\--- Day 13: A Maze of Twisty Little Cubicles ---
----------

You arrive at the first floor of this new building to discover a much less welcoming environment than the shiny atrium of the last one. Instead, you are in a maze of twisty little cubicles, all alike.

Every location in this area is addressed by a pair of non-negative integers (`x,y`). Each such coordinate is either a wall or an open space. You can't move diagonally. The cube maze starts at `0,0` and seems to extend infinitely toward *positive* `x` and `y`; negative values are *invalid*, as they represent a location outside the building. You are in a small waiting area at `1,1`.

While it seems chaotic, a nearby morale-boosting poster explains, the layout is actually quite logical. You can determine whether a given `x,y` coordinate will be a wall or an open space using a simple system:

* Find `x*x + 3*x + 2*x*y + y + y*y`.
* Add the office designer's favorite number (your puzzle input).
* Find the [binary representation](https://en.wikipedia.org/wiki/Binary_number) of that sum; count the *number* of [bits](https://en.wikipedia.org/wiki/Bit) that are `1`.
  * If the number of bits that are `1` is *even*, it's an *open space*.
  * If the number of bits that are `1` is *odd*, it's a *wall*.

For example, if the office designer's favorite number were `10`, drawing walls as `#` and open spaces as `.`, the corner of the building containing `0,0` would look like this:

```
  0123456789
0 .#.####.##
1 ..#..#...#
2 #....##...
3 ###.#.###.
4 .##..#..#.
5 ..##....#.
6 #...##.###

```

Now, suppose you wanted to reach `7,4`. The shortest route you could take is marked as `O`:

```
  0123456789
0 .#.####.##
1 .O#..#...#
2 #OOO.##...
3 ###O#.###.
4 .##OO#OO#.
5 ..##OOO.#.
6 #...##.###

```

Thus, reaching `7,4` would take a minimum of `11` steps (starting from your current location, `1,1`).

What is the *fewest number of steps required* for you to reach `31,39`?

Your puzzle answer was `90`.

\--- Part Two ---
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*How many locations* (distinct `x,y` coordinates, including your starting location) can you reach in at most `50` steps?

Your puzzle answer was `135`.

Both parts of this puzzle are complete! They provide two gold stars: \*\*

At this point, all that is left is for you to [admire your Advent calendar](/2016).

Your puzzle input was `1352`.