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: Runtime Error)

N = int(input())
ans = [0]*36

def bit(inp,ans):
    if inp == 0:
        ans[0] = 0
        inp2 = 0
    
    if inp > 0:
        b = [1,5,21,85,341,1365,5461,21845,87381,349525,1398101,5592405,22369621,89478485,357913941,1431655765]
        pcount = 0
        for ii in range(len(b)):
            if inp <= b[ii]:
                inp2 = inp - 4**ii
                break
            pcount = pcount + 1
        ans[pcount*2] = 1
        
    if inp < 0:
        b2 = [-2,-10,-42,-170,-682,-2730,-10922,-43690,-174762,-699050,-2796202,-11184810,-44739242,-178956970,-715827882]
        pcount = 0
        for ii in range(len(b2)):
            if inp >= b2[ii]:
                inp2 = inp + 2 * (4**ii)
                break
            pcount = pcount + 1
        ans[pcount*2+1] = 1
        
    return inp2,ans

    
while N != 0:
    N,ans = bit(N,ans)

fi = ans[::-1]
fistr = [str(n) for n in fi]
m = ''.join(fistr)
mm = int(m)

print(mm)