diff --git a/2022/helpers.py b/2022/helpers.py
index 353f3db..edace33 100644
--- a/2022/helpers.py
+++ b/2022/helpers.py
@@ -1,6 +1,7 @@
 from numpy.typing import ArrayLike
 import numpy as np
-from functools import cmp_to_key
+from functools import cmp_to_key, cache
+from itertools import permutations
 from math import prod
 from time import perf_counter_ns
 import re