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())

bin=[]
p = ['00','10','01','11']
m = ['00','11','01','10']
ans=[]
if N < 0:
    N = -1*N
    minus = True
else:
    minus = False
if N == 0:
    print(0)
else:
    while(N != 0):
        n = N % 4
        N = N // 4
        if minus:
            ans.append(m[n])
            if n == 3: N += 1
        else:
            ans.append(p[n])
            if n == 2 or n == 3: N += 1
    bin.append(n)
    ans ="".join(ans)
    ans = ans[::-1]
    print(ans[ans.find('1'):])