diff --git a/day08.py b/day08.py
index 6036651..1613592 100644
--- a/day08.py
+++ b/day08.py
@@ -46,20 +46,20 @@ class Day(AOCDay):
         inst, nodes = self.parse_input()
         i_len = len(inst)
         check_nodes = [x for x in nodes if x.endswith("A")]
-        nodes_dp = defaultdict(dict)
+        z_steps = []
         for node in check_nodes:
             cur_step = 0
             cur_node = node
-            while (cur_node, cur_step % i_len) not in nodes_dp[node]:
-                nodes_dp[node][(cur_node, cur_step % i_len)] = cur_step
+            while not cur_node.endswith("Z"):
                 if inst[cur_step % i_len] == "L":
                     cur_node = nodes[cur_node][0]
                 else:
                     cur_node = nodes[cur_node][1]
 
                 cur_step += 1
+            z_steps.append(cur_step)
 
-        return math.lcm(*[v for node in check_nodes for k, v in nodes_dp[node].items() if k[0].endswith("Z")])
+        return math.lcm(*z_steps)
 
 
 if __name__ == "__main__":