Advent of code day 14 recursive cached bruteforce

from collections import Counter
import numpy as np
import functools
import time

with open("input.txt", "r") as input_file:
    lines = input_file.read().splitlines()

start_state = lines[0]
rules = dict()
for line in lines[2:]:
    pair, output = line.split(" -> ")
    rules[pair] = output

@functools.lru_cache(10000)
def get_counts_for_pair(pair, depth):
    rule_output = rules.get(pair)
    if rule_output is None or depth == 0:
        if pair[0] == pair[1]:
            return {pair[0]: 2}
        else:
            return {pair[0]: 1, pair[1]: 1}
    else:
        c = Counter()
        c.update(get_counts_for_pair(pair[0] + rule_output, depth - 1))
        c.update(get_counts_for_pair(rule_output + pair[1], depth - 1))
        c.update({rule_output: -1})
        return c

letter_counts = Counter()
letter_counts.update(get_counts_for_pair(start_state[0] + start_state[1], 40))
for letter_index in range(1,len(start_state) - 1):
    pair = start_state[letter_index] + start_state[letter_index + 1]
    letter_counts.update(get_counts_for_pair(pair, 40))
    letter_counts.update({start_state[letter_index]: -1})

raw_counts = np.array(list(letter_counts.values()))
print(np.max(raw_counts) - np.min(raw_counts))