A Strange Game
Two players are engaged in a simple game on an n×n board. The first player controls a white piece, while the second player controls a black piece. The game proceeds in turns, with the white player moving first.
The white player can move their piece one square in any of the four cardinal directions: left, right, up, or down. On their turn, the black player can also move in one of these four directions, but they have the option to move their piece either one or two squares. The objective is to capture the opponent's piece, and the player who does so first wins the game.
Your task is to determine the winner and the number of moves required for victory, assuming both players play optimally.
Input
The input consists of five numbers: n (2 ≤ n ≤ 20), followed by the coordinates of the white and black pieces.
Output
Output WHITE x if the white player wins, BLACK x if the black player wins, or DRAW if the game ends in a draw. Here, x represents the total number of half-moves made by both players until the game concludes.