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)

function Main(input){
	var N = input;
  var arr = [];
  
  if(N == 0)return "0";
  
 	while(N != 0){
  	var m = N % (-2);
  	var x = (N - m) / -2;
  	if(m < 0){x++;m+=2}
    arr.push(m);
    N = x;
  }
  return arr.reverse().join("");
}

// If you are interested in the algorithms I used, 
// there is no need to read down from this line.

((b,c,d)=>"undefined"!=typeof require?console.log(Main(require("fs").readFileSync("/dev/stdin","utf8"))):[b=b.split("\n").slice(1,-1).join("\n"),c=function(){try{return Main(b)}catch(f){return f.stack||f.message}}(),d=typeof c,"string"==d||(c=JSON.stringify(c)),$("<form>").append([[10,b],0,[1,d],0,[10,c]].map(f=>$(f?"<textarea>":"<br>",f&&{rows:f[0],cols:40,text:f[1]}))).appendTo("body")])(`
0
`);