





from __future__ import annotations




def     a__ (					lowercase__  ,    lowercase__  ,    lowercase__  ,    lowercase__  ,    lowercase__  ,    ):






   '''simple docstring'''






   UpperCAmelCase_											=len(lowercase__  )

   # 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(lowercase__  ):
      # 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]  ,    lowercase__  ,    lowercase__  ,    )




def     a__ (					lowercase__  ):






   '''simple docstring'''






   UpperCAmelCase_											=[]
   depth_first_search([]  ,    []  ,    []  ,    lowercase__  ,    lowercase__  )

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

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


if __name__ == "__main__":
     import doctest

     doctest.testmod()
     n_queens_solution(4)











import unittest

import numpy as np

from transformers.testing_utils import require_pytesseract, require_torch
from transformers.utils import is_pytesseract_available, is_torch_available

from ...test_image_processing_common import ImageProcessingSavingTestMixin, prepare_image_inputs


if is_torch_available():
     import torch

if is_pytesseract_available():
     from PIL import Image

     from transformers import LayoutLMvaImageProcessor

class      A       (	unittest.TestCase						):



      def __init__(	self:						Optional[Any]		,  _lowerCAmelCase:						Tuple		,  _lowerCAmelCase:						Dict=7		,  _lowerCAmelCase:						int=3		,  _lowerCAmelCase:						int=18		,  _lowerCAmelCase:						Optional[int]=30		,  _lowerCAmelCase:						List[str]=400		,  _lowerCAmelCase:						Tuple=True		,  _lowerCAmelCase:						Optional[Any]=None		,  _lowerCAmelCase:						Optional[int]=True		,  )						->    Union[str, Any]:
         '''simple docstring'''

         UpperCAmelCase_											=size if size is not None else {"height": 18, "width": 18}
         UpperCAmelCase_											=parent
         UpperCAmelCase_											=batch_size
         UpperCAmelCase_											=num_channels
         UpperCAmelCase_											=image_size
         UpperCAmelCase_											=min_resolution
         UpperCAmelCase_											=max_resolution
         UpperCAmelCase_											=do_resize
         UpperCAmelCase_											=size
         UpperCAmelCase_											=apply_ocr






      def 	lowerCAmelCase__    (	self:						Optional[Any]       )						->    List[str]:
         '''simple docstring'''

         return {"do_resize": self.do_resize, "size": self.size, "apply_ocr": self.apply_ocr}

@require_torch
@require_pytesseract
class      A       (	__lowercase		,      unittest.TestCase						):
      _snake_case							     =LayoutLMvaImageProcessor if is_pytesseract_available() else None



      def 	lowerCAmelCase__    (	self:						Tuple       )						->    Dict:
         '''simple docstring'''

         UpperCAmelCase_											=LayoutLMvaImageProcessingTester(self       )



      @property
      def 	lowerCAmelCase__    (	self:						str       )						->    int:
         '''simple docstring'''

         return self.image_processor_tester.prepare_image_processor_dict()



      def 	lowerCAmelCase__    (	self:						Tuple       )						->    Union[str, Any]:
         '''simple docstring'''

         UpperCAmelCase_											=self.image_processing_class(**self.image_processor_dict       )
         self.assertTrue(hasattr(_lowerCAmelCase		,  "do_resize"       )       )
         self.assertTrue(hasattr(_lowerCAmelCase		,  "size"       )       )
         self.assertTrue(hasattr(_lowerCAmelCase		,  "apply_ocr"       )       )



      def 	lowerCAmelCase__    (	self:						str       )						->    Any:
         '''simple docstring'''

         UpperCAmelCase_											=self.image_processing_class.from_dict(self.image_processor_dict       )
         self.assertEqual(image_processor.size		,  {"height": 18, "width": 18}       )

         UpperCAmelCase_											=self.image_processing_class.from_dict(self.image_processor_dict		,  size=42       )
         self.assertEqual(image_processor.size		,  {"height": 42, "width": 42}       )



      def 	lowerCAmelCase__    (	self:						List[Any]       )						->    List[Any]:
         '''simple docstring'''

         pass



      def 	lowerCAmelCase__    (	self:						Dict       )						->    Optional[Any]:
         '''simple docstring'''

         UpperCAmelCase_											=self.image_processing_class(**self.image_processor_dict       )
         # create random PIL images
         UpperCAmelCase_											=prepare_image_inputs(self.image_processor_tester		,  equal_resolution=_lowerCAmelCase       )
         for image in image_inputs:
            self.assertIsInstance(_lowerCAmelCase		,  Image.Image       )

         # Test not batched input
         UpperCAmelCase_											=image_processing(image_inputs[0]		,  return_tensors="pt"       )
         self.assertEqual(
             encoding.pixel_values.shape		,  (
                 1,
                 self.image_processor_tester.num_channels,
                 self.image_processor_tester.size["height"],
                 self.image_processor_tester.size["width"],
             )		,  )

         self.assertIsInstance(encoding.words		,  _lowerCAmelCase       )
         self.assertIsInstance(encoding.boxes		,  _lowerCAmelCase       )

         # Test batched
         UpperCAmelCase_											=image_processing(_lowerCAmelCase		,  return_tensors="pt"       ).pixel_values
         self.assertEqual(
             encoded_images.shape		,  (
                 self.image_processor_tester.batch_size,
                 self.image_processor_tester.num_channels,
                 self.image_processor_tester.size["height"],
                 self.image_processor_tester.size["width"],
             )		,  )



      def 	lowerCAmelCase__    (	self:						List[Any]       )						->    Dict:
         '''simple docstring'''

         UpperCAmelCase_											=self.image_processing_class(**self.image_processor_dict       )
         # create random numpy tensors
         UpperCAmelCase_											=prepare_image_inputs(self.image_processor_tester		,  equal_resolution=_lowerCAmelCase		,  numpify=_lowerCAmelCase       )
         for image in image_inputs:
            self.assertIsInstance(_lowerCAmelCase		,  np.ndarray       )

         # Test not batched input
         UpperCAmelCase_											=image_processing(image_inputs[0]		,  return_tensors="pt"       ).pixel_values
         self.assertEqual(
             encoded_images.shape		,  (
                 1,
                 self.image_processor_tester.num_channels,
                 self.image_processor_tester.size["height"],
                 self.image_processor_tester.size["width"],
             )		,  )

         # Test batched
         UpperCAmelCase_											=image_processing(_lowerCAmelCase		,  return_tensors="pt"       ).pixel_values
         self.assertEqual(
             encoded_images.shape		,  (
                 self.image_processor_tester.batch_size,
                 self.image_processor_tester.num_channels,
                 self.image_processor_tester.size["height"],
                 self.image_processor_tester.size["width"],
             )		,  )



      def 	lowerCAmelCase__    (	self:						List[Any]       )						->    List[str]:
         '''simple docstring'''

         UpperCAmelCase_											=self.image_processing_class(**self.image_processor_dict       )
         # create random PyTorch tensors
         UpperCAmelCase_											=prepare_image_inputs(self.image_processor_tester		,  equal_resolution=_lowerCAmelCase		,  torchify=_lowerCAmelCase       )
         for image in image_inputs:
            self.assertIsInstance(_lowerCAmelCase		,  torch.Tensor       )

         # Test not batched input
         UpperCAmelCase_											=image_processing(image_inputs[0]		,  return_tensors="pt"       ).pixel_values
         self.assertEqual(
             encoded_images.shape		,  (
                 1,
                 self.image_processor_tester.num_channels,
                 self.image_processor_tester.size["height"],
                 self.image_processor_tester.size["width"],
             )		,  )

         # Test batched
         UpperCAmelCase_											=image_processing(_lowerCAmelCase		,  return_tensors="pt"       ).pixel_values
         self.assertEqual(
             encoded_images.shape		,  (
                 self.image_processor_tester.batch_size,
                 self.image_processor_tester.num_channels,
                 self.image_processor_tester.size["height"],
                 self.image_processor_tester.size["width"],
             )		,  )






      def 	lowerCAmelCase__    (	self:						Any       )						->    Optional[int]:
         '''simple docstring'''

         UpperCAmelCase_											=LayoutLMvaImageProcessor()

         from datasets import load_dataset

         UpperCAmelCase_											=load_dataset("hf-internal-testing/fixtures_docvqa"		,  split="test"       )

         UpperCAmelCase_											=Image.open(ds[0]["file"]       ).convert("RGB"       )

         UpperCAmelCase_											=image_processing(_lowerCAmelCase		,  return_tensors="pt"       )

         self.assertEqual(encoding.pixel_values.shape		,  (1, 3, 224, 224)       )
         self.assertEqual(len(encoding.words       )		,  len(encoding.boxes       )       )

         # fmt: off
         # the words and boxes were obtained with Tesseract 4.1.1
         UpperCAmelCase_											=[["11:14", "to", "11:39", "a.m", "11:39", "to", "11:44", "a.m.", "11:44", "a.m.", "to", "12:25", "p.m.", "12:25", "to", "12:58", "p.m.", "12:58", "to", "4:00", "p.m.", "2:00", "to", "5:00", "p.m.", "Coffee", "Break", "Coffee", "will", "be", "served", "for", "men", "and", "women", "in", "the", "lobby", "adjacent", "to", "exhibit", "area.", "Please", "move", "into", "exhibit", "area.", "(Exhibits", "Open)", "TRRF", "GENERAL", "SESSION", "(PART", "|)", "Presiding:", "Lee", "A.", "Waller", "TRRF", "Vice", "President", "“Introductory", "Remarks”", "Lee", "A.", "Waller,", "TRRF", "Vice", "Presi-", "dent", "Individual", "Interviews", "with", "TRRF", "Public", "Board", "Members", "and", "Sci-", "entific", "Advisory", "Council", "Mem-", "bers", "Conducted", "by", "TRRF", "Treasurer", "Philip", "G.", "Kuehn", "to", "get", "answers", "which", "the", "public", "refrigerated", "warehousing", "industry", "is", "looking", "for.", "Plus", "questions", "from", "the", "floor.", "Dr.", "Emil", "M.", "Mrak,", "University", "of", "Cal-", "ifornia,", "Chairman,", "TRRF", "Board;", "Sam", "R.", "Cecil,", "University", "of", "Georgia", "College", "of", "Agriculture;", "Dr.", "Stanley", "Charm,", "Tufts", "University", "School", "of", "Medicine;", "Dr.", "Robert", "H.", "Cotton,", "ITT", "Continental", "Baking", "Company;", "Dr.", "Owen", "Fennema,", "University", "of", "Wis-", "consin;", "Dr.", "Robert", "E.", "Hardenburg,", "USDA.", "Questions", "and", "Answers", "Exhibits", "Open", "Capt.", "Jack", "Stoney", "Room", "TRRF", "Scientific", "Advisory", "Council", "Meeting", "Ballroom", "Foyer"]]  # noqa: E231
         UpperCAmelCase_											=[[[141, 57, 214, 69], [228, 58, 252, 69], [141, 75, 216, 88], [230, 79, 280, 88], [142, 260, 218, 273], [230, 261, 255, 273], [143, 279, 218, 290], [231, 282, 290, 291], [143, 342, 218, 354], [231, 345, 289, 355], [202, 362, 227, 373], [143, 379, 220, 392], [231, 382, 291, 394], [144, 714, 220, 726], [231, 715, 256, 726], [144, 732, 220, 745], [232, 736, 291, 747], [144, 769, 218, 782], [231, 770, 256, 782], [141, 788, 202, 801], [215, 791, 274, 804], [143, 826, 204, 838], [215, 826, 240, 838], [142, 844, 202, 857], [215, 847, 274, 859], [334, 57, 427, 69], [440, 57, 522, 69], [369, 75, 461, 88], [469, 75, 516, 88], [528, 76, 562, 88], [570, 76, 667, 88], [675, 75, 711, 87], [721, 79, 778, 88], [789, 75, 840, 88], [369, 97, 470, 107], [484, 94, 507, 106], [518, 94, 562, 107], [576, 94, 655, 110], [668, 94, 792, 109], [804, 95, 829, 107], [369, 113, 465, 125], [477, 116, 547, 125], [562, 113, 658, 125], [671, 116, 748, 125], [761, 113, 811, 125], [369, 131, 465, 143], [477, 133, 548, 143], [563, 130, 698, 145], [710, 130, 802, 146], [336, 171, 412, 183], [423, 171, 572, 183], [582, 170, 716, 184], [728, 171, 817, 187], [829, 171, 844, 186], [338, 197, 482, 212], [507, 196, 557, 209], [569, 196, 595, 208], [610, 196, 702, 209], [505, 214, 583, 226], [595, 214, 656, 227], [670, 215, 807, 227], [335, 259, 543, 274], [556, 259, 708, 272], [372, 279, 422, 291], [435, 279, 460, 291], [474, 279, 574, 292], [587, 278, 664, 291], [676, 278, 738, 291], [751, 279, 834, 291], [372, 298, 434, 310], [335, 341, 483, 354], [497, 341, 655, 354], [667, 341, 728, 354], [740, 341, 825, 354], [335, 360, 430, 372], [442, 360, 534, 372], [545, 359, 687, 372], [697, 360, 754, 372], [765, 360, 823, 373], [334, 378, 428, 391], [440, 378, 577, 394], [590, 378, 705, 391], [720, 378, 801, 391], [334, 397, 400, 409], [370, 416, 529, 429], [544, 416, 576, 432], [587, 416, 665, 428], [677, 416, 814, 429], [372, 435, 452, 450], [465, 434, 495, 447], [511, 434, 600, 447], [611, 436, 637, 447], [649, 436, 694, 451], [705, 438, 824, 447], [369, 453, 452, 466], [464, 454, 509, 466], [522, 453, 611, 469], [625, 453, 792, 469], [370, 472, 556, 488], [570, 472, 684, 487], [697, 472, 718, 485], [732, 472, 835, 488], [369, 490, 411, 503], [425, 490, 484, 503], [496, 490, 635, 506], [645, 490, 707, 503], [718, 491, 761, 503], [771, 490, 840, 503], [336, 510, 374, 521], [388, 510, 447, 522], [460, 510, 489, 521], [503, 510, 580, 522], [592, 509, 736, 525], [745, 509, 770, 522], [781, 509, 840, 522], [338, 528, 434, 541], [448, 528, 596, 541], [609, 527, 687, 540], [700, 528, 792, 541], [336, 546, 397, 559], [407, 546, 431, 559], [443, 546, 525, 560], [537, 546, 680, 562], [688, 546, 714, 559], [722, 546, 837, 562], [336, 565, 449, 581], [461, 565, 485, 577], [497, 565, 665, 581], [681, 565, 718, 577], [732, 565, 837, 580], [337, 584, 438, 597], [452, 583, 521, 596], [535, 584, 677, 599], [690, 583, 787, 596], [801, 583, 825, 596], [338, 602, 478, 615], [492, 602, 530, 614], [543, 602, 638, 615], [650, 602, 676, 614], [688, 602, 788, 615], [802, 602, 843, 614], [337, 621, 502, 633], [516, 621, 615, 637], [629, 621, 774, 636], [789, 621, 827, 633], [337, 639, 418, 652], [432, 640, 571, 653], [587, 639, 731, 655], [743, 639, 769, 652], [780, 639, 841, 652], [338, 658, 440, 673], [455, 658, 491, 670], [508, 658, 602, 671], [616, 658, 638, 670], [654, 658, 835, 674], [337, 677, 429, 689], [337, 714, 482, 726], [495, 714, 548, 726], [561, 714, 683, 726], [338, 770, 461, 782], [474, 769, 554, 785], [489, 788, 562, 803], [576, 788, 643, 801], [656, 787, 751, 804], [764, 788, 844, 801], [334, 825, 421, 838], [430, 824, 574, 838], [584, 824, 723, 841], [335, 844, 450, 857], [464, 843, 583, 860], [628, 862, 755, 875], [769, 861, 848, 878]]]  # noqa: E231
         # fmt: on

         self.assertListEqual(encoding.words		,  _lowerCAmelCase       )
         self.assertListEqual(encoding.boxes		,  _lowerCAmelCase       )

         # with apply_OCR = False
         UpperCAmelCase_											=LayoutLMvaImageProcessor(apply_ocr=_lowerCAmelCase       )

         UpperCAmelCase_											=image_processing(_lowerCAmelCase		,  return_tensors="pt"       )

         self.assertEqual(encoding.pixel_values.shape		,  (1, 3, 224, 224)       )




