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 Rust (1.15.1) (judge verdict: Accepted)

macro_rules !input {(source =$s :expr ,$($r :tt ) *) =>{let mut iter =$s .split_whitespace () ;let mut next =||{iter .next () .unwrap () } ;input_inner !{next ,$($r ) *} } ;($($r :tt ) *) =>{let stdin =std ::io ::stdin () ;let mut bytes =std ::io ::Read ::bytes (std ::io ::BufReader ::new (stdin .lock () ) ) ;let mut next =move ||->String {bytes .by_ref () .map (|r |r .unwrap () as char ) .skip_while (|c |c .is_whitespace () ) .take_while (|c |!c .is_whitespace () ) .collect () } ;input_inner !{next ,$($r ) *} } ;}
macro_rules !input_inner {($next :expr ) =>{} ;($next :expr ,) =>{} ;($next :expr ,$var :ident :$t :tt $($r :tt ) *) =>{let $var =read_value !($next ,$t ) ;input_inner !{$next $($r ) *} } ;}
macro_rules !read_value {($next :expr ,($($t :tt ) ,*) ) =>{($(read_value !($next ,$t ) ) ,*) } ;($next :expr ,[$t :tt ;$len :expr ] ) =>{(0 ..$len ) .map (|_ |read_value !($next ,$t ) ) .collect ::<Vec <_ >>() } ;($next :expr ,chars ) =>{read_value !($next ,String ) .chars () .collect ::<Vec <char >>() } ;($next :expr ,usize1 ) =>{read_value !($next ,usize ) -1 } ;($next :expr ,$t :ty ) =>{$next () .parse ::<$t >() .expect ("Parse error" ) } ;}

fn main() {
   input! {
      n: i64,
   }
   if n == 0 {
      println!("0");
   } else if n > 0 {
      let mut x = 1;
      let mut y = 0;
      while x < n {
         y += 2;
         x += 1 << y;
      }
      let d = x - n;
      let mut mt = vec![0u8; y + 1];
      mt[0] = 1;
      for i in 0..y {
         if (d >> i) & 1 == 1 {
            if i % 2 == 1 {
               mt[y - i] = 1;
            }
         } else {
            if i % 2 == 0 {
               mt[y - i] = 1;
            }
         }
      }
      for m in mt {
         print!("{}", m);
      }
      println!("");
   } else {
      let n = -n;
      let mut x = 2;
      let mut y = 1;
      while x < n {
         y += 2;
         x += 1 << y;
      }
      let d = x - n;
      let mut mt = vec![0u8; y + 1];
      mt[0] = 1;
      for i in 0..y {
         if (d >> i) & 1 == 0 {
            if i % 2 == 1 {
               mt[y - i] = 1;
            }
         } else {
            if i % 2 == 0 {
               mt[y - i] = 1;
            }
         }
      }
      for m in mt {
         print!("{}", m);
      }
      println!("");
   }
}