def main(): # Read input grid = [] for _ in range(4): grid.append(list(map(int, input().split()))) # Determine target positions and find the blank (0) position target_positions = {} blank_pos = None for i in range(4): for j in range(4): num = grid[i][j] if num == 0: blank_pos = (i + 1, j + 1) # Convert to 1-based index else: target_positions[num] = (i + 1, j + 1) # Store as 1-based # Condition 1: Solvability check (parity of inversion count and blank row difference) # Compute inversion count of target (excluding 0) flattened = [] for row in grid: for num in row: if num != 0: flattened.append(num) inversion = 0 for i in range(len(flattened)): for j in range(i + 1, len(flattened)): if flattened[i] > flattened[j]: inversion += 1 initial_blank_row = 4 target_blank_row = blank_pos[0] row_diff = abs(initial_blank_row - target_blank_row) condition1 = (inversion % 2) == (row_diff % 2) if not condition1: print("No") return # Condition 2: All manhattan distances between initial and target positions are 0 or 1 condition2 = True for num in range(1, 16): # Numbers 1 to 15 # Initial position of num is based on standard initial 15-puzzle initial_i = (num - 1) // 4 + 1 initial_j = (num - 1) % 4 + 1 target_pos = target_positions.get(num) if target_pos is None: # This shouldn't happen as per the problem statement print("No") return dx = abs(initial_i - target_pos[0]) dy = abs(initial_j - target_pos[1]) if dx + dy > 1: condition2 = False break if not condition2: print("No") return # Condition3: D and K must have the same parity # Compute D (Manhattan distance of blank's movement) initial_blank = (4, 4) D = abs(initial_blank[0] - blank_pos[0]) + abs(initial_blank[1] - blank_pos[1]) # Compute K (number of moved tiles) K = 0 for num in range(1, 16): initial_i = (num - 1) // 4 + 1 initial_j = (num - 1) % 4 + 1 target_i, target_j = target_positions[num] if initial_i != target_i or initial_j != target_j: K += 1 if (D % 2) != (K % 2): print("No") return print("Yes") if __name__ == "__main__": main()