def word_exists(board, word):
    if not word:
        return True
    if not board or not board[0]:
        return False
    rows, cols = len(board), len(board[0])
    used = set()
    def visit(r, c, i):
        if not (0 <= r < rows and 0 <= c < cols):
            return False
        if (r, c) in used or board[r][c] != word[i]:
            return False
        if i == len(word) - 1:
            return True
        used.add((r, c))
        found = any(visit(r + dr, c + dc, i + 1)
                    for dr, dc in ((1,0),(-1,0),(0,1),(0,-1)))
        used.remove((r, c))
        return found
    return any(visit(r, c, 0) for r in range(rows) for c in range(cols))