101052: [AtCoder]ABC105 C - Base -2 Number

Memory Limit：256 MB Time Limit：2 S
Judge Style：Text Compare Creator：
Submit：0 Solved：0

Description

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

Input

题意翻译

对于任意一个数 $a_1a_2......a_x$ 满足 $\sum_{i=1}^{x}a_i\times base^{x-i}=A$ ， 那么称 $a_1a_2......a_x$ 为 $A$ 的 $base$ 进制表示的数，其中 $0\le a_1,a_2......,a_x< |base|$ 。 给出一个整数 $N$ ， 满足 $-10^{9}\le N \le 10^{9}$ ，请计算出其 $-2$ 进制表示的数。

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