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: Accepted)

/* Coached by rainboy */
#include <stdio.h>
#include <stdlib.h>

#define INF 0x3f3f3f3f

char cc[64];
int cnt;

void encode(int n) {
	if (n == 0)
		return;
	if (n % 2 == 0) {
		encode(-n / 2);
		cc[cnt++] = '0';
	} else {
		encode(-(n - 1) / 2);
		cc[cnt++] = '1';
	}
}

int main() {
	int n;

	scanf("%d", &n);
	if (n == 0) {
		printf("0\n");
		return 0;
	}
	encode(n);
	printf("%s\n", cc);
	return 0;
}