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(s){
  var n = +s;
  if(n === 0){console.log(0);return;}
  var ans = [], i = 1, j = 1;
  while(n && Math.abs(n) < 9e9){
    if(Math.abs(n) & i){
      ans.push(1);
      n -= j;
    }
    else ans.push(0);
    i *= 2;
    j *= -2;
  }
  console.log(ans.reverse().join(""));
}

Main(require("fs").readFileSync("/dev/stdin","utf8"));