import sys from functools import lru_cache def main(): input = sys.stdin.read().split() idx = 0 N = int(input[idx]); idx +=1 P_A = float(input[idx]); idx +=1 P_B = float(input[idx]); idx +=1 A = list(map(int, input[idx:idx+N])) idx +=N B = list(map(int, input[idx:idx+N])) A_sorted = sorted(A) B_sorted = sorted(B) # Precompute the indices for quick lookup a_index_map = {a: i for i, a in enumerate(A_sorted)} b_index_map = {b: i for i, b in enumerate(B_sorted)} initial_a_mask = (1 << N) - 1 initial_b_mask = (1 << N) - 1 @lru_cache(maxsize=None) def dp(a_mask, b_mask, current_diff): if a_mask == 0 and b_mask == 0: return 1.0 if current_diff > 0 else 0.0 # Get A's remaining cards a_remaining = [] for i in range(N): if (a_mask & (1 << i)): a_remaining.append(A_sorted[i]) k_A = len(a_remaining) # Get B's remaining cards b_remaining = [] for i in range(N): if (b_mask & (1 << i)): b_remaining.append(B_sorted[i]) k_B = len(b_remaining) # Compute probabilities for A's choices a_probs = {} if k_A == 1: a = a_remaining[0] a_probs[a] = 1.0 elif k_A > 1: min_a = a_remaining[0] a_probs[min_a] = P_A other_prob = (1.0 - P_A) / (k_A - 1) for a in a_remaining[1:]: a_probs[a] = other_prob # Compute probabilities for B's choices b_probs = {} if k_B == 1: b = b_remaining[0] b_probs[b] = 1.0 elif k_B > 1: min_b = b_remaining[0] b_probs[min_b] = P_B other_prob = (1.0 - P_B) / (k_B - 1) for b in b_remaining[1:]: b_probs[b] = other_prob total = 0.0 for a, prob_a in a_probs.items(): for b, prob_b in b_probs.items(): delta = (a + b) if a > b else -(a + b) a_idx = a_index_map[a] next_a_mask = a_mask & ~(1 << a_idx) b_idx = b_index_map[b] next_b_mask = b_mask & ~(1 << b_idx) total += prob_a * prob_b * dp(next_a_mask, next_b_mask, current_diff + delta) return total result = dp(initial_a_mask, initial_b_mask, 0) print("{0:.15f}".format(result)) if __name__ == '__main__': main()