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)

#!python3

# input
N = int(input())


def solve(x):
    ans = []
    while x != 1:
        if x % 2 == 1:
            ans.append(1)
            x = (x - 1) // -2
        else:
            ans.append(0)
            x //= -2
    
    ans.append(1)
    s = sum([-2 ** i for i in range(len(ans)) if ans[i] == 1])
    if s != x:
        ans = ans[::-1]
    print("".join(map(str, ans)))


def main():
    if N == 0:
        print(0)
    else:
        solve(N)


if __name__ == "__main__":
    main()