maybe

import chess

def simplify_fen_string(fen):
    """Simplify the FEN string to just include the position of pieces without turn, castling, etc."""
    parts = fen.split(' ')
    simplified_fen = ' '.join(parts[:4])
    return simplified_fen

def evaluate_position(board):
    """Evaluate the board position to determine if it's a checkmate, stalemate, or ongoing game."""
    if board.is_checkmate():
        if board.turn == chess.WHITE:
            return -1000  # White is checkmated, black wins
        else:
            return 1000   # Black is checkmated, white wins
    elif board.is_stalemate() or board.is_insufficient_material() or board.can_claim_draw():
        return 0  # Game is a draw
    return None  # Game is still ongoing

def create_AR_entry(fen, result, parent):
    """Create an entry for the analysis record (AR)."""
    return {
        'fen': fen,
        'parent': parent,
        'children': [],
        'result': result,
        'sequence': []
    }

def generate_positions(board, AR, parent_fen):
    """Generate all possible game positions from the current board state."""
    current_fen = board.fen()
    if len(AR) % 100000 == 0:
        print(len(AR))

    if current_fen in AR:
        return  # Avoid processing the same position twice

    result = evaluate_position(board)
    AR[current_fen] = create_AR_entry(simplify_fen_string(current_fen), result, parent_fen)

    if parent_fen:
        AR[parent_fen]['children'].append(current_fen)

    if result is not None:
        return  # Stop further generation if the game has ended

    for move in board.legal_moves:
        board.push(move)
        generate_positions(board, AR, current_fen)
        board.pop()

def propagate_upwards(AR, child_fen):
    """Recursively update parent nodes based on the results of child nodes."""
    child_node = AR[child_fen]
    parent_fen = child_node['parent']

    while parent_fen:
        parent_node = AR[parent_fen]
        if parent_node['result'] is None or abs(child_node['result']) < abs(parent_node['result']):
            parent_node['result'] = -child_node['result']
            parent_node['sequence'] = [child_fen] + child_node['sequence']
        child_fen = parent_fen
        child_node = parent_node
        parent_fen = child_node['parent']

def back_propagation(AR):
    """Propagate the results from the leaf nodes to the root based on the analysis record."""
    for fen in AR:
        node = AR[fen]
        if node['result'] is not None and node['parent']:
            propagate_upwards(AR, fen)

def main():
    initial_fen = "8/8/8/8/3Q4/5K2/8/4k3 w - - 0 1"
    board = chess.Board(initial_fen)
    AR = {}
    generate_positions(board, AR, None)
    back_propagation(AR)

    # Output results
    initial_entry = AR[initial_fen]
    print(f"Result for initial position: {initial_entry['result']}")
    print("Optimal sequence of moves:")
    for fen in initial_entry['sequence']:
        print(chess.Board(fen))
        print()

main()