"""simple docstring"""



import tensorflow as tf

from ...tf_utils import shape_list






class 				snake_case__     (   tf.keras.layers.Layer   ):


 def __init__(				self  ,						lowerCamelCase  ,						lowerCamelCase  ,						lowerCamelCase  ,						lowerCamelCase  ,						lowerCamelCase=1  ,						lowerCamelCase=False  ,						**lowerCamelCase		):
        super().__init__(**lowerCamelCase		)

        __a     				=  vocab_size
        __a     				=  d_embed
        __a     				=  d_proj

        __a     				=  cutoffs + [vocab_size]
        __a     				=  [0] + self.cutoffs
        __a     				=  div_val

        __a     				=  self.cutoffs[0]
        __a     				=  len(self.cutoffs		) - 1
        __a     				=  self.shortlist_size + self.n_clusters
        __a     				=  keep_order

        __a     				=  []
        __a     				=  []


 def 		a__ (				self  ,						lowerCamelCase		):
        if self.n_clusters > 0:
               __a     				=  self.add_weight(
                   shape=(self.n_clusters, self.d_embed)  ,						initializer="zeros"  ,						trainable=lowerCamelCase  ,						name="cluster_weight"		)
               __a     				=  self.add_weight(
                   shape=(self.n_clusters,)  ,						initializer="zeros"  ,						trainable=lowerCamelCase  ,						name="cluster_bias"		)

        if self.div_val == 1:
               for i in range(len(self.cutoffs		)		):
                      if self.d_proj != self.d_embed:
                             __a     				=  self.add_weight(
                                 shape=(self.d_embed, self.d_proj)  ,						initializer="zeros"  ,						trainable=lowerCamelCase  ,						name=F"out_projs_._{i}"  ,						)
                             self.out_projs.append(lowerCamelCase		)
                      else:
                             self.out_projs.append(lowerCamelCase		)
                      __a     				=  self.add_weight(
                          shape=(self.vocab_size, self.d_embed)  ,						initializer="zeros"  ,						trainable=lowerCamelCase  ,						name=F"out_layers_._{i}_._weight"  ,						)
                      __a     				=  self.add_weight(
                          shape=(self.vocab_size,)  ,						initializer="zeros"  ,						trainable=lowerCamelCase  ,						name=F"out_layers_._{i}_._bias"  ,						)
                      self.out_layers.append((weight, bias)		)
        else:
               for i in range(len(self.cutoffs		)		):
                      __a				, __a     				=  self.cutoff_ends[i], self.cutoff_ends[i + 1]
                      __a     				=  self.d_embed // (self.div_val**i)

                      __a     				=  self.add_weight(
                          shape=(d_emb_i, self.d_proj)  ,						initializer="zeros"  ,						trainable=lowerCamelCase  ,						name=F"out_projs_._{i}"		)
                      self.out_projs.append(lowerCamelCase		)
                      __a     				=  self.add_weight(
                          shape=(r_idx - l_idx, d_emb_i)  ,						initializer="zeros"  ,						trainable=lowerCamelCase  ,						name=F"out_layers_._{i}_._weight"  ,						)
                      __a     				=  self.add_weight(
                          shape=(r_idx - l_idx,)  ,						initializer="zeros"  ,						trainable=lowerCamelCase  ,						name=F"out_layers_._{i}_._bias"  ,						)
                      self.out_layers.append((weight, bias)		)
        super().build(lowerCamelCase		)


 @staticmethod
 def 		a__ (				lowerCamelCase  ,						lowerCamelCase  ,						lowerCamelCase  ,						lowerCamelCase=None		):
        __a     				=  x
        if proj is not None:
               __a     				=  tf.einsum("ibd,ed->ibe"  ,						lowerCamelCase  ,						lowerCamelCase		)
        return tf.einsum("ibd,nd->ibn"  ,						lowerCamelCase  ,						lowerCamelCase		) + b


 @staticmethod
 def 		a__ (				lowerCamelCase  ,						lowerCamelCase		):
        __a     				=  shape_list(lowerCamelCase		)
        __a     				=  tf.range(lp_size[0]  ,						dtype=target.dtype		)
        __a     				=  tf.stack([r, target]  ,						1		)
        return tf.gather_nd(lowerCamelCase  ,						lowerCamelCase		)






 def 		a__ (				self  ,						lowerCamelCase  ,						lowerCamelCase  ,						lowerCamelCase=True  ,						lowerCamelCase=False		):
        __a     				=  0
        if self.n_clusters == 0:
               __a     				=  self._logit(lowerCamelCase  ,						self.out_layers[0][0]  ,						self.out_layers[0][1]  ,						self.out_projs[0]		)
               if target is not None:
                      __a     				=  tf.nn.sparse_softmax_cross_entropy_with_logits(labels=lowerCamelCase  ,						logits=lowerCamelCase		)
               __a     				=  tf.nn.log_softmax(lowerCamelCase  ,						axis=-1		)
        else:
               __a     				=  shape_list(lowerCamelCase		)
               __a     				=  []
               __a     				=  tf.zeros(hidden_sizes[:2]		)
               for i in range(len(self.cutoffs		)		):
                      __a				, __a     				=  self.cutoff_ends[i], self.cutoff_ends[i + 1]
                      if target is not None:
                             __a     				=  (target >= l_idx) & (target < r_idx)
                             __a     				=  tf.where(lowerCamelCase		)
                             __a     				=  tf.boolean_mask(lowerCamelCase  ,						lowerCamelCase		) - l_idx

                      if self.div_val == 1:
                             __a     				=  self.out_layers[0][0][l_idx:r_idx]
                             __a     				=  self.out_layers[0][1][l_idx:r_idx]
                      else:
                             __a     				=  self.out_layers[i][0]
                             __a     				=  self.out_layers[i][1]

                      if i == 0:
                             __a     				=  tf.concat([cur_W, self.cluster_weight]  ,						0		)
                             __a     				=  tf.concat([cur_b, self.cluster_bias]  ,						0		)

                             __a     				=  self._logit(lowerCamelCase  ,						lowerCamelCase  ,						lowerCamelCase  ,						self.out_projs[0]		)
                             __a     				=  tf.nn.log_softmax(lowerCamelCase		)
                             out.append(head_logprob[..., : self.cutoffs[0]]		)
                             if target is not None:
                                    __a     				=  tf.boolean_mask(lowerCamelCase  ,						lowerCamelCase		)
                                    __a     				=  self._gather_logprob(lowerCamelCase  ,						lowerCamelCase		)
                      else:
                             __a     				=  self._logit(lowerCamelCase  ,						lowerCamelCase  ,						lowerCamelCase  ,						self.out_projs[i]		)
                             __a     				=  tf.nn.log_softmax(lowerCamelCase		)
                             __a     				=  self.cutoffs[0] + i - 1  # No probability for the head cluster
                             __a     				=  head_logprob[..., cluster_prob_idx, None] + tail_logprob
                             out.append(lowerCamelCase		)
                             if target is not None:
                                    __a     				=  tf.boolean_mask(lowerCamelCase  ,						lowerCamelCase		)
                                    __a     				=  tf.boolean_mask(lowerCamelCase  ,						lowerCamelCase		)
                                    __a     				=  self._gather_logprob(lowerCamelCase  ,						lowerCamelCase		)
                                    cur_logprob += cur_head_logprob[:, self.cutoff_ends[1] + i - 1]
                      if target is not None:
                             loss += tf.scatter_nd(lowerCamelCase  ,						-cur_logprob  ,						shape_list(lowerCamelCase		)		)
               __a     				=  tf.concat(lowerCamelCase  ,						axis=-1		)

        if target is not None:
               if return_mean:
                      __a     				=  tf.reduce_mean(lowerCamelCase		)
               # Add the training-time loss value to the layer using `self.add_loss()`.
               self.add_loss(lowerCamelCase		)

               # Log the loss as a metric (we could log arbitrary metrics,
               # including different metrics for training and inference.
               self.add_metric(lowerCamelCase  ,						name=self.name  ,						aggregation="mean" if return_mean else ""		)

        return out

"""simple docstring"""



from __future__ import annotations



def 					_lowerCamelCase(					a ,  a ,  a ,  a ,  a ,  ):
       __a     				=  len(a							)

       # If row is equal to the size of the board it means there are a queen in each row in
       # the current board (possible_board)
       if row == n:
              # We convert the variable possible_board that looks like this: [1, 3, 0, 2] to
              # this: ['. Q . . ', '. . . Q ', 'Q . . . ', '. . Q . ']
              boards.append([". " * i + "Q " + ". " * (n - 1 - i) for i in possible_board]							)
              return

       # We iterate each column in the row to find all possible results in each row
       for col in range(a							):
              # We apply that we learned previously. First we check that in the current board
              # (possible_board) there are not other same value because if there is it means
              # that there are a collision in vertical. Then we apply the two formulas we
              # learned before:
              #
              # 45º: y - x = b or 45: row - col = b
              # 135º: y + x = b or row + col = b.
              #
              # And we verify if the results of this two formulas not exist in their variables
              # respectively.  (diagonal_right_collisions, diagonal_left_collisions)
              #
              # If any or these are True it means there is a collision so we continue to the
              # next value in the for loop.
              if (
                  col in possible_board
                  or row - col in diagonal_right_collisions
                  or row + col in diagonal_left_collisions
              ):
                     continue

              # If it is False we call dfs function again and we update the inputs
              depth_first_search(
                  [*possible_board, col] ,  [*diagonal_right_collisions, row - col] ,  [*diagonal_left_collisions, row + col] ,  a ,  a ,  )



def 					_lowerCamelCase(					a							):
       __a     				=  []
       depth_first_search([] ,  [] ,  [] ,  a ,  a							)

       # Print all the boards
       for board in boards:
              for column in board:
                     print(a							)
              print(""							)

       print(len(a							) ,  "solutions were found."							)


if __name__ == "__main__":
   import doctest

   doctest.testmod()
   n_queens_solution(4)
