All Squares

Geometrically every square has one well defined centre point. On a grid that holds only when the sides of the square span an odd number of points. Every odd number can be written as $2k+1$, so a square whose sides are $2k+1$ points long is said to have size $k$.

A pattern of squares is built with these rules.

1. The largest square has size $k$, so its sides are $2k+1$ points long, and it sits at the centre of a grid of size 1024, whose sides are 2049 points long.
2. The smallest permissible square has size 1 and the largest has size 512, so $1 \le k \le 512$.
3. A square of size $s > 1$ has a square of size $s / 2$ centred on each of its 4 corners. The division is integer division, so $9 / 2 = 4$. A square of size 1 puts nothing on its corners.
4. The top left corner of the grid has coordinates $(0, 0)$.

A value of $k$ therefore fixes one pattern. The picture below shows the pattern for $k = 15$.

Any point of the grid is surrounded by zero or more squares. A point lying on the border of a square counts as surrounded by that square.

Read a value of $k$ and the coordinates of a point, then report how many squares surround the point.

Each line of input holds 3 integers: $k$, the $x$ coordinate of the point, and the $y$ coordinate of the point, with $1 \le k \le 512$ and $0 \le x, y \le 2048$. The input ends with a line holding three zeroes, 0 0 0, which is not a query.

Print one line for every query line of the input. Each line holds the number of squares that surround the given point.