## NEG2 - The Moronic Cowmpouter

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Inexperienced in the digital arts, the cows tried to build a calculating engine (yes, it's a cowmpouter) using binary numbers (base 2) but instead built one based on base negative 2! They were quite pleased since numbers expressed in base -2 do not have a sign bit.

You know number bases have place values that start at 1 (base to the 0 power) and proceed right-to-left to base^1, base^2, and so on. In base -2, the place values are 1, -2, 4, -8, 16, -32, ... (reading from right to left). Thus, counting from 1 goes like this: 1, 110, 111, 100, 101, 11010, 11011, 11000, 11001, and so on.

Eerily, negative numbers are also represented with 1's and 0's but no sign. Consider counting from -1 downward: 11, 10, 1101, 1100, 1111, and so on.

Please help the cows convert ordinary decimal integers (range -2,000,000,000 .. 2,000,000,000) to their counterpart representation in base -2.

### Input

A single integer to be converted to base -2

### Output

A single integer with no leading zeroes that is the input integer converted to base -2. The value 0 is expressed as 0, with exactly one 0.

### Example

```Input:
-13

Output:
110111```

## Code Examples

### #1 Code Example with C++ Programming

```Code - C++ Programming```

``````#include <iostream>
using namespace std;

int main()
{

signed long long int N;
string remainder;
cin >> N;
if (N == 0)
{
cout << 0;
return 0;
}
while (N != 0)
{
int r = N % (-2);
N = N / (-2);
if (r < 0)
{
r += 2;
N += 1;
}
remainder = to_string(r) + remainder;
}
cout << remainder;
}``````
Copy The Code &

Input

cmd
-13

Output

cmd
110111