#!/usr/bin/env python3
from sys import argv
if len(argv) <= 1: NUM = 1
if len(argv) >= 2: NUM = int(argv[1])

if len(argv) <= 2: KEY = None
if len(argv) >= 3: KEY = int(argv[2])

def is_connected(capset0, capset1):
    """Decides whether the two capsets are connected.
    
    In this case, capsets are connected if you can get from
    one to the other by changing NUM cards or fewer."""
    count = 0
    for card in capset0:
        if card in capset1:
            continue
        count += 1
    return count <= NUM

def next_connected(disconnected):
    """Finds the next partition of connected capsets."""
    newly_connected = [disconnected.pop()]
    connected = []
    while newly_connected:
        check_capsets = iter(newly_connected[:])
        connected.extend(newly_connected)
        newly_connected = []
        for con_capset in check_capsets:
            for index, dis_capset in reversed(list(enumerate(disconnected[:]))):
                if is_connected(con_capset, dis_capset):
                    newly_connected.append(disconnected.pop(index))
    return connected

def main():
    capsets = {}
    capset_file = open("capset.out", "r")
    for line in capset_file:
        capset = tuple(line[1:-2].split(" "))
        if len(capset) in capsets:
            capsets[len(capset)].append(capset)
        else:
            capsets[len(capset)] = [capset]
    capset_file.close()

    connecteds = {}
    if KEY == None:
        keys = sorted(capsets.keys())
    else:
        keys = [KEY]
    for key in keys:
        connecteds[key] = []
    for key in keys:
        while capsets[key]:
            connecteds[key].append(next_connected(capsets[key]))
        print("\nFor length {} there are {} partitions.".format(key, len(connecteds[key])))
        lengths = list(map(len, connecteds[key]))
        for length in sorted(set(lengths)):
            print("There are {} capsets with length {}.".format(lengths.count(length), length))

if __name__ == "__main__": main()