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 Go (1.6) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"os"
)

func main() {
	scanner := bufio.NewScanner(os.Stdin)
	var N int
	scanner.Scan()
	fmt.Sscanf(scanner.Text(), "%d", &N)
	fmt.Println(rec(N))
}

func rec(n int) string {
	var str string

	if n == 0 {
		return "0"
	}
	if n == 1 {
		return "1"
	}

	if n%2 == 0 {
		// even
		str = rec(n/(-2)) + "0"
	} else {
		// odd
		str = rec((n-1)/(-2)) + "1"
	}

	return str
}