Most Landmarks in View

You stand at location, an (x, y) tuple, and there are landmarks at points, a list of (x, y) tuples (all integers). You cannot walk, but you can turn on the spot to face any direction. Your field of view is a slice of the plane angle degrees wide with you at its tip: facing direction d, you see every landmark whose direction from you is at most angle / 2 degrees away from d on either side, edges included. Landmarks never block each other.

A landmark at your own position is always visible, whichever way you face.

Write most_visible(points, angle, location) that returns the largest number of landmarks you can see at the same time.

Examples

most_visible([(3, 1), (2, 2), (1, 3), (-2, 0)], 60, (0, 0))    # returns 3
most_visible([(1, 1), (-1, -1), (0, 0), (5, 5)], 90, (0, 0))   # returns 3
most_visible([(1, 0), (0, 1), (-1, 0), (0, -1)], 360, (0, 0))  # returns 4

In the first example the directions to the first three landmarks are about 18, 45 and 72 degrees, which fit in a 60 degree view; (-2, 0) is behind you. In the second, (1, 1) and (5, 5) lie in the same direction, and (0, 0) is where you stand, so you see three.

Constraints

• 1 to 100,000 landmarks; the same position can appear more than once, and each one counts.
• Coordinates are between -10,000 and 10,000.
• angle is a whole number from 1 to 360.
• In every test, making angle a millionth of a degree wider or narrower would not change the answer, so tiny rounding errors in computed angles cannot change your result.