C - Base -2 Number

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 $N$.

-9

1011

As $(-2)^0 + (-2)^1 + (-2)^3 = 1 + (-2) + (-8) = -9$, 1011 is the base $-2$ representation of $-9$.

123456789

11000101011001101110100010101

0

0