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)

n = int(input())
gu = [1]
ki = [0]
for i in range(0, 20):
  gu.append(gu[-1] + (-2)**(2 + 2*i))
  ki.append(ki[-1] + (-2)**(1 + 2*i))
ans = []
for i in range(20):
  if gu[-2-i] < n <= gu[-1-i]:
    ans.append('1')
    n-= (gu[-1-i]-gu[-2-i])
  else:
    ans.append('0')
  if ki[-1-i] <= n < ki[-2-i]:
    ans.append('1')
    n -= (ki[-1-i]-ki[-2-i])
  else:
    ans.append('0')
ans.append(str(n))
print(str(int(''.join(ans))))