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 Python (3.4.3) (judge verdict: Accepted)

import sys
N = int(input())
if N == -1:
  print('11')
  sys.exit()
if N == 0:
  print('0')
  sys.exit()
if N == 1:
  print('1')
  sys.exit()

def num(N):
  mi = 0
  ma = 1
  k = 1
  while mi > N or ma < N:
    mi = min(mi,mi+(-2)**k)
    ma = max(ma,ma+(-2)**k)
    k += 1
  return k-1
rem = 0
ansli = []
def ans(N):
  while abs(N)>0:
    ansli.append(num(N))
    N = N-(-2)**num(N)
  return ansli

ans(N)
answer = ''
m = max(ansli)
while m >= 0:
  if m in ansli:
    answer += '1'
  else:
    answer += '0'
  m += -1
  
print(answer)