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 JavaScript (node.js v5.12) (judge verdict: Accepted)

var toInt = x=>parseInt(x,10);
var toIntArr = arr=>arr.map(x=>toInt(x));
var abs = x=>x>0?x:-x;
function min(){var rest = arguments,val=rest[0];for(var i=1;i<rest.length;i++)if(rest[i]<val)val = rest[i];return val}
function max(){var rest = arguments,val=rest[0];for(var i=1;i<rest.length;i++)if(rest[i]>val)val = rest[i];return val}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));
 
function Main(input){
	var input = input.split('\n');
	var n = toInt(input[0]);
	var s = [];
	var x,y,z;
	if(n===0){
		console.log(0);
		return 0;
	}
	while(n!==0){
		if(n>0){
			x = (Math.ceil(Math.log2(3*n+1)/2)-1)*2;
		}else{
			x = (Math.ceil(Math.log2(1-3*n/2)/2))*2-1;
		}
		s[Math.floor(x)] = 1;
		n -= Math.pow(-2,x);
	}
	var l = s.length;
	var ans = '';
	for(var i = l-1; i > -1; i--){
		if(s[i]!==1) s[i] = 0;
		ans += s[i].toString(10);
	}
	console.log(ans);
	

}