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: Wrong Answer)

package main

import (
	"fmt"
)

func main() {
	var N int
	fmt.Scanf("%d", &N)
	flg := false
	m := 1073741824
	M := m
	for x := -536870912; x != 0; x /= -2 {
		min := (4 - m) / 6
		max := (M - 1) / 3
		//fmt.Printf("%d %d %d %d\n", x, N, min, max)
		if min <= N && N <= max {
			if flg == true {
				fmt.Print("0")
			}
		} else {
			N -= x
			flg = true
			fmt.Print("1")
		}
		if x < 0 {
			M /= 4
		} else {
			m /= 4
		}
	}
	if !flg {
		fmt.Print("0")
	}
	fmt.Print("\n")
}