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"
	"math"
	"os"
	"strconv"
)

func main() {
	s := IOInitialize()
	N := Int(s)
	l2 := []int{}
	for i := 0; i <= 31; i++ {
		l2 = append(l2, pow(-2, i))
	}
	posSumLis := []int{}
	negaSumLis := []int{}
	posSum := 0
	negaSum := 0
	for i, num := range l2 {
		if i == 0 {
			posSum += num
			posSumLis = append(posSumLis, posSum)
			continue
		}
		if i%2 == 0 {
			posSum += num
			posSumLis = append(posSumLis, posSum)
		} else {
			negaSum += num
			negaSumLis = append(negaSumLis, negaSum)
		}
	}
	if N == 0 {
		fmt.Println("0")
		return
	}
	indexes := getIndexes(N, l2, posSumLis, negaSumLis)
	maxIndex := indexes[0]
	res := ""
	for i := 0; i <= maxIndex; i++ {
		if isInSlice(indexes, i) {
			res = "1" + res
		} else {
			res = "0" + res
		}
	}
	fmt.Println(res)
}

func isInSlice(slice []int, num int) bool {
	for _, _num := range slice {
		if num == _num {
			return true
		}
	}
	return false
}

func serachIndex(N int, posSumLis []int, negaSumLis []int) int {
	var index int
	if N > 0 {
		for i, num := range posSumLis {
			if N == 1 {
				index = 0
				break
			}
			if num >= N && posSumLis[i-1] < N {
				index = i * 2
				break
			}
		}
	} else {
		for i, num := range negaSumLis {
			if N == -1 || N == -2 {
				index = 1
				break
			}
			if num <= N && posSumLis[i-1] > N {
				index = i*2 + 1
				break
			}
		}
	}
	return index
}

func getIndexes(N int, l2 []int, posSumLis []int, negaSumLis []int) []int {
	indexes := []int{}
	index := serachIndex(N, posSumLis, negaSumLis)
	indexes = append(indexes, index)
	if l2[index] == N {
		return indexes
	}
	_indexes := getIndexes(N-l2[index], l2, posSumLis, negaSumLis)
	indexes = append(indexes, _indexes...)
	return indexes
}

func pow(p, q int) int {
	return int(math.Pow(float64(p), float64(q)))
}

func IOInitialize() *bufio.Scanner {
	s := bufio.NewScanner(os.Stdin)
	s.Split(bufio.ScanWords)
	return s
}

func Int(s *bufio.Scanner) int {
	if !s.Scan() {
		panic("scan error")
	}

	value, err := strconv.Atoi(s.Text())
	if err != nil {
		panic("text to int error")
	}
	return value
}