from itertools import permutations
v = [1,2,3]
p = permutations(v)
for t in list(p):
  print([0] + list(t) + [0])

[0, 1, 2, 3, 0]
[0, 1, 3, 2, 0]
[0, 2, 1, 3, 0]
[0, 2, 3, 1, 0]
[0, 3, 1, 2, 0]
[0, 3, 2, 1, 0]

INT_INF = -1

if s != INT_INF and edges[v][u] != INT_INF:
    if ret == INT_INF:
        ret = s + edges[v][u]
    else:
        ret = min(ret, s + edges[v][u])

from typing import List

INT_INF = -1

class Graph:
    v_num: int
    edges: List[List[int]]

    def __init__(self, v_num: int):
        self.v_num = v_num
        self.edges = [[INT_INF for c in range(v_num)] for r in range(v_num)]
    
    def setDist(self, src: int, dest: int, dist: int):
        self.edges[src][dest] = dist


class TSPSolver:
    g: Graph
    dp: List[List[int]]

    def __init__(self, g: Graph):
        self.g = g
        self.dp = [[None for c in range(g.v_num)] for r in range(1 << g.v_num)]
    
    def solve(self) -> int:
        return self._recurse(0, 0)
    
    def _recurse(self, v: int, state: int) -> int:
        """
    
        :param v:
        :param state:
        :return: -1 means INF
        """
        dp = self.dp
        edges = self.g.edges
    
        if dp[state][v] is not None:
            return dp[state][v]
    
        if (state == (1 << self.g.v_num) - 1) and (v == 0):
            dp[state][v] = 0
            return dp[state][v]
    
        ret: int = INT_INF
        for u in range(self.g.v_num):
            if (state & (1 << u)) == 0:
                s: int = self._recurse(u, state | 1 << u)
                if s != INT_INF and edges[v][u] != INT_INF:
                    if ret == INT_INF:
                        ret = s + edges[v][u]
                    else:
                        ret = min(ret, s + edges[v][u])
        dp[state][v] = ret
        return ret


def main():
    V, E = map(int, input().split())
    g: Graph = Graph(V)
    for _ in range(E):
        src, dest, dist = map(int, input().split())
        g.setDist(src, dest, dist)

    tsp: TSPSolver = TSPSolver(g)
    print(tsp.solve())


if __name__ == "__main__":
    main()

def simulate_bruteforce(n: int) -> bool:
    """
    Simulates one round. Unbounded time complexity.
    :param n: total number of seats
    :return: True if last one has last seat, otherwise False
    """

    seats = [False for _ in range(n)]

    for i in range(n-1):
        if i == 0:  # first one, always random
            seats[random.randint(0, n - 1)] = True
        else:
            if not seats[i]:  # i-th has his seat
                seats[i] = True
            else:
                while True:
                    rnd = random.randint(0, n - 1) # random until no conflicts
                    if not seats[rnd]:
                        seats[rnd] = True
                        break
    return not seats[n-1]

class Solution:
    def nthPersonGetsNthSeat(self, n: int) -> float:
        return 1.0 if n == 1 else 0.5

def simulate_online(n: int) -> bool:
    """
    Simulates one round of complexity O(N).
    :param n: total number of seats
    :return: True if last one has last seat, otherwise False
    """

    seats = [i for i in range(n)]

    def swap(i, j):
        tmp = seats[i]
        seats[i] = seats[j]
        seats[j] = tmp

    # for each person, the seats array idx available are [i, n-1]
    for i in range(n-1):
        if i == 0:  # first one, always random
            rnd = random.randint(0, n - 1)
            swap(rnd, 0)
        else:
            if seats[i] == i:  # i-th still has his seat
                pass
            else:
                rnd = random.randint(i, n - 1)  # selects idx from [i, n-1]
                swap(rnd, i)
    return seats[n-1] == n - 1

def simulate(n: int) -> bool:
    """
    Simulates one round of complexity O(N).
    :param n: total number of seats
    :return: True if last one has last seat, otherwise False
    """

    seats = [False for _ in range(n)]

    for i in range(n-1):
        if i == 0:  # first one, always random
            rnd = random.randint(0, n - 1)
            seats[rnd] = True
        else:
            if not seats[i]:  # i-th still has his seat
                seats[i] = True
            else:
                # 0 must not be available, now we have 0 and [i+1, n-1],
                rnd = random.randint(i, n - 1)
                if rnd == i:
                    seats[0] = True
                else:
                    seats[rnd] = True
    return not seats[n-1]

class TreeNode:
    """
    MCTS Tree Node
    """

    c_puct: ClassVar[int] = 5  # class-wise global param c_puct, exploration weight factor.

    _parent: TreeNode
    _children: Dict[int, TreeNode]  # map from action to TreeNode
    _visit_num: int
    _Q: float   # Q value of the node, which is the mean action value.
    _prior: float

class TreeNode:

    def get_puct(self) -> float:
        """
        Computes AlphaGo Zero PUCT (polynomial upper confidence trees) of the node.

        :return: Node PUCT value.
        """
        U = (TreeNode.c_puct * self._prior * np.sqrt(self._parent._visit_num) / (1 + self._visit_num))
        return self._Q + U

class TreeNode:

    def select(self) -> Tuple[Pos, TreeNode]:
        """
        Selects an action(Pos) having max UCB value.

        :return: Action and corresponding node
        """
        return max(self._children.items(), key=lambda act_node: act_node[1].get_puct())

class TreeNode:

    def propagate_to_root(self, leaf_value: float):
        """
        Updates current node with observed leaf_value and propagates to root node.

        :param leaf_value:
        :return:
        """
        if self._parent:
            self._parent.propagate_to_root(-leaf_value)
        self._update(leaf_value)

    def _update(self, leaf_value: float):
        """
        Updates the node by newly observed leaf_value.

        :param leaf_value:
        :return:
        """
        self._visit_num += 1
        # new Q is updated towards deviation from existing Q
        self._Q += 0.5 * (leaf_value - self._Q)

class MCTSAlphaGoZeroPlayer(BaseAgent):

    def _next_step_play_act_probs(self, game: ConnectNGame) -> Tuple[List[Pos], ActionProbs]:
        """
        For the given game status, run playouts number of times specified by self._playout_num.
        Returns the action distribution according to AlphaGo Zero MCTS play formula.

        :param game:
        :return: actions and their probability
        """

        for n in range(self._playout_num):
            self._playout(copy.deepcopy(game))

        act_visits = [(act, node._visit_num) for act, node in self._current_root._children.items()]
        acts, visits = zip(*act_visits)
        act_probs = softmax(1.0 / MCTSAlphaGoZeroPlayer.temperature * np.log(np.array(visits) + 1e-10))

        return acts, act_probs

class MCTSAlphaGoZeroPlayer(BaseAgent):

    def get_action(self, board: PyGameBoard) -> Pos:
        """
        Method defined in BaseAgent.

        :param board:
        :return: next move for the given game board.
        """
        return self._get_action(copy.deepcopy(board.connect_n_game))[0]

    def _get_action(self, game: ConnectNGame) -> Tuple[MoveWithProb]:
        epsilon = 0.25
        avail_pos = game.get_avail_pos()
        move_probs: ActionProbs = np.zeros(game.board_size * game.board_size)
        assert len(avail_pos) > 0

        # the pi defined in AlphaGo Zero paper
        acts, act_probs = self._next_step_play_act_probs(game)
        move_probs[list(acts)] = act_probs
        if self._is_training:
            # add Dirichlet Noise when training in favour of exploration
            p_ = (1-epsilon) * act_probs + epsilon * np.random.dirichlet(0.3 * np.ones(len(act_probs)))
            move = np.random.choice(acts, p=p_)
            assert move in game.get_avail_pos()
        else:
            move = np.random.choice(acts, p=act_probs)

        self.reset()
        return move, move_probs

class MCTSAlphaGoZeroPlayer(BaseAgent):

    def self_play_one_game(self, game: ConnectNGame) \
            -> List[Tuple[NetGameState, ActionProbs, NDArray[(Any), np.float]]]:
        """

        :param game:
        :return:
            Sequence of (s, pi, z) of a complete game play. The number of list is the game play length.
        """

        states: List[NetGameState] = []
        probs: List[ActionProbs] = []
        current_players: List[np.float] = []

        while not game.game_over:
            move, move_probs = self._get_action(game)
            states.append(convert_game_state(game))
            probs.append(move_probs)
            current_players.append(game.current_player)
            game.move(move)

        current_player_z = np.zeros(len(current_players))
        current_player_z[np.array(current_players) == game.game_result] = 1.0
        current_player_z[np.array(current_players) == -game.game_result] = -1.0
        self.reset()

        return list(zip(states, probs, current_player_z))

class MCTSAlphaGoZeroPlayer(BaseAgent):
    
    def _playout(self, game: ConnectNGame):
        """
        From current game status, run a sequence down to a leaf node, either because game ends or unexplored node.
        Get the leaf value of the leaf node, either the actual reward of game or action value returned by policy net.
        And propagate upwards to root node.

        :param game:
        """
        player_id = game.current_player

        node = self._current_root
        while True:
            if node.is_leaf():
                break
            act, node = node.select()
            game.move(act)

        # now game state is a leaf node in the tree, either a terminal node or an unexplored node
        act_and_probs: Iterator[MoveWithProb]
        act_and_probs, leaf_value = self._policy_value_net.policy_value_fn(game)

        if not game.game_over:
            # case where encountering an unexplored leaf node, update leaf_value estimated by policy net to root
            for act, prob in act_and_probs:
                game.move(act)
                child_node = node.expand(act, prob)
                game.undo()
        else:
            # case where game ends, update actual leaf_value to root
            if game.game_result == ConnectNGame.RESULT_TIE:
                leaf_value = ConnectNGame.RESULT_TIE
            else:
                leaf_value = 1 if game.game_result == player_id else -1
            leaf_value = float(leaf_value)

        # Update leaf_value and propagate up to root node
        node.propagate_to_root(-leaf_value)

NetGameState = NDArray[(4, Any, Any), np.int]


def convert_game_state(game: ConnectNGame) -> NetGameState:
    """
    Converts game state to type NetGameState as ndarray.

    :param game:
    :return:
        Of shape 4 * board_size * board_size.
        [0] is current player positions.
        [1] is opponent positions.
        [2] is last move location.
        [3] all 1 meaning move by black player, all 0 meaning move by white.
    """
    state_matrix = np.zeros((4, game.board_size, game.board_size))

    if game.action_stack:
        actions = np.array(game.action_stack)
        move_curr = actions[::2]
        move_oppo = actions[1::2]
        for move in move_curr:
            state_matrix[0][move] = 1.0
        for move in move_oppo:
            state_matrix[1][move] = 1.0
        # indicate the last move location
        state_matrix[2][actions[-1]] = 1.0
    if len(game.action_stack) % 2 == 0:
        state_matrix[3][:, :] = 1.0  # indicate the colour to play
    return state_matrix[:, ::-1, :]

def backward_step(self, state_batch: List[NetGameState], probs_batch: List[ActionProbs],
               value_batch: List[NDArray[(Any), np.float]], lr) -> Tuple[float, float]:
    if self.use_gpu:
        state_batch = Variable(torch.FloatTensor(state_batch).cuda())
        probs_batch = Variable(torch.FloatTensor(probs_batch).cuda())
        value_batch = Variable(torch.FloatTensor(value_batch).cuda())
    else:
        state_batch = Variable(torch.FloatTensor(state_batch))
        probs_batch = Variable(torch.FloatTensor(probs_batch))
        value_batch = Variable(torch.FloatTensor(value_batch))

    self.optimizer.zero_grad()
    for param_group in self.optimizer.param_groups:
        param_group['lr'] = lr

    log_act_probs, value = self.policy_value_net(state_batch)
    # loss = (z - v)^2 - pi*T * log(p) + c||theta||^2
    value_loss = F.mse_loss(value.view(-1), value_batch)
    policy_loss = -torch.mean(torch.sum(probs_batch * log_act_probs, 1))
    loss = value_loss + policy_loss
    loss.backward()
    self.optimizer.step()
    entropy = -torch.mean(torch.sum(torch.exp(log_act_probs) * log_act_probs, 1))
    return loss.item(), entropy.item()

import sys
import pygame
pygame.init()
display = pygame.display.set_mode((800,600))
clock = pygame.time.Clock()

while True:
	for event in pygame.event.get():
		if event.type == pygame.QUIT:
			sys.exit(0)
		else:
			pygame.display.update()
			clock.tick(1)

class PyGameBoard:

	def __init__(self, connectNGame: ConnectNGame):
		self.connectNGame = connectNGame
		pygame.init()

	def next_user_input(self) -> Tuple[int, int]:
		self.action = None
		while not self.action:
			self.check_event()
			self._render()
			self.clock.tick(60)
		return self.action
  
  def move(self, r: int, c: int) -> int:
		return self.connectNGame.move(r, c)
  
if __name__ == '__main__':
	connectNGame = ConnectNGame()
	pygameBoard = PyGameBoard(connectNGame)
	while not pygameBoard.isGameOver():
		pos = pygameBoard.next_user_input()
		pygameBoard.move(*pos)

	pygame.quit()

def check_event(self):
	for e in pygame.event.get():
		if e.type == pygame.QUIT:
			pygame.quit()
			sys.exit(0)
		elif e.type == pygame.MOUSEBUTTONDOWN:
			self._handle_user_input(e)
    
def _handle_user_input(self, e: Event) -> Tuple[int, int]:
	origin_x = self.start_x - self.edge_size
	origin_y = self.start_y - self.edge_size
	size = (self.board_size - 1) * self.grid_size + self.edge_size * 2
	pos = e.pos
	if origin_x <= pos[0] <= origin_x + size and origin_y <= pos[1] <= origin_y + size:
		if not self.connectNGame.gameOver:
			x = pos[0] - origin_x
			y = pos[1] - origin_y
			r = int(y // self.grid_size)
			c = int(x // self.grid_size)
			valid = self.connectNGame.checkAction(r, c)
			if valid:
				self.action = (r, c)
				return self.action

class ConnectNGym(gym.Env):

	def reset(self) -> ConnectNGame:
		"""Resets the state of the environment and returns an initial observation.

		Returns:
			observation (object): the initial observation.
		"""
		raise NotImplementedError


	def step(self, action: Tuple[int, int]) -> Tuple[ConnectNGame, int, bool, None]:
		"""Run one timestep of the environment's dynamics. When end of
		episode is reached, you are responsible for calling `reset()`
		to reset this environment's state.

		Accepts an action and returns a tuple (observation, reward, done, info).

		Args:
			action (object): an action provided by the agent

		Returns:
			observation (object): agent's observation of the current environment
			reward (float) : amount of reward returned after previous action
			done (bool): whether the episode has ended, in which case further step() calls will return undefined results
			info (dict): contains auxiliary diagnostic information (helpful for debugging, and sometimes learning)
		"""
		raise NotImplementedError



	def render(self, mode='human'):
		"""
		Renders the environment.

		The set of supported modes varies per environment. (And some
		environments do not support rendering at all.) By convention,
		if mode is:

		- human: render to the current display or terminal and
			return nothing. Usually for human consumption.
		- rgb_array: Return an numpy.ndarray with shape (x, y, 3),
			representing RGB values for an x-by-y pixel image, suitable
			for turning into a video.
		- ansi: Return a string (str) or StringIO.StringIO containing a
			terminal-style text representation. The text can include newlines
			and ANSI escape sequences (e.g. for colors).

		Note:
		Make sure that your class's metadata 'render.modes' key includes
		the list of supported modes. It's recommended to call super()
		in implementations to use the functionality of this method.

		Args:
			mode (str): the mode to render with
		"""
		raise NotImplementedError

def reset(self) -> ConnectNGame

def step(self, action: Tuple[int, int]) -> Tuple[ConnectNGame, int, bool, None]

def render(self, mode='human')

class ConnectNGym(gym.Env):

	def __init__(self, pygameBoard: PyGameBoard, isGUI=True, displaySec=2):
		self.pygameBoard = pygameBoard
		self.isGUI = isGUI
		self.displaySec = displaySec
		self.action_space = spaces.Discrete(pygameBoard.board_size * pygameBoard.board_size)
		self.observation_space = spaces.Discrete(pygameBoard.board_size * pygameBoard.board_size)
		self.seed()
		self.reset()

	def reset(self) -> ConnectNGame:
		self.pygameBoard.connectNGame.reset()
		return copy.deepcopy(self.pygameBoard.connectNGame)

	def step(self, action: Tuple[int, int]) -> Tuple[ConnectNGame, int, bool, None]:
		# assert self.action_space.contains(action)

		r, c = action
		reward = REWARD_NONE
		result = self.pygameBoard.move(r, c)
		if self.pygameBoard.isGameOver():
			reward = result

		return copy.deepcopy(self.pygameBoard.connectNGame), reward, not result is None, None

	def render(self, mode='human'):
		if not self.isGUI:
			self.pygameBoard.connectNGame.drawText()
			time.sleep(self.displaySec)
		else:
			self.pygameBoard.display(sec=self.displaySec)

	def get_available_actions(self) -> List[Tuple[int, int]]:
		return self.pygameBoard.getAvailablePositions()

def similarStatus(self, status: Tuple[Tuple[int, ...]]) -> List[Tuple[Tuple[int, ...]]]:
	ret = []
	rotatedS = status
	for _ in range(4):
		rotatedS = self.rotate(rotatedS)
		ret.append(rotatedS)
	return ret

def rotate(self, status: Tuple[Tuple[int, ...]]) -> Tuple[Tuple[int, ...]]:
	N = len(status)
	board = [[ConnectNGame.AVAILABLE] * N for _ in range(N)]

	for r in range(N):
		for c in range(N):
			board[c][N - 1 - r] = status[r][c]

	return tuple([tuple(board[i]) for i in range(N)])

class PlannedMinimaxStrategy(Strategy):
	def __init__(self, game: ConnectNGame):
		super().__init__()
		self.game = copy.deepcopy(game)
		self.dpMap = {}  # game_status => result, move
		self.result = self.minimax(game.getStatus())


	def action(self, game: ConnectNGame) -> Tuple[int, Tuple[int, int]]:
		game = copy.deepcopy(game)

		player = game.currentPlayer
		bestResult = player * -1  # assume opponent win as worst result
		bestMove = None
		for move in game.getAvailablePositions():
			game.move(*move)
			status = game.getStatus()
			game.undo()

			result = self.dpMap[status]

			if player == ConnectNGame.PLAYER_A:
				bestResult = max(bestResult, result)
			else:
				bestResult = min(bestResult, result)
			# update bestMove if any improvement
			bestMove = move if bestResult == result else bestMove
			print(f'move {move} => {result}')

		return bestResult, bestMove

class BaseAgent(object):
	def __init__(self):
		pass

	def act(self, game: PyGameBoard, available_actions):
		return random.choice(available_actions)

class AIAgent(BaseAgent):
	def __init__(self, strategy: Strategy):
		self.strategy = strategy

	def act(self, game: PyGameBoard, available_actions):
		result, move = self.strategy.action(game.connectNGame)
		assert move in available_actions
		return move

class HumanAgent(BaseAgent):
	def __init__(self):
		pass

	def act(self, game: PyGameBoard, available_actions):
		return game.next_user_input()

def play_ai_vs_ai(env: ConnectNGym):
	plannedMinimaxAgent = AIAgent(PlannedMinimaxStrategy(env.pygameBoard.connectNGame))
	play(env, plannedMinimaxAgent, plannedMinimaxAgent)


def play(env: ConnectNGym, agent1: BaseAgent, agent2: BaseAgent):
	agents = [agent1, agent2]

	while True:
		env.reset()
		done = False
		agent_id = -1
		while not done:
			agent_id = (agent_id + 1) % 2
			available_actions = env.get_available_actions()
			agent = agents[agent_id]
			action = agent.act(pygameBoard, available_actions)
			_, reward, done, info = env.step(action)
			env.render(True)

			if done:
				print(f'result={reward}')
				time.sleep(3)
				break


if __name__ == '__main__':
	pygameBoard = PyGameBoard(connectNGame=ConnectNGame(board_size=3, N=3))
	env = ConnectNGym(pygameBoard)
	env.render(True)

	play_ai_vs_ai(env)

# AC
from typing import List

class Solution:
    def tictactoe(self, moves: List[List[int]]) -> str:
        board = [[0] * 3 for _ in range(3)]
        for idx, xy in enumerate(moves):
            player = 1 if idx % 2 == 0 else -1
            board[xy[0]][xy[1]] = player

        turn = 0
        row, col = [0, 0, 0], [0, 0, 0]
        diag1, diag2 = False, False
        for r in range(3):
            for c in range(3):
                turn += board[r][c]
                row[r] += board[r][c]
                col[c] += board[r][c]
                if r == c:
                    diag1 += board[r][c]
                if r + c == 2:
                    diag2 += board[r][c]

        oWin = any(row[r] == 3 for r in range(3)) or any(col[c] == 3 for c in range(3)) or diag1 == 3 or diag2 == 3
        xWin = any(row[r] == -3 for r in range(3)) or any(col[c] == -3 for c in range(3)) or diag1 == -3 or diag2 == -3

        return "A" if oWin else "B" if xWin else "Draw" if len(moves) == 9 else "Pending"

# AC
from typing import List

class Solution:
    def checkWin(self, r: int, c: int) -> bool:
        north = self.getConnectedNum(r, c, -1, 0)
        south = self.getConnectedNum(r, c, 1, 0)

        east = self.getConnectedNum(r, c, 0, 1)
        west = self.getConnectedNum(r, c, 0, -1)

        south_east = self.getConnectedNum(r, c, 1, 1)
        north_west = self.getConnectedNum(r, c, -1, -1)

        north_east = self.getConnectedNum(r, c, -1, 1)
        south_west = self.getConnectedNum(r, c, 1, -1)

        if (north + south + 1 >= 3) or (east + west + 1 >= 3) or \
                (south_east + north_west + 1 >= 3) or (north_east + south_west + 1 >= 3):
            return True
        return False

    def getConnectedNum(self, r: int, c: int, dr: int, dc: int) -> int:
        player = self.board[r][c]
        result = 0
        i = 1
        while True:
            new_r = r + dr * i
            new_c = c + dc * i
            if 0 <= new_r < 3 and 0 <= new_c < 3:
                if self.board[new_r][new_c] == player:
                    result += 1
                else:
                    break
            else:
                break
            i += 1
        return result

    def tictactoe(self, moves: List[List[int]]) -> str:
        self.board = [[0] * 3 for _ in range(3)]
        for idx, xy in enumerate(moves):
            player = 1 if idx % 2 == 0 else -1
            self.board[xy[0]][xy[1]] = player

        # only check last move
        r, c = moves[-1]
        win = self.checkWin(r, c)
        if win:
            return "A" if len(moves) % 2 == 1 else "B"

        return "Draw" if len(moves) == 9 else "Pending"

# AC
from typing import List

class Solution:

    def convertCell(self, c:str):
        return 1 if c == 'X' else -1 if c == 'O' else 0

    def validTicTacToe(self, board: List[str]) -> bool:
        turn = 0
        row, col = [0, 0, 0], [0, 0, 0]
        diag1, diag2 = False, False
        for r in range(3):
            for c in range(3):
                turn += self.convertCell(board[r][c])
                row[r] += self.convertCell(board[r][c])
                col[c] += self.convertCell(board[r][c])
                if r == c:
                    diag1 += self.convertCell(board[r][c])
                if r + c == 2:
                    diag2 += self.convertCell(board[r][c])

        xWin = any(row[r] == 3 for r in range(3)) or any(col[c] == 3 for c in range(3)) or diag1 == 3 or diag2 == 3
        oWin = any(row[r] == -3 for r in range(3)) or any(col[c] == -3 for c in range(3)) or diag1 == -3 or diag2 == -3
        if (xWin and turn == 0) or (oWin and turn == 1):
            return False
        return (turn == 0 or turn == 1) and (not xWin or not oWin)

# AC
class TicTacToe:

    def __init__(self, n:int):
        """
        Initialize your data structure here.
        :type n: int
        """
        self.row, self.col, self.diag1, self.diag2, self.n = [0] * n, [0] * n, 0, 0, n

    def move(self, row:int, col:int, player:int) -> int:
        """
        Player {player} makes a move at ({row}, {col}).
        @param row The row of the board.
        @param col The column of the board.
        @param player The player, can be either 1 or 2.
        @return The current winning condition, can be either:
                0: No one wins.
                1: Player 1 wins.
                2: Player 2 wins.
        """
        if player == 2:
            player = -1

        self.row[row] += player
        self.col[col] += player
        if row == col:
            self.diag1 += player
        if row + col == self.n - 1:
            self.diag2 += player

        if self.n in [self.row[row], self.col[col], self.diag1, self.diag2]:
            return 1
        if -self.n in [self.row[row], self.col[col], self.diag1, self.diag2]:
            return 2
        return 0

class ConnectNGame:

    PLAYER_A = 1
    PLAYER_B = -1
    AVAILABLE = 0
    RESULT_TIE = 0
    RESULT_A_WIN = 1
    RESULT_B_WIN = -1

    def __init__(self, N:int = 3, board_size:int = 3):
        assert N <= board_size
        self.N = N
        self.board_size = board_size
        self.board = [[ConnectNGame.AVAILABLE] * board_size for _ in range(board_size)]
        self.gameOver = False
        self.gameResult = None
        self.currentPlayer = ConnectNGame.PLAYER_A
        self.remainingPosNum = board_size * board_size
        self.actionStack = []

    def move(self, r: int, c: int) -> int:
        """

        :param r:
        :param c:
        :return: None: game ongoing
        """
        assert self.board[r][c] == ConnectNGame.AVAILABLE
        self.board[r][c] = self.currentPlayer
        self.actionStack.append((r, c))
        self.remainingPosNum -= 1
        if self.checkWin(r, c):
            self.gameOver = True
            self.gameResult = self.currentPlayer
            return self.currentPlayer
        if self.remainingPosNum == 0:
            self.gameOver = True
            self.gameResult = ConnectNGame.RESULT_TIE
            return ConnectNGame.RESULT_TIE
        self.currentPlayer *= -1

    def undo(self):
        if len(self.actionStack) > 0:
            lastAction = self.actionStack.pop()
            r, c = lastAction
            self.board[r][c] = ConnectNGame.AVAILABLE
            self.currentPlayer = ConnectNGame.PLAYER_A if len(self.actionStack) % 2 == 0 else ConnectNGame.PLAYER_B
            self.remainingPosNum += 1
            self.gameOver = False
            self.gameResult = None
        else:
            raise Exception('No lastAction')

    def getAvailablePositions(self) -> List[Tuple[int, int]]:
        return [(i,j) for i in range(self.board_size) for j in range(self.board_size) if self.board[i][j] == ConnectNGame.AVAILABLE]

    def getStatus(self) -> Tuple[Tuple[int, ...]]:
        return tuple([tuple(self.board[i]) for i in range(self.board_size)])

class Strategy(ABC):

    def __init__(self):
        super().__init__()

    @abstractmethod
    def action(self, game: ConnectNGame) -> Tuple[int, Tuple[int, int]]:
        pass

class MinimaxStrategy(Strategy):
    def action(self, game: ConnectNGame) -> Tuple[int, Tuple[int, int]]:
        self.game = copy.deepcopy(game)
        result, move = self.minimax()
        return result, move

    def minimax(self) -> Tuple[int, Tuple[int, int]]:
        game = self.game
        bestMove = None
        assert not game.gameOver
        if game.currentPlayer == ConnectNGame.PLAYER_A:
            ret = -math.inf
            for pos in game.getAvailablePositions():
                move = pos
                result = game.move(*pos)
                if result is None:
                    assert not game.gameOver
                    result, oppMove = self.minimax()
                game.undo()
                ret = max(ret, result)
                bestMove = move if ret == result else bestMove
                if ret == 1:
                    return 1, move
            return ret, bestMove
        else:
            ret = math.inf
            for pos in game.getAvailablePositions():
                move = pos
                result = game.move(*pos)
                if result is None:
                    assert not game.gameOver
                    result, oppMove = self.minimax()
                game.undo()
                ret = min(ret, result)
                bestMove = move if ret == result else bestMove
                if ret == -1:
                    return -1, move
            return ret, bestMove

class CountingMinimaxStrategy(Strategy):
    def action(self, game: ConnectNGame) -> Tuple[int, Tuple[int, int]]:
        self.game = copy.deepcopy(game)
        self.dpMap = {}
        result, move = self.minimax(game.getStatus())
        return result, move

    def minimax(self, gameStatus: Tuple[Tuple[int, ...]]) -> Tuple[int, Tuple[int, int]]:
        # print(f'Current {len(strategy.dpMap)}')

        if gameStatus in self.dpMap:
            return self.dpMap[gameStatus]

        game = self.game
        bestMove = None
        assert not game.gameOver
        if game.currentPlayer == ConnectNGame.PLAYER_A:
            ret = -math.inf
            for pos in game.getAvailablePositions():
                move = pos
                result = game.move(*pos)
                if result is None:
                    assert not game.gameOver
                    result, oppMove = self.minimax(game.getStatus())
                    self.dpMap[game.getStatus()] = result, oppMove
                else:
                    self.dpMap[game.getStatus()] = result, move
                game.undo()
                ret = max(ret, result)
                bestMove = move if ret == result else bestMove
            self.dpMap[gameStatus] = ret, bestMove
            return ret, bestMove
        else:
            ret = math.inf
            for pos in game.getAvailablePositions():
                move = pos
                result = game.move(*pos)

                if result is None:
                    assert not game.gameOver
                    result, oppMove = self.minimax(game.getStatus())
                    self.dpMap[game.getStatus()] = result, oppMove
                else:
                    self.dpMap[game.getStatus()] = result, move
                game.undo()
                ret = min(ret, result)
                bestMove = move if ret == result else bestMove
            self.dpMap[gameStatus] = ret, bestMove
            return ret, bestMove


if __name__ == '__main__':
    tic_tac_toe = ConnectNGame(N=3, board_size=3)
    strategy = CountingMinimaxStrategy()
    strategy.action(tic_tac_toe)
    print(f'Game States Number {len(strategy.dpMap)}')

class AlphaBetaStrategy(Strategy):
    def action(self, game: ConnectNGame) -> Tuple[int, Tuple[int, int]]:
        self.game = game
        result, move = self.alpha_beta(self.game.getStatus(), -math.inf, math.inf)
        return result, move

    def alpha_beta(self, gameStatus: Tuple[Tuple[int, ...]], alpha:int=None, beta:int=None) -> Tuple[int, Tuple[int, int]]:
        game = self.game
        bestMove = None
        assert not game.gameOver
        if game.currentPlayer == ConnectNGame.PLAYER_A:
            ret = -math.inf
            for pos in game.getAvailablePositions():
                move = pos
                result = game.move(*pos)
                if result is None:
                    assert not game.gameOver
                    result, oppMove = self.alpha_beta(game.getStatus(), alpha, beta)
                game.undo()
                alpha = max(alpha, result)
                ret = max(ret, result)
                bestMove = move if ret == result else bestMove
                if alpha >= beta or ret == 1:
                    return ret, move
            return ret, bestMove
        else:
            ret = math.inf
            for pos in game.getAvailablePositions():
                move = pos
                result = game.move(*pos)
                if result is None:
                    assert not game.gameOver
                    result, oppMove = self.alpha_beta(game.getStatus(), alpha, beta)
                game.undo()
                beta = min(beta, result)
                ret = min(ret, result)
                bestMove = move if ret == result else bestMove
                if alpha >= beta or ret == -1:
                    return ret, move
            return ret, bestMove

class AlphaBetaDPStrategy(Strategy):
    def action(self, game: ConnectNGame) -> Tuple[int, Tuple[int, int]]:
        self.game = game
        self.alphaBetaStack = [(-math.inf, math.inf)]
        result, move = self.alpha_beta_dp(self.game.getStatus())
        return result, move

    @lru_cache(maxsize=None)
    def alpha_beta_dp(self, gameStatus: Tuple[Tuple[int, ...]]) -> Tuple[int, Tuple[int, int]]:
        alpha, beta = self.alphaBetaStack[-1]
        game = self.game
        bestMove = None
        assert not game.gameOver
        if game.currentPlayer == ConnectNGame.PLAYER_A:
            ret = -math.inf
            for pos in game.getAvailablePositions():
                move = pos
                result = game.move(*pos)
                if result is None:
                    assert not game.gameOver
                    self.alphaBetaStack.append((alpha, beta))
                    result, oppMove = self.alpha_beta_dp(game.getStatus())
                    self.alphaBetaStack.pop()
                game.undo()
                alpha = max(alpha, result)
                ret = max(ret, result)
                bestMove = move if ret == result else bestMove
                if alpha >= beta or ret == 1:
                    return ret, move
            return ret, bestMove
        else:
            ret = math.inf
            for pos in game.getAvailablePositions():
                move = pos
                result = game.move(*pos)
                if result is None:
                    assert not game.gameOver
                    self.alphaBetaStack.append((alpha, beta))
                    result, oppMove = self.alpha_beta_dp(game.getStatus())
                    self.alphaBetaStack.pop()
                game.undo()
                beta = min(beta, result)
                ret = min(ret, result)
                bestMove = move if ret == result else bestMove
                if alpha >= beta or ret == -1:
                    return ret, move
            return ret, bestMove

# TLE
# Time Complexity: O(exponential)
class Solution_BruteForce:

    def canWinNim(self, n: int) -> bool:
        if n <= 3:
            return True
        for i in range(1, 4):
            if not self.canWinNim(n - i):
                return True
        return False

# RecursionError: maximum recursion depth exceeded in comparison n=1348820612
# Time Complexity: O(N)
class Solution_DP:
    from functools import lru_cache
    @lru_cache(maxsize=None)
    def canWinNim(self, n: int) -> bool:
        if n <= 3:
            return True
        for i in range(1, 4):
            if not self.canWinNim(n - i):
                return True
        return False

# TLE for 1348820612
# Time Complexity: O(N)
class Solution:
    def canWinNim(self, n: int) -> bool:
        if n <= 3:
            return True
        last3, last2, last1 = True, True, True
        for i in range(4, n+1):
            this = not (last3 and last2 and last1)
            last3, last2, last1 = last2, last1, this
        return last1

# AC
# Time Complexity: O(1)
class Solution:
    def canWinNim(self, n: int) -> bool:
        return not (n % 4 == 0)

# AC
# Time Complexity: O(2^N)
# Slow: 6300ms
from typing import List

class Solution:

    def maxDiff(self, l: int, r:int) -> int:
        if l == r:
            return self.nums[l]
        return max(self.nums[l] - self.maxDiff(l + 1, r), self.nums[r] - self.maxDiff(l, r - 1))

    def PredictTheWinner(self, nums: List[int]) -> bool:
        self.nums = nums
        return self.maxDiff(0, len(nums) - 1) >= 0