#!/usr/bin/env python3

from pprint import pprint

with open('input.txt', 'r') as f:
    coords = [x.strip().split(', ') for x in f.readlines()]
    coords = [tuple(map(lambda y: int(y), x)) for x in coords]

# print(coords)

def distance(p1, p2):
    """Manhattan distance"""
    return abs(p2[0] - p1[0]) + abs(p2[1] - p1[1])

def get_closest_idx(coords, point):
    """Returns the index of the point that is closest to the point or None"""
    distances = [distance(x, point) for x in coords]
    min_dist = min(distances)
    return distances.index(min_dist) if distances.count(min_dist) == 1 else None

def is_infinite_area(coords, idx, delta=10000):
    """Determines if point coords[idx] has infinite area
    
    A point has infinite area if it is closest to any of the four points:
      * (x, y + delta)
      * (x, y - delta) 
      * (x + delta, y)
      * (x - delte, y)
    """
    point = coords[idx]
    far_points = [
        (point[0], point[1] + delta),
        (point[0], point[1] - delta),
        (point[0] + delta, point[1]),
        (point[0] - delta, point[1])
    ]

    for far in far_points:
        if get_closest_idx(coords, far) == idx:
            return True
    return False    

def get_circle(point, radius):
    """Returns an array of all points with distance radius to point"""
    if radius == 0:
        return [point]

    x = point[0]
    y = point[1]
    d_x = radius
    d_y = 0
    circle = list()

    while d_y < radius:
        circle.append((x + d_x, y + d_y))    
        circle.append((x - d_x, y - d_y))    
        circle.append((x + d_y, y - d_x))    
        circle.append((x - d_y, y + d_x))    

        d_x -= 1
        d_y += 1

    return circle

def main():
    areas = list()
    area_map = dict()

    for idx, point in enumerate(coords):
        if is_infinite_area(coords, idx):
            continue

        is_relevant = True
        radius = 0
        area = 0
        while is_relevant:
            # print(f'Radius {radius}')
            is_relevant = False
            for p2 in get_circle(point, radius):
                if idx == get_closest_idx(coords, p2):
                    is_relevant = True
                    area += 1
            radius += 1
        areas.append(area)
        print(f'Point {point}: Area: {area}')

    print('Largest Area', max(areas))
main()