import sys; sys.dont_write_bytecode = True;
from utils import *
import typing


def do_case(inp: str, sample=False):
    # READ THE PROBLEM FROM TOP TO BOTTOM OK
    def sprint(*a, **k): sample and print(*a, **k)
    lines: typing.List[str] = inp.splitlines()
    paras: typing.List[typing.List[str]] = lmap(str.splitlines, inp.split("\n\n"))
    out = 0

    scanners = []
    for para in paras:
        points = lmap(ints, para[1:])
        scanners.append(points)
        # print(len(points))
    
    # assume scanner 0 is good

    FACINGS = [x for i in [-1, 1] for x in [[i, 0, 0], [0, i, 0], [0, 0, i]]]

    def cross(a, b):
        c = [a[1]*b[2] - a[2]*b[1],
            a[2]*b[0] - a[0]*b[2],
            a[0]*b[1] - a[1]*b[0]]

        return c
    
    def common(a, b):
        aset = set(map(tuple, a))
        # return b's points, but now relative to a
        for facing in FACINGS:
            for up in [f for f in FACINGS if all(abs(x) != abs(y) for x, y in zip(f, facing) if x or y)]:
                
                # facing's
                right = cross(facing, up)

                matrix = [facing, up, right]
                new_b = [matvec(matrix, vec) for vec in b]

                for a_point in a:
                    for b_point in new_b:
                        # assume they're the same
                        # add a-b to all b
                        delta = padd(a_point, pneg(b_point))
                        new_new_b = [padd(delta, b) for b in new_b]
                        if len(aset.intersection(map(tuple, new_new_b))) >= 12:
                            return new_new_b
        return None
    
    # if sample:
    #     print(common(scanners[0], scanners[1]))
    #     quit()
    good_scanners = [None] * len(scanners)
    good_scanners[0] = scanners[0]
    done_scanners = [False] * len(scanners)
    while True:
        for i in range(len(scanners)):
            if good_scanners[i] and not done_scanners[i]:
                for j in range(len(scanners)):
                    if i != j and good_scanners[j] is None:
                        test = common(good_scanners[i], scanners[j])
                        # sprint(test)
                        if test is not None:
                            good_scanners[j] = test
                done_scanners[i] = True
        print(done_scanners, lmap(bool, good_scanners))
        if all(done_scanners):
            break
    
    out = set(tuple(point) for points in good_scanners for point in points)
    out = len(out)

    
    if out:
        print("out:    ", out)
    return  # RETURNED VALUE DOESN'T DO ANYTHING, PRINT THINGS INSTEAD

with open('./2021/19.input') as input_file:
	do_case(input_file.read())