtime Error)

#include <stdio.h>

int main(void)
{
	int N,Y,i,y,z;
	scanf("%d", &N);

	int x[5000];

	if (N != 0) {
		printf("1");
	}
	else
	{
		printf("0");
	}

	for (y = 0;N !=1;y++)
	{
		if (N < 0)
		{
			N = -N;
			if (N != 2) {
				N = N + 2;
			}
			Y = N % 2;
			N = -N;
			N = N / (-2);
			x[y] = Y;
		}
		else {
			N = N;
			Y = N % 2;
			N = N / (-2);
			x[y] = Y;
		}
	}

	for (z = y-1; z >= 0; z--) {
		printf("%d", x[z]);
	}
}