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: Wrong Answer)

// C: Base -2
"use strict";

const DEBUG_MODE = false;
const rawInput = DEBUG_MODE
  ? "-9"
  : require("fs")
    .readFileSync("/dev/stdin", "utf8")
    .trim();

const process = inputRaw => {
  let input = parseInt(inputRaw);
  let result = "";

  while (input !== 0) {
    let remainder = input % -2;
    input = parseInt(input / -2);

    if (remainder < 0) {
      remainder *= -1;
      input += 1;
    }

    result = Number(remainder).toString() + result;
  }

  console.log(result);
};

process(rawInput);