import sys from itertools import combinations def main(): input = sys.stdin.read().split() ptr = 0 R = int(input[ptr]) ptr += 1 C = int(input[ptr]) ptr += 1 P = [] for _ in range(R): row = list(map(int, input[ptr:ptr + C])) ptr += C P.append(row) S = [] for _ in range(R): row = list(map(int, input[ptr:ptr + C])) ptr += C S.append(row) # Precompute neighbors for each cell neighbors = [[[] for _ in range(C)] for _ in range(R)] for i in range(R): for j in range(C): # Check up if i > 0: neighbors[i][j].append((i-1, j)) # Check left if j > 0: neighbors[i][j].append((i, j-1)) # Check right if j < C - 1: neighbors[i][j].append((i, j+1)) # Initialize x x = [[0.0 for _ in range(C)] for _ in range(R)] for i in range(R): for j in range(C): p = P[i][j] / 100.0 s = S[i][j] initial_points = 4 - s t_ij = max(0, 4 - initial_points) if t_ij == 0: x[i][j] = p # Iterate until convergence max_iterations = 100000 threshold = 1e-12 for _ in range(max_iterations): new_x = [[0.0 for _ in range(C)] for _ in range(R)] for i in range(R): for j in range(C): p = P[i][j] / 100.0 if p == 0.0: new_x[i][j] = 0.0 continue s = S[i][j] initial_points = 4 - s t_ij = max(0, 4 - initial_points) # Check if initial_points is sufficient on its own if initial_points >= 4: new_x[i][j] = p continue # Get active neighbors act_neighbors = neighbors[i][j] m = len(act_neighbors) if m < t_ij: prob = 0.0 else: prob = 0.0 # Enumerate all subsets of size >= t_ij for k in range(t_ij, m + 1): for subset in combinations(act_neighbors, k): product = 1.0 for (ni, nj) in act_neighbors: if (ni, nj) in subset: product *= x[ni][nj] else: product *= (1.0 - x[ni][nj]) prob += product new_x[i][j] = p * prob # Check for convergence max_change = 0.0 for i in range(R): for j in range(C): diff = abs(new_x[i][j] - x[i][j]) if diff > max_change: max_change = diff x = new_x if max_change < threshold: break # Calculate the expected value expected = 0.0 for i in range(R): for j in range(C): expected += x[i][j] print("{:.10f}".format(expected)) if __name__ == "__main__": main()