├── .gitignore
├── LICENSE
├── README.md
├── data
    └── test.csv
├── data_load.py
├── fig
    └── training_curve.png
├── generate_sudoku.py
├── hyperparams.py
├── modules.py
├── results
    └── model.ckpt-23844.txt
├── test.py
└── train.py


/.gitignore:
--------------------------------------------------------------------------------
1 | *.pyc
2 | asset/
3 | data/
4 | _*
5 | *~
6 | 
7 | 
8 | 


--------------------------------------------------------------------------------
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--------------------------------------------------------------------------------
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675 | 


--------------------------------------------------------------------------------
/README.md:
--------------------------------------------------------------------------------
  1 | # Can Convolutional Neural Networks Crack Sudoku Puzzles?
  2 | 
  3 | Sudoku is a popular number puzzle that requires you to fill blanks in a 9X9 grid with digits so that each column, each row, and each of the nine 3×3 subgrids contains all of the digits from 1 to 9. There have been various approaches to solving that, including computational ones. In this project, I show that simple convolutional neural networks have the potential to crack Sudoku without any rule-based postprocessing.
  4 | 
  5 | ## Requirements
  6 |   * NumPy >= 1.11.1
  7 |   * TensorFlow == 1.1
  8 | 	
  9 | ## Background
 10 | * To see what Sudoku is, check the [wikipedia](https://en.wikipedia.org/wiki/Sudoku)
 11 | * To investigate this task comprehensively, read through [McGuire et al. 2013](https://arxiv.org/pdf/1201.0749.pdf).
 12 | 
 13 | ## Dataset
 14 | * 1M games were generated using `generate_sudoku.py` for training. I've uploaded them on the Kaggle dataset storage. They are available [here](https://www.kaggle.com/bryanpark/sudoku/downloads/sudoku.zip).
 15 | * 30 authentic games were collected from http://1sudoku.com.
 16 | 
 17 | ## Model description
 18 | * 10 blocks of convolution layers of kernel size 3.
 19 | 
 20 | ## File description
 21 |   * `generate_sudoku.py` create sudoku games. You don't have to run this. Instead, download [pre-generated games](https://www.kaggle.com/bryanpark/sudoku/downloads/sudoku.zip).
 22 |   * `hyperparams.py` includes all adjustable hyper parameters.
 23 |   * `data_load.py` loads data and put them in queues so multiple mini-bach data are generated in parallel.
 24 |   * `modules.py` contains some wrapper functions.
 25 |   * `train.py` is for training.
 26 |   * `test.py` is for test.
 27 |   
 28 | 
 29 | ## Training
 30 | * STEP 1. Download and extract [training data](https://www.kaggle.com/bryanpark/sudoku).
 31 | * STEP 2. Run `python train.py`. Or download the [pretrained file](https://www.dropbox.com/s/ipnwnorc7nz5hpe/logdir.tar.gz?dl=0).
 32 | 
 33 | ## Test
 34 | * Run `python test.py`.
 35 | 
 36 | ## Evaluation Metric
 37 | 
 38 | Accuracy is defined as 
 39 | 
 40 | Number of blanks where the prediction matched the solution / Number of blanks.
 41 | 
 42 | ## Results
 43 | 
 44 | After a couple of hours of training, the training curve seems to reach the optimum. 
 45 | 
 46 | <img src="fig/training_curve.png">
 47 | I use a simple trick in inference. Instead of cracking the whole blanks all at once, I fill in a single blank where the prediction is the most probable among the all predictions. As can be seen below, my model scored 0.86 in accuracy. Details are available in the `results` folder.
 48 | 
 49 | 
 50 |  
 51 | | Level  |  Accuracy (#correct/#blanks=acc.) |
 52 | | ---    |---     |
 53 | |Easy|**47/47 = 1.00**|
 54 | |Easy|**45/45 = 1.00**|
 55 | |Easy|**47/47 = 1.00**|
 56 | |Easy|**45/45 = 1.00**|
 57 | |Easy|**47/47 = 1.00**|
 58 | |Easy|**46/46 = 1.00**|
 59 | |Medium|33/53 = 0.62|
 60 | |Medium|**55/55 = 1.00**|
 61 | |Medium|**55/55 = 1.00**|
 62 | |Medium|**53/53 = 1.00**|
 63 | |Medium|33/52 = 0.63|
 64 | |Medium|51/56 = 0.91|
 65 | |Hard|29/56 = 0.52|
 66 | |Hard|**55/55 = 1.00**|
 67 | |Hard|27/55 = 0.49|
 68 | |Hard|**57/57 = 1.00**|
 69 | |Hard|35/55 = 0.64|
 70 | |Hard|15/56 = 0.27|
 71 | |Expert|**56/56 = 1.00**|
 72 | |Expert|**55/55 = 1.00**|
 73 | |Expert|**54/54 = 1.00**|
 74 | |Expert|**55/55 = 1.00**|
 75 | |Expert|17/55 = 0.31|
 76 | |Expert|**54/54 = 1.00**|
 77 | |Evil|**50/50 = 1.00**|
 78 | |Evil|**50/50 = 1.00**|
 79 | |Evil|**49/49 = 1.00**|
 80 | |Evil|28/53 = 0.53|
 81 | |Evil|**51/51 = 1.00**|
 82 | |Evil|**51/51 = 1.00**|
 83 | |Total Accuracy| 1345/1568 = _0.86_|
 84 | 
 85 | ## References
 86 | 
 87 | If you use this code for research, please cite:
 88 | 
 89 | ```
 90 | @misc{sudoku2018,
 91 |   author = {Park, Kyubyong},
 92 |   title = {Can Convolutional Neural Networks Crack Sudoku Puzzles?},
 93 |   year = {2018},
 94 |   publisher = {GitHub},
 95 |   journal = {GitHub repository},
 96 |   howpublished = {\url{https://github.com/Kyubyong/sudoku}}
 97 | }
 98 | ```
 99 | 
100 | ## Papers that referenced this repository
101 | 
102 |   * [OptNet: Differentiable Optimization as a Layer in Neural Networks](http://proceedings.mlr.press/v70/amos17a/amos17a.pdf)
103 |   * [Recurrent Relational Networks for Complex Relational Reasoning](https://arxiv.org/abs/1711.08028)
104 |   * [SATNet: Bridging deep learning and logical reasoning using a differentiable satisfiability solver](https://arxiv.org/abs/1905.12149)
105 | 
106 | 


--------------------------------------------------------------------------------
/data/test.csv:
--------------------------------------------------------------------------------
 1 | quizzes,solutions
 2 | 080032001703080002500007030050001970600709008047200050020600009800090305300820010,489532761713486592562917834258341976631759248947268153125673489876194325394825617
 3 | 000009007060000800789062350430600590090508020018004073043210786005000040100400000,351849267264753819789162354432671598697538421518924673943215786875396142126487935
 4 | 900401007047508000010700408002100003309000206400003700706009050000305690200604001,928461537647538129513792468872156943359847216461923785736219854184375692295684371
 5 | 100000203078026401340107000050002806080000010601700020000801042804530160506000009,165498273978326451342157698457912836289643715631785924793861542824539167516274389
 6 | 600200400015000020024100003102090305030501060507040208200009630050000870009008002,673285491815934726924176583162897345438521967597643218281759634356412879749368152
 7 | 021400080400150000605038400503607200000090000008504906006710509000043007040005120,321479685489156372675238491593687214264391758718524936836712549152943867947865123
 8 | 500901008008000500060040090600104007009000800700209003090010070007000600300708005,574961238918327546263845791682134957439576812751289463895612374127453689346798125
 9 | 400006080003040500000300000809401300100000007005709102000004000006030200030800001,452916783683247519791358624879421356124563897365789142218674935946135278537892461
10 | 000050340003400009000700012900060005040000090700030004150007000200001800074020000,617259348823416579495783612932164785546872193781935264158397426269541837374628951
11 | 000080100050039080109700300060000200720000016005000030002003804070910020003050000,237485169456139782189726345361547298724398516895261437912673854578914623643852971
12 | 007008000030901620060000008140307060000090000070605091500000040013804050000500200,927468135835971624461253978149387562356192487278645391592716843613824759784539216
13 | 010305600000200091070000200400010000007080300000060005001000030860007000003106080,912345678346278591578691243435712869627589314189463725751824936864937152293156487
14 | 200100004000800500070050900690205000000070000000604015006080030004003000900002008,259137684461829573378456921693215847145378296782694315526781439814963752937542168
15 | 471002008208001000000000002090018000004000500000320090700000000000600907300200465,471932658268451379935876142693518724824769531157324896746195283582643917319287465
16 | 210500000570942000008000000400000280000605000063000001000000100000214097000006053,214538769576942318938167425459371286721685934863429571697853142385214697142796853
17 | 004029000000006703000000050100700036900000008380004002050000000603200000000310200,734529681519846723862173459145782936927631548386954172251468397673295814498317265
18 | 000050310400130600000008004065000003080000050300000970700800000006071009048060000,879654312452139687613728594965487123187392456324516978791843265536271849248965731
19 | 000040003400008020030900500509000006004090700700000409003001060010500002600070000,195247683476358921238916574589734216364192758721685439953421867817569342642873195
20 | 000300029008050006013000080800070000060090050000060001030000290900010600570002000,657348129298157436413629587849571362361294758725863941134786295982415673576932814
21 | 000309800400010020560008001830000100000000000002000086600700039070050002001203000,217369845489517623563428971835672194196834257742195386624781539378956412951243768
22 | 000609000209000000700010380000800041028090650670001000093020006000000405000905000,381649572259783164746512389935876241128394657674251938593428716862137495417965823
23 | 080400300000009004053700090800000045001000900320000008070004610900300000002008070,789415326216839754453726891897163245641582937325947168578294613964371582132658479
24 | 000004380800000002000895700000080073007000500410050000009513000300000007085600000,971264385854731692263895741592186473637429518418357269749513826326948157185672934
25 | 060000050307000800800200007106008000004375100000400903600002009003000702090000030,469783251327651894815294367136928475984375126752416983678132549543869712291547638
26 | 050400000070350014001890200018000000005186900000000580002075100560013090000008020,253461879879352614641897253718539462425186937936724581382975146564213798197648325
27 | 090600000012080000087951000860190000030020080000038091000317560000060270000005010,593672148612483957487951326865194732139726485724538691248317569351869274976245813
28 | 900006007006014000010900460060350002029000750800029040038007020000840300600100009,943586217786214935215973468467351892329468751851729643538697124192845376674132589
29 | 000008015103000800509010004020509000300000009000601050400020508002000107930700000,247368915163954872589217364624539781315872649798641253476123598852496137931785426
30 | 000910003803075200020000900070400102050000040204007030005000060006730501400068000,547912683893675214621843975379486152158329746264157839735291468986734521412568397
31 | 397050000000001300006030905000006052060507030950300000705040600008200000000070423,397654281542981376186732945873496152264517839951328764725143698438269517619875423
32 | 


--------------------------------------------------------------------------------
/data_load.py:
--------------------------------------------------------------------------------
 1 | # -*- coding: utf-8 -*-
 2 | #/usr/bin/python2
 3 | '''
 4 | By kyubyong park. kbpark.linguist@gmail.com. 
 5 | https://www.github.com/kyubyong/sudoku
 6 | '''
 7 | import tensorflow as tf
 8 | import numpy as np
 9 | from hyperparams import Hyperparams as hp
10 | 
11 | def load_data(type="train"):
12 |     '''Loads training / test data.
13 |     
14 |     Args
15 |       type: A string. Either `train` or `test`.
16 |     
17 |     Returns:
18 |       X: A 3-D array of float. Entire quizzes. 
19 |          Has the shape of (# total games, 9, 9) 
20 |       Y: A 3-D array of int. Entire solutions.
21 |         Has the shape of (# total games, 9, 9)
22 |     '''
23 |     fpath = hp.train_fpath if type=="train" else hp.test_fpath
24 |     lines = open(fpath, 'r').read().splitlines()[1:]
25 |     nsamples = len(lines)
26 |     
27 |     X = np.zeros((nsamples, 9*9), np.float32)  
28 |     Y = np.zeros((nsamples, 9*9), np.int32) 
29 |     
30 |     for i, line in enumerate(lines):
31 |         quiz, solution = line.split(",")
32 |         for j, (q, s) in enumerate(zip(quiz, solution)):
33 |             X[i, j], Y[i, j] = q, s
34 |     
35 |     X = np.reshape(X, (-1, 9, 9))
36 |     Y = np.reshape(Y, (-1, 9, 9))
37 |     return X, Y
38 |         
39 | def get_batch_data():
40 |     '''Returns batch data.
41 |     
42 |     Returns:
43 |       A Tuple of x, y, and num_batch
44 |         x: A `Tensor` of float. Has the shape of (batch_size, 9, 9, 1).
45 |         y: A `Tensor` of int. Has the shape of (batch_size, 9, 9).
46 |         num_batch = A Python int. Number of batches.
47 |     '''
48 |     X, Y = load_data(type="train")
49 |     
50 |     # Create Queues
51 |     input_queues = tf.train.slice_input_producer([tf.convert_to_tensor(X, tf.float32), 
52 |                                                   tf.convert_to_tensor(Y, tf.int32)]) 
53 |     
54 |     # create batch queues
55 |     x, y = tf.train.shuffle_batch(input_queues,
56 |                                   num_threads=8,
57 |                                   batch_size=hp.batch_size, 
58 |                                   capacity=hp.batch_size*64,
59 |                                   min_after_dequeue=hp.batch_size*32, 
60 |                                   allow_smaller_final_batch=False)
61 |     # calc total batch count
62 |     num_batch = len(X) // hp.batch_size 
63 |     
64 |     return x, y, num_batch  # (N, 9, 9), (N, 9, 9), ()
65 | 


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/fig/training_curve.png:
--------------------------------------------------------------------------------
https://raw.githubusercontent.com/Kyubyong/sudoku/cb611230ad602aafebe6914c3e53c81671bba605/fig/training_curve.png


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/generate_sudoku.py:
--------------------------------------------------------------------------------
  1 | #!/usr/bin/python2
  2 | """
  3 | This is adapted from https://www.ocf.berkeley.edu/~arel/sudoku/main.html.
  4 | Generates 1 million Sudoku games. 
  5 | Kyubyong Park. kbpark.linguist@gmail.com www.github.com/kyubyong
  6 | """
  7 | 
  8 | import random, copy
  9 | import numpy as np
 10 | 
 11 | sample  = [ [3,4,1,2,9,7,6,8,5],
 12 |             [2,5,6,8,3,4,9,7,1],
 13 |             [9,8,7,1,5,6,3,2,4],
 14 |             [1,9,2,6,7,5,8,4,3],
 15 |             [8,7,5,4,2,3,1,9,6],
 16 |             [6,3,4,9,1,8,2,5,7],
 17 |             [5,6,3,7,8,9,4,1,2],
 18 |             [4,1,9,5,6,2,7,3,8],
 19 |             [7,2,8,3,4,1,5,6,9] ]
 20 |             
 21 | """
 22 | Randomly arrange numbers in a grid while making all rows, columns and
 23 | squares (sub-grids) contain the numbers 1 through 9.
 24 | 
 25 | For example, "sample" (above) could be the output of this function. """
 26 | def construct_puzzle_solution():
 27 |     # Loop until we're able to fill all 81 cells with numbers, while
 28 |     # satisfying the constraints above.
 29 |     while True:
 30 |         try:
 31 |             puzzle  = [[0]*9 for i in range(9)] # start with blank puzzle
 32 |             rows    = [set(range(1,10)) for i in range(9)] # set of available
 33 |             columns = [set(range(1,10)) for i in range(9)] #   numbers for each
 34 |             squares = [set(range(1,10)) for i in range(9)] #   row, column and square
 35 |             for i in range(9):
 36 |                 for j in range(9):
 37 |                     # pick a number for cell (i,j) from the set of remaining available numbers
 38 |                     choices = rows[i].intersection(columns[j]).intersection(squares[(i/3)*3 + j/3])
 39 |                     choice  = random.choice(list(choices))
 40 |         
 41 |                     puzzle[i][j] = choice
 42 |         
 43 |                     rows[i].discard(choice)
 44 |                     columns[j].discard(choice)
 45 |                     squares[(i/3)*3 + j/3].discard(choice)
 46 | 
 47 |             # success! every cell is filled.
 48 |             return puzzle
 49 |             
 50 |         except IndexError:
 51 |             # if there is an IndexError, we have worked ourselves in a corner (we just start over)
 52 |             pass
 53 | 
 54 | """
 55 | Randomly pluck out cells (numbers) from the solved puzzle grid, ensuring that any
 56 | plucked number can still be deduced from the remaining cells.
 57 | 
 58 | For deduction to be possible, each other cell in the plucked number's row, column,
 59 | or square must not be able to contain that number. """
 60 | def pluck(puzzle, n=0):
 61 | 
 62 |     """
 63 |     Answers the question: can the cell (i,j) in the puzzle "puz" contain the number
 64 |     in cell "c"? """
 65 |     def canBeA(puz, i, j, c):
 66 |         v = puz[c/9][c%9]
 67 |         if puz[i][j] == v: return True
 68 |         if puz[i][j] in range(1,10): return False
 69 |             
 70 |         for m in range(9): # test row, col, square
 71 |             # if not the cell itself, and the mth cell of the group contains the value v, then "no"
 72 |             if not (m==c/9 and j==c%9) and puz[m][j] == v: return False
 73 |             if not (i==c/9 and m==c%9) and puz[i][m] == v: return False
 74 |             if not ((i/3)*3 + m/3==c/9 and (j/3)*3 + m%3==c%9) and puz[(i/3)*3 + m/3][(j/3)*3 + m%3] == v:
 75 |                 return False
 76 | 
 77 |         return True
 78 | 
 79 | 
 80 |     """
 81 |     starts with a set of all 81 cells, and tries to remove one (randomly) at a time
 82 |     but not before checking that the cell can still be deduced from the remaining cells. """
 83 |     cells     = set(range(81))
 84 |     cellsleft = cells.copy()
 85 |     while len(cells) > n and len(cellsleft):
 86 |         cell = random.choice(list(cellsleft)) # choose a cell from ones we haven't tried
 87 |         cellsleft.discard(cell) # record that we are trying this cell
 88 | 
 89 |         # row, col and square record whether another cell in those groups could also take
 90 |         # on the value we are trying to pluck. (If another cell can, then we can't use the
 91 |         # group to deduce this value.) If all three groups are True, then we cannot pluck
 92 |         # this cell and must try another one.
 93 |         row = col = square = False
 94 | 
 95 |         for i in range(9):
 96 |             if i != cell/9:
 97 |                 if canBeA(puzzle, i, cell%9, cell): row = True
 98 |             if i != cell%9:
 99 |                 if canBeA(puzzle, cell/9, i, cell): col = True
100 |             if not (((cell/9)/3)*3 + i/3 == cell/9 and ((cell/9)%3)*3 + i%3 == cell%9):
101 |                 if canBeA(puzzle, ((cell/9)/3)*3 + i/3, ((cell/9)%3)*3 + i%3, cell): square = True
102 | 
103 |         if row and col and square:
104 |             continue # could not pluck this cell, try again.
105 |         else:
106 |             # this is a pluckable cell!
107 |             puzzle[cell/9][cell%9] = 0 # 0 denotes a blank cell
108 |             cells.discard(cell) # remove from the set of visible cells (pluck it)
109 |             # we don't need to reset "cellsleft" because if a cell was not pluckable
110 |             # earlier, then it will still not be pluckable now (with less information
111 |             # on the board).
112 | 
113 |     # This is the puzzle we found, in all its glory.
114 |     return (puzzle, len(cells))
115 |     
116 |     
117 | """
118 | That's it.
119 | 
120 | If we want to make a puzzle we can do this:
121 |     pluck(construct_puzzle_solution())
122 |     
123 | The following functions are convenience functions for doing just that...
124 | """
125 | 
126 | 
127 | 
128 | """
129 | This uses the above functions to create a new puzzle. It attempts to
130 | create one with 28 (by default) given cells, but if it can't, it returns
131 | one with as few givens as it is able to find.
132 | 
133 | This function actually tries making 100 puzzles (by default) and returns
134 | all of them. The "best" function that follows this one selects the best
135 | one of those.
136 | """
137 | def run(n = 28, iter=100):
138 |     all_results = {}
139 | #     print "Constructing a sudoku puzzle."
140 | #     print "* creating the solution..."
141 |     a_puzzle_solution = construct_puzzle_solution()
142 |     
143 | #     print "* constructing a puzzle..."
144 |     for i in range(iter):
145 |         puzzle = copy.deepcopy(a_puzzle_solution)
146 |         (result, number_of_cells) = pluck(puzzle, n)
147 |         all_results.setdefault(number_of_cells, []).append(result)
148 |         if number_of_cells <= n: break
149 |  
150 |     return all_results, a_puzzle_solution
151 | 
152 | def best(set_of_puzzles):
153 |     # Could run some evaluation function here. For now just pick
154 |     # the one with the fewest "givens".
155 |     return set_of_puzzles[min(set_of_puzzles.keys())][0]
156 | 
157 | def display(puzzle):
158 |     for row in puzzle:
159 |         print ' '.join([str(n or '_') for n in row])
160 | 
161 |     
162 | # """ Controls starts here """
163 | # results = run(n=0)       # find puzzles with as few givens as possible.
164 | # puzzle  = best(results)  # use the best one of those puzzles.
165 | # display(puzzle)          # display that puzzle.
166 | 
167 | 
168 | def main(num):
169 |     '''
170 |     Generates `num` games of Sudoku.
171 |     '''
172 |     quizzes = np.zeros((num, 9, 9), np.int32)
173 |     solutions = np.zeros((num, 9, 9), np.int32)
174 |     for i in range(num):
175 |         all_results, solution = run(n=23, iter=10)
176 |         quiz = best(all_results)
177 |         
178 |         quizzes[i] = quiz
179 |         solutions[i] = solution
180 | 
181 |         if (i+1) % 1000 == 0:
182 |             print i+1
183 |             np.save('data/sudoku.npz', quizzes=quizzes, solutions=solutions)
184 | 
185 | if __name__ == "__main__":
186 |     main(1000000)
187 |     print "Done!"


--------------------------------------------------------------------------------
/hyperparams.py:
--------------------------------------------------------------------------------
 1 | class Hyperparams:
 2 |     '''Hyper parameters'''
 3 |     # data
 4 |     train_fpath = '../v2/data/sudoku.csv'
 5 |     test_fpath = '../v2/data/test.csv'
 6 |     
 7 |     # model
 8 |     num_blocks = 10
 9 |     num_filters = 512
10 |     filter_size = 3
11 |     
12 |     # training scheme
13 |     lr = 0.0001
14 |     logdir = "logdir"
15 |     batch_size = 64
16 |     num_epochs = 3
17 |     
18 | 


--------------------------------------------------------------------------------
/modules.py:
--------------------------------------------------------------------------------
  1 | # -*- coding: utf-8 -*-
  2 | #/usr/bin/python2
  3 | '''
  4 | By kyubyong park. kbpark.linguist@gmail.com. 
  5 | https://www.github.com/kyubyong/sudoku
  6 | '''
  7 | 
  8 | from __future__ import print_function
  9 | import tensorflow as tf
 10 | from hyperparams import Hyperparams as hp
 11 | 
 12 | def normalize(inputs, 
 13 |               type="bn",
 14 |               decay=.99,
 15 |               is_training=True, 
 16 |               activation_fn=None,
 17 |               scope="normalize"):
 18 |     '''Applies {batch|layer} normalization.
 19 |     
 20 |     Args:
 21 |       inputs: A tensor with 2 or more dimensions, where the first dimension has
 22 |         `batch_size`. If type is `bn`, the normalization is over all but 
 23 |         the last dimension. Or if type is `ln`, the normalization is over 
 24 |         the last dimension. Note that this is different from the native 
 25 |         `tf.contrib.layers.batch_norm`. For this I recommend you change
 26 |         a line in ``tensorflow/contrib/layers/python/layers/layer.py` 
 27 |         as follows.
 28 |         Before: mean, variance = nn.moments(inputs, axis, keep_dims=True)
 29 |         After: mean, variance = nn.moments(inputs, [-1], keep_dims=True)
 30 |       type: A string. Either "bn" or "ln".
 31 |       decay: Decay for the moving average. Reasonable values for `decay` are close
 32 |         to 1.0, typically in the multiple-nines range: 0.999, 0.99, 0.9, etc.
 33 |         Lower `decay` value (recommend trying `decay`=0.9) if model experiences
 34 |         reasonably good training performance but poor validation and/or test
 35 |         performance.
 36 |       is_training: Whether or not the layer is in training mode. W
 37 |       activation_fn: Activation function.
 38 |       scope: Optional scope for `variable_scope`.
 39 |       
 40 |     Returns:
 41 |       A tensor with the same shape and data dtype as `inputs`.
 42 |     '''
 43 |     if type=="bn":
 44 |         inputs_shape = inputs.get_shape()
 45 |         inputs_rank = inputs_shape.ndims
 46 |         
 47 |         # use fused batch norm if inputs_rank in [2, 3, 4] as it is much faster.
 48 |         # pay attention to the fact that fused_batch_norm requires shape to be rank 4 of NHWC.
 49 |         if inputs_rank in [2, 3, 4]:
 50 |             if inputs_rank==2:
 51 |                 inputs = tf.expand_dims(inputs, axis=1)
 52 |                 inputs = tf.expand_dims(inputs, axis=2)
 53 |             elif inputs_rank==3:
 54 |                 inputs = tf.expand_dims(inputs, axis=1)
 55 |             
 56 |             outputs = tf.contrib.layers.batch_norm(inputs=inputs, 
 57 |                                                decay=decay,
 58 |                                                center=True, 
 59 |                                                scale=True, 
 60 |                                                activation_fn=None, 
 61 |                                                updates_collections=None,
 62 |                                                is_training=is_training,
 63 |                                                scope=scope,
 64 |                                                zero_debias_moving_mean=True,
 65 |                                                fused=True)
 66 |             # restore original shape
 67 |             if inputs_rank==2:
 68 |                 outputs = tf.squeeze(outputs, axis=[1, 2])
 69 |             elif inputs_rank==3:
 70 |                 outputs = tf.squeeze(outputs, axis=1)
 71 |         else: # fallback to naive batch norm
 72 |             outputs = tf.contrib.layers.batch_norm(inputs=inputs, 
 73 |                                                decay=decay,
 74 |                                                center=True, 
 75 |                                                scale=True, 
 76 |                                                activation_fn=activation_fn, 
 77 |                                                updates_collections=None,
 78 |                                                is_training=is_training,
 79 |                                                scope=scope,
 80 |                                                fused=False)    
 81 |     elif type=="ln":
 82 |         outputs = tf.contrib.layers.layer_norm(inputs=inputs, 
 83 |                                             center=True, 
 84 |                                             scale=True, 
 85 |                                             activation_fn=None, 
 86 |                                             scope=scope)
 87 |     elif type=="in": # instance normalization
 88 |         with tf.variable_scope(scope):
 89 |             inputs_shape = inputs.get_shape()
 90 |             params_shape = inputs_shape[-1:]
 91 |             
 92 |             mean, variance = tf.nn.moments(inputs, [1], keep_dims=True)
 93 |             gamma = tf.get_variable("gamma", 
 94 |                                     shape=params_shape, 
 95 |                                     dtype=tf.float32, 
 96 |                                     initializer=tf.ones_initializer)
 97 |             beta = tf.get_variable("beta", 
 98 |                                     shape=params_shape, 
 99 |                                     dtype=tf.float32, 
100 |                                     initializer=tf.zeros_initializer)
101 |             normalized = (inputs - mean) / tf.sqrt(variance+1e-8)
102 |             outputs = normalized * gamma + beta
103 |             
104 |     else: # None
105 |         outputs = inputs
106 |     
107 |     if activation_fn is not None:
108 |         outputs = activation_fn(outputs)
109 |     
110 |     return outputs
111 | 
112 | def conv(inputs, 
113 |          filters=None, 
114 |          size=1, 
115 |          rate=1, 
116 |          padding="SAME", 
117 |          use_bias=False,
118 |          is_training=True,
119 |          activation_fn=None,
120 |          decay=0.99,
121 |          norm_type=None,
122 |          scope="conv",
123 |          reuse=None):
124 |     '''Applies convolution to `inputs`.
125 |     
126 |     Args:
127 |       inputs: A 3D or 4D tensor with shape of [batch, (height), width, depth].
128 |       filters: An int. Number of outputs (=activation maps)
129 |       size: An int. Filter size.
130 |       rate: An int. Dilation rate.
131 |       padding: Either `same` or `valid` or `causal` (case-insensitive).
132 |       use_bias: A boolean.
133 |       is_training: A boolean.
134 |       decay: A float of (0, 1).
135 |       activation_fn: A string.
136 |       norm_type: Either `bn`, `ln`, or `in`.
137 |       scope: Optional scope for `variable_scope`.
138 |       reuse: Boolean, whether to reuse the weights of a previous layer
139 |         by the same name.
140 |     
141 |     Returns:
142 |       A tensor of the same shape and dtypes as `inputs`.
143 |     '''
144 |     ndims = inputs.get_shape().ndims
145 |     conv_fn = tf.layers.conv1d if ndims==3 else tf.layers.conv2d
146 |     
147 |     with tf.variable_scope(scope):
148 |         if padding.lower()=="causal":
149 |             assert ndims==3, "if causal is true, the rank must be 3."
150 |             # pre-padding for causality
151 |             pad_len = (size - 1) * rate  # padding size
152 |             inputs = tf.pad(inputs, [[0, 0], [pad_len, 0], [0, 0]])
153 |             padding = "valid"
154 |         
155 |         if filters is None:
156 |             filters = inputs.get_shape().as_list[-1]
157 |         
158 |         params = {"inputs":inputs, "filters":filters, "kernel_size":size,
159 |                 "dilation_rate":rate, "padding":padding, 
160 |                 "use_bias":use_bias, "reuse":reuse}
161 |         outputs = conv_fn(**params)
162 |         outputs = normalize(outputs, type=norm_type, decay=decay, 
163 |                   is_training=is_training, activation_fn=activation_fn)
164 |     return outputs
165 | 
166 | 


--------------------------------------------------------------------------------
/results/model.ckpt-23844.txt:
--------------------------------------------------------------------------------
  1 | qz: _8__32__17_3_8___25____7_3__5___197_6__7_9__8_472___5__2_6____98___9_3_53__82__1_
  2 | sn: 489532761713486592562917834258341976631759248947268153125673489876194325394825617
  3 | pd: 489532761713486592562917834258341976631759248947268153125673489876194325394825617
  4 | accuracy = 47/47 = 1.00
  5 | 
  6 | qz: _____9__7_6____8__789_6235_43_6__59__9_5_8_2__18__4_73_4321_786__5____4_1__4_____
  7 | sn: 351849267264753819789162354432671598697538421518924673943215786875396142126487935
  8 | pd: 351849267264753819789162354432671598697538421518924673943215786875396142126487935
  9 | accuracy = 45/45 = 1.00
 10 | 
 11 | qz: 9__4_1__7_475_8____1_7__4_8__21____33_9___2_64____37__7_6__9_5____3_569_2__6_4__1
 12 | sn: 928461537647538129513792468872156943359847216461923785736219854184375692295684371
 13 | pd: 928461537647538129513792468872156943359847216461923785736219854184375692295684371
 14 | accuracy = 47/47 = 1.00
 15 | 
 16 | qz: 1_____2_3_78_264_134_1_7____5___28_6_8_____1_6_17___2____8_1_428_453_16_5_6_____9
 17 | sn: 165498273978326451342157698457912836289643715631785924793861542824539167516274389
 18 | pd: 165498273978326451342157698457912836289643715631785924793861542824539167516274389
 19 | accuracy = 45/45 = 1.00
 20 | 
 21 | qz: 6__2__4___15____2__241____31_2_9_3_5_3_5_1_6_5_7_4_2_82____963__5____87___9__8__2
 22 | sn: 673285491815934726924176583162897345438521967597643218281759634356412879749368152
 23 | pd: 673285491815934726924176583162897345438521967597643218281759634356412879749368152
 24 | accuracy = 47/47 = 1.00
 25 | 
 26 | qz: _214___8_4__15____6_5_384__5_36_72______9______85_49_6__671_5_9____43__7_4___512_
 27 | sn: 321479685489156372675238491593687214264391758718524936836712549152943867947865123
 28 | pd: 321479685489156372675238491593687214264391758718524936836712549152943867947865123
 29 | accuracy = 46/46 = 1.00
 30 | 
 31 | qz: 5__9_1__8__8___5___6__4__9_6__1_4__7__9___8__7__2_9__3_9__1__7___7___6__3__7_8__5
 32 | sn: 574961238918327546263845791682134957439576812751289463895612374127453689346798125
 33 | pd: 574961238918372546263845791632184957459637824781259463895416372147523689326798145
 34 | accuracy = 33/53 = 0.62
 35 | 
 36 | qz: 4____6_8___3_4_5_____3_____8_94_13__1_______7__57_91_2_____4_____6_3_2___3_8____1
 37 | sn: 452916783683247519791358624879421356124563897365789142218674935946135278537892461
 38 | pd: 452916783683247519791358624879421356124563897365789142218674935946135278537892461
 39 | accuracy = 55/55 = 1.00
 40 | 
 41 | qz: ____5_34___34____9___7___129___6___5_4_____9_7___3___415___7___2____18___74_2____
 42 | sn: 617259348823416579495783612932164785546872193781935264158397426269541837374628951
 43 | pd: 617259348823416579495783612932164785546872193781935264158397426269541837374628951
 44 | accuracy = 55/55 = 1.00
 45 | 
 46 | qz: ____8_1___5__39_8_1_97__3___6____2__72_____16__5____3___2__38_4_7_91__2___3_5____
 47 | sn: 237485169456139782189726345361547298724398516895261437912673854578914623643852971
 48 | pd: 237485169456139782189726345361547298724398516895261437912673854578914623643852971
 49 | accuracy = 53/53 = 1.00
 50 | 
 51 | qz: __7__8____3_9_162__6______814_3_7_6_____9_____7_6_5_915______4__138_4_5____5__2__
 52 | sn: 927468135835971624461253978149387562356192487278645391592716843613824759784539216
 53 | pd: 297468315835971624461253978149387562658192437372645891526719143913824756784536289
 54 | accuracy = 33/52 = 0.63
 55 | 
 56 | qz: _1_3_56_____2___91_7____2__4___1______7_8_3______6___5__1____3_86___7_____31_6_8_
 57 | sn: 912345678346278591578691243435712869627589314189463725751824936864937152293156487
 58 | pd: 912345678346278591578691243435712869627589317189763425751824936864937152293156784
 59 | accuracy = 51/56 = 0.91
 60 | 
 61 | qz: 2__1____4___8__5___7__5_9__69_2_5_______7_______6_4_15__6_8__3___4__3___9____2__8
 62 | sn: 259137684461829573378456921693215847145378296782694315526781439814963752937542168
 63 | pd: 265139784439827561178456923697215847541378296382694315756981432824763159913542678
 64 | accuracy = 29/56 = 0.52
 65 | 
 66 | qz: 471__2__82_8__1___________2_9__18_____4___5_____32__9_7___________6__9_73__2__465
 67 | sn: 471932658268451379935876142693518724824769531157324896746195283582643917319287465
 68 | pd: 471932658268451379935876142693518724824769531157324896746195283582643917319287465
 69 | accuracy = 55/55 = 1.00
 70 | 
 71 | qz: 21_5_____57_942_____8______4_____28____6_5____63_____1______1_____214_97_____6_53
 72 | sn: 214538769576942318938167425459371286721685934863429571697853142385214697142796853
 73 | pd: 214583769576942318398761425457139286182675934963428571829357142635214897741896653
 74 | accuracy = 27/55 = 0.49
 75 | 
 76 | qz: __4_29________67_3_______5_1__7___369_______838___4__2_5_______6_32________31_2__
 77 | sn: 734529681519846723862173459145782936927631548386954172251468397673295814498317265
 78 | pd: 734529681519846723862173459145782936927631548386954172251468397673295814498317265
 79 | accuracy = 57/57 = 1.00
 80 | 
 81 | qz: ____5_31_4__13_6_______8__4_65_____3_8_____5_3_____97_7__8_______6_71__9_48_6____
 82 | sn: 879654312452139687613728594965487123187392456324516978791843265536271849248965731
 83 | pd: 879654312452139687631728594965717423287493156314586979793845261526371849148962735
 84 | accuracy = 35/55 = 0.64
 85 | 
 86 | qz: ____4___34____8_2__3_9__5__5_9_____6__4_9_7__7_____4_9__3__1_6__1_5____26___7____
 87 | sn: 195247683476358921238916574589734216364192758721685439953421867817569342642873195
 88 | pd: 216745893495138627837926514589417236364892751721653489173281965918564372652379148
 89 | accuracy = 15/56 = 0.27
 90 | 
 91 | qz: ___3___29__8_5___6_13____8_8___7_____6__9__5_____6___1_3____29_9___1_6__57___2___
 92 | sn: 657348129298157436413629587849571362361294758725863941134786295982415673576932814
 93 | pd: 657348129298157436413629587849571362361294758725863941134786295982415673576932814
 94 | accuracy = 56/56 = 1.00
 95 | 
 96 | qz: ___3_98__4___1__2_56___8__183____1_____________2____866__7___39_7__5___2__12_3___
 97 | sn: 217369845489517623563428971835672194196834257742195386624781539378956412951243768
 98 | pd: 217369845489517623563428971835672194196834257742195386624781539378956412951243768
 99 | accuracy = 55/55 = 1.00
100 | 
101 | qz: ___6_9___2_9______7___1_38____8___41_28_9_65_67___1____93_2___6______4_5___9_5___
102 | sn: 381649572259783164746512389935876241128394657674251938593428716862137495417965823
103 | pd: 381649572259783164746512389935876241128394657674251938593428716862137495417965823
104 | accuracy = 54/54 = 1.00
105 | 
106 | qz: _8_4__3_______9__4_537___9_8______45__1___9__32______8_7___461_9__3_______2__8_7_
107 | sn: 789415326216839754453726891897163245641582937325947168578294613964371582132658479
108 | pd: 789415326216839754453726891897163245641582937325947168578294613964371582132658479
109 | accuracy = 55/55 = 1.00
110 | 
111 | qz: _____438_8_______2___8957______8__73__7___5__41__5______9513___3_______7_856_____
112 | sn: 971264385854731692263895741592186473637429518418357269749513826326948157185672934
113 | pd: 197264385854371692632895714526489173917132546413756829749513268361928457285647931
114 | accuracy = 17/55 = 0.31
115 | 
116 | qz: _6_____5_3_7___8__8__2____71_6__8_____43751_____4__9_36____2__9__3___7_2_9_____3_
117 | sn: 469783251327651894815294367136928475984375126752416983678132549543869712291547638
118 | pd: 469783251327651894815294367136928475984375126752416983678132549543869712291547638
119 | accuracy = 54/54 = 1.00
120 | 
121 | qz: _5_4______7_35__14__189_2___18________51869________58___2_751__56__13_9______8_2_
122 | sn: 253461879879352614641897253718539462425186937936724581382975146564213798197648325
123 | pd: 253461879879352614641897253718539462425186937936724581382975146564213798197648325
124 | accuracy = 50/50 = 1.00
125 | 
126 | qz: _9_6______12_8_____87951___86_19_____3__2__8_____38_91___31756_____6_27______5_1_
127 | sn: 593672148612483957487951326865194732139726485724538691248317569351869274976245813
128 | pd: 593672148612483957487951326865194732139726485724538691248317569351869274976245813
129 | accuracy = 50/50 = 1.00
130 | 
131 | qz: 9____6__7__6_14____1_9__46__6_35___2_29___75_8___29_4__38__7_2____84_3__6__1____9
132 | sn: 943586217786214935215973468467351892329468751851729643538697124192845376674132589
133 | pd: 943586217786214935215973468467351892329468751851729643538697124192845376674132589
134 | accuracy = 49/49 = 1.00
135 | 
136 | qz: _____8_151_3___8__5_9_1___4_2_5_9___3_______9___6_1_5_4___2_5_8__2___1_793_7_____
137 | sn: 247368915163954872589217364624539781315872649798641253476123598852496137931785426
138 | pd: 267498915143297865589316724624579381315842679798631452476123598852964137931785246
139 | accuracy = 28/53 = 0.53
140 | 
141 | qz: ___91___38_3_752___2____9___7_4__1_2_5_____4_2_4__7_3___5____6___673_5_14___68___
142 | sn: 547912683893675214621843975379486152158329746264157839735291468986734521412568397
143 | pd: 547912683893675214621843975379486152158329746264157839735291468986734521412568397
144 | accuracy = 51/51 = 1.00
145 | 
146 | qz: 397_5_________13____6_3_9_5_____6_52_6_5_7_3_95_3_____7_5_4_6____82_________7_423
147 | sn: 397654281542981376186732945873496152264517839951328764725143698438269517619875423
148 | pd: 397654281542981376186732945873496152264517839951328764725143698438269517619875423
149 | accuracy = 51/51 = 1.00
150 | 
151 | Total accuracy = 1345/1568 = 0.86
152 | 
153 | 


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/test.py:
--------------------------------------------------------------------------------
 1 | # -*- coding: utf-8 -*-
 2 | #/usr/bin/python2
 3 | '''
 4 | By kyubyong park. kbpark.linguist@gmail.com. 
 5 | https://www.github.com/kyubyong/sudoku
 6 | '''
 7 | from __future__ import print_function
 8 | import tensorflow as tf
 9 | import numpy as np
10 | from train import Graph
11 | from data_load import load_data
12 | from hyperparams import Hyperparams as hp
13 | import os
14 | 
15 | def write_to_file(x, y, preds, fout):
16 |     '''Writes to file.
17 |     Args:
18 |       x: A 3d array with shape of [N, 9, 9]. Quizzes where blanks are represented as 0's.
19 |       y: A 3d array with shape of [N, 9, 9]. Solutions.
20 |       preds: A 3d array with shape of [N, 9, 9]. Predictions.
21 |       fout: A string. File path of the output file where the results will be written.
22 |     '''
23 |     with open(fout, 'w') as fout:
24 |         total_hits, total_blanks = 0, 0
25 |         for xx, yy, pp in zip(x.reshape(-1, 9*9), y.reshape(-1, 9*9), preds.reshape(-1, 9*9)): # sample-wise
26 |             fout.write("qz: {}\n".format("".join(str(num) if num != 0 else "_" for num in xx)))
27 |             fout.write("sn: {}\n".format("".join(str(num) for num in yy)))
28 |             fout.write("pd: {}\n".format("".join(str(num) for num in pp)))
29 | 
30 |             expected = yy[xx == 0]
31 |             got = pp[xx == 0]
32 | 
33 |             num_hits = np.equal(expected, got).sum()
34 |             num_blanks = len(expected)
35 | 
36 |             fout.write("accuracy = %d/%d = %.2f\n\n" % (num_hits, num_blanks, float(num_hits) / num_blanks))
37 | 
38 |             total_hits += num_hits
39 |             total_blanks += num_blanks
40 |         fout.write("Total accuracy = %d/%d = %.2f\n\n" % (total_hits, total_blanks, float(total_hits) / total_blanks))
41 | 
42 | 
43 | def test():
44 |     x, y = load_data(type="test")
45 |     
46 |     g = Graph(is_training=False)
47 |     with g.graph.as_default():    
48 |         sv = tf.train.Supervisor()
49 |         with sv.managed_session(config=tf.ConfigProto(allow_soft_placement=True)) as sess:
50 |             # Restore parameters
51 |             sv.saver.restore(sess, tf.train.latest_checkpoint(hp.logdir))
52 |             print("Restored!")
53 |             
54 |             # Get model name
55 |             mname = open(hp.logdir + '/checkpoint', 'r').read().split('"')[1] # model name
56 |             
57 | 	    if not os.path.exists('results'): os.mkdir('results')
58 |             fout = 'results/{}.txt'.format(mname)
59 |             import copy
60 |             _preds = copy.copy(x)
61 |             while 1:
62 |                 istarget, probs, preds = sess.run([g.istarget, g.probs, g.preds], {g.x:_preds, g.y: y})
63 |                 probs = probs.astype(np.float32)
64 |                 preds = preds.astype(np.float32)
65 |                 
66 |                 probs *= istarget #(N, 9, 9)
67 |                 preds *= istarget #(N, 9, 9)
68 | 
69 |                 probs = np.reshape(probs, (-1, 9*9)) #(N, 9*9)
70 |                 preds = np.reshape(preds, (-1, 9*9))#(N, 9*9)
71 |                 
72 |                 _preds = np.reshape(_preds, (-1, 9*9))
73 |                 maxprob_ids = np.argmax(probs, axis=1) # (N, ) <- blanks of the most probable prediction
74 |                 maxprobs = np.max(probs, axis=1, keepdims=False)
75 |                 for j, (maxprob_id, maxprob) in enumerate(zip(maxprob_ids, maxprobs)):
76 |                     if maxprob != 0:
77 |                         _preds[j, maxprob_id] = preds[j, maxprob_id]
78 |                 _preds = np.reshape(_preds, (-1, 9, 9))
79 |                 _preds = np.where(x==0, _preds, y) # # Fill in the non-blanks with correct numbers
80 | 
81 |                 if np.count_nonzero(_preds) == _preds.size: break
82 | 
83 |             write_to_file(x.astype(np.int32), y, _preds.astype(np.int32), fout)
84 |                     
85 | if __name__ == '__main__':
86 |     test()
87 |     print("Done")
88 | 


--------------------------------------------------------------------------------
/train.py:
--------------------------------------------------------------------------------
 1 | # -*- coding: utf-8 -*-
 2 | #/usr/bin/python2
 3 | '''
 4 | By kyubyong park. kbpark.linguist@gmail.com. 
 5 | https://www.github.com/kyubyong/sudoku
 6 | '''
 7 | from __future__ import print_function
 8 | import tensorflow as tf
 9 | from hyperparams import Hyperparams as hp
10 | from data_load import load_data, get_batch_data
11 | from modules import conv
12 | from tqdm import tqdm
13 | 
14 | class Graph(object):
15 |     def __init__(self, is_training=True):
16 |         self.graph = tf.Graph()
17 |         with self.graph.as_default():
18 |             # inputs
19 |             if is_training:
20 |                 self.x, self.y, self.num_batch = get_batch_data() # (N, 9, 9)
21 |             else:
22 |                 self.x = tf.placeholder(tf.float32, (None, 9, 9))
23 |                 self.y = tf.placeholder(tf.int32, (None, 9, 9))
24 |             self.enc = tf.expand_dims(self.x, axis=-1) # (N, 9, 9, 1)
25 |             self.istarget = tf.to_float(tf.equal(self.x, tf.zeros_like(self.x))) # 0: blanks
26 |             
27 |             # network
28 |             for i in range(hp.num_blocks):
29 |                 with tf.variable_scope("conv2d_{}".format(i)):
30 |                     self.enc = conv(self.enc, 
31 |                                     filters=hp.num_filters, 
32 |                                     size=hp.filter_size,
33 |                                     is_training=is_training,
34 |                                     norm_type="bn",
35 |                                     activation_fn=tf.nn.relu)
36 |             
37 |             # outputs        
38 |             self.logits = conv(self.enc, 10, 1, scope="logits") # (N, 9, 9, 1)
39 |             self.probs = tf.reduce_max(tf.nn.softmax(self.logits), axis=-1) #( N, 9, 9)
40 |             self.preds = tf.to_int32(tf.arg_max(self.logits, dimension=-1)) #( N, 9, 9)
41 |             
42 |             # accuracy
43 |             self.hits = tf.to_float(tf.equal(self.preds, self.y)) * self.istarget
44 |             self.acc = tf.reduce_sum(self.hits) / (tf.reduce_sum(self.istarget) + 1e-8)
45 |             tf.summary.scalar("acc", self.acc)
46 |                                        
47 |             if is_training:
48 |                 # Loss
49 |                 self.ce = tf.nn.sparse_softmax_cross_entropy_with_logits(labels=self.y, logits=self.logits)
50 |                 self.loss = tf.reduce_sum(self.ce * self.istarget) / (tf.reduce_sum(self.istarget))
51 |                 
52 |                 # Training Scheme
53 |                 self.global_step = tf.Variable(0, name='global_step', trainable=False)
54 |                 self.optimizer = tf.train.AdamOptimizer(learning_rate=hp.lr)
55 |                 self.train_op = self.optimizer.minimize(self.loss, global_step=self.global_step)
56 |                 tf.summary.scalar("loss", self.loss)
57 |             
58 |             self.merged = tf.summary.merge_all()
59 |             
60 | def main():
61 |     g = Graph(); print("Training Graph loaded")
62 |     with g.graph.as_default():# Training 
63 |         sv = tf.train.Supervisor(logdir=hp.logdir,
64 |                                  save_model_secs=60)
65 |         with sv.managed_session() as sess:
66 |             for epoch in range(1, hp.num_epochs+1): 
67 |                 if sv.should_stop(): break
68 |                 for step in tqdm(range(g.num_batch), total=g.num_batch, ncols=70, leave=False, unit='b'):
69 |                     sess.run(g.train_op)
70 |                     if step%10==0:
71 |                         print(sess.run([g.loss, g.acc]))
72 | 
73 |                 # Write checkpoint files at every epoch
74 |                 gs = sess.run(g.global_step) 
75 |                 sv.saver.save(sess, hp.logdir + '/model_epoch_%02d_gs_%d' % (epoch, gs))
76 |                 
77 | if __name__ == "__main__":
78 |     main(); print("Done")
79 | 


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