seppl/sudoku_collapse
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add py files, not working yet

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This commit is contained in:
Joseph Hopfmüller
2023-02-04 18:13:09 +01:00
parent ff3907077b
commit 6262a7c836
3 changed files with 904 additions and 0 deletions
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165
sudoku.py Normal file
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from copy import deepcopy
import random
class sudoku_grid():
def __init__(self, prefilled_cells):
# cell = {'possible': set([i for i in range(1,10)]), 'solution': 0}
self.grid = [[{'possible': set([i for i in range(1,10)]), 'solution': 0} for _ in range(9)] for _ in range(9)]
# prefilled_cells is a nested list (9x9) of values (1-9), 0 specifies an empty cell
try:
ctr = 0
if len(prefilled_cells) != 9:
raise ValueError.add_note(f'wrong number of rows')
for i in range(9):
if len(prefilled_cells[i]) != 9:
raise ValueError.add_note(f'wrong number of cells in row {i}')
for j in range(9):
# if prefilled_cell in valid range: fill in matching cell an mark as solved
if 1 <= prefilled_cells[i][j] <= 9:
self.grid[i][j]['possible'] = {prefilled_cells[i][j]}
self.grid[i][j]['solution'] = prefilled_cells[i][j]
ctr += 1
if ctr == 0:
raise ValueError.add_note(f'prefilled_cells is empty')
except ValueError as e:
print(f'{e}')
def __str__(self):
retstr = 'sudoku: \n'
for i in range(9):
for j in range(9):
if self.grid[i][j]['solution']:
current_val = self.grid[i][j]['solution']
retstr += f'{current_val} '
else:
retstr += '_ '
if j == 2 or j == 5:
retstr += '# '
if i == 2 or i == 5:
retstr += '\n# # # # # # # # # # # '
retstr += '\n'
return retstr
def removeValue(self, row, col, value):
if self.grid[row][col]['possible']:
self.grid[row][col]['possible'].discard(value)
pass
def iterate(self):
# iterate over all cells
for i in range(9):
for j in range(9):
# get the value
current_value = self.grid[i][j]['solution']
if current_value:
for k in range(9):
self.removeValue(i, k, current_value) # remove value from current row
self.removeValue(k, j, current_value) # remove value from current column
for k in range(3):
for l in range(3):
self.removeValue((i//3)*3+(i+k)%3, (j//3)*3+(j+l)%3, current_value) # remove value from current 3x3 box
current_set = set()
add = 0
for k in range(8):
current_set = current_set and self.grid[i][(j+k)%9]['possible']
current_set = current_set and self.grid[(i+k)%9][j]['possible']
if (i//3)*3+k//3 == i and (j//3)*3+k%3 == j:
add = 1
l = k + add
row = (i//3)*3+l//3
col = (j//3)*3+l%3
current_set = current_set and self.grid[row][col]['possible']
new_set = self.grid[i][j]['possible']-self.grid[i][j]['possible'].intersection(current_set)
if new_set:
self.grid[i][j]['possible'] = new_set
for i in range(9):
for j in range(9):
if len(self.grid[i][j]['possible']) == 1:
self.grid[i][j]['solution'] = list(self.grid[i][j]['possible'])[0]
def find_lowest_entropy(self):
lowest_i = -1
lowest_j = -1
sols = None
lowest_e = 10
for i in range(9):
for j in range(9):
if self.grid[i][j]['solution']:
continue
e = len(self.grid[i][j]['possible'])
if e < lowest_e:
sols = list(self.grid[i][j]['possible'])
lowest_i = i
lowest_j = j
lowest_e = e
if lowest_e == 0:
lowest_i = -1
lowest_j = -1
sols = None
lowest_e = 10
return (lowest_i, lowest_j, lowest_e, sols)
return (lowest_i, lowest_j, lowest_e, sols)
def collapse_cell(self, row, col):
if self.grid[row][col]['solution']:
return None
possible = self.grid[row][col]['possible']
if len(possible) == 1:
self.grid[row][col]['solution'] = list(possible)[0]
def single_solutions_exist(self):
for i in range(9):
for j in range(9):
if self.grid[i][j]['possible']:
if len(self.grid[i][j]['possible']) == 1:
return True
return False
def is_solved(self):
for i in range(9):
for j in range(9):
if not self.grid[i][j]['solution']:
return False
return True
iteration = 1
if __name__ == '__main__':
prefilled = [ [0,4,9,7,0,5,0,0,0],
[0,0,0,0,0,4,0,0,3],
[6,0,1,2,0,0,0,7,0],
[0,0,0,0,9,1,0,0,5],
[0,2,4,0,6,8,7,3,1],
[1,5,8,0,2,7,4,9,0],
[0,0,0,0,0,2,6,4,0],
[0,6,0,1,0,0,0,0,0],
[4,0,5,0,0,0,3,0,2]]
sudoku = sudoku_grid(prefilled)
print(sudoku)
while not sudoku.is_solved():
sudoku.iterate()
# cnt = 0
# [row, col, entropy, solutions] = sudoku.find_lowest_entropy()
# if row == -1:
# print(f'No solution found! Iteration {iteration}')
# break
# print(f'Lowest Entropy in Iteration {iteration} ({cnt}): {entropy} in ({row},{col}) with solutions {solutions}')
# sudoku.collapse_cell(row, col)
# while sudoku.single_solutions_exist():
# cnt += 1
# [row, col, entropy, solutions] = sudoku.find_lowest_entropy()
# print(f'Lowest Entropy in Iteration {iteration} ({cnt}): {entropy} in ({row},{col}) with solutions {solutions}')
# sudoku.collapse_cell(row,col)
# print(sudoku)
iteration += 1
print(sudoku)

9
test.py Normal file
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with open('test.txt', 'w') as file:
file.write('(i.j),k,l,(m.n)\n')
for i in range(9):
for j in range(9):
for k in range(3):
for l in range(3):
m = (i//3)*3+(i+k)%3
n = (j//3)*3+(j+l)%3
file.write(f'({i}.{j}),{k},{l},({m}.{n})\n')

730
test.txt Normal file
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(i.j),k,l,(m.n)
(0.0),0,0,(0.0)
(0.0),0,1,(0.1)
(0.0),0,2,(0.2)
(0.0),1,0,(1.0)
(0.0),1,1,(1.1)
(0.0),1,2,(1.2)
(0.0),2,0,(2.0)
(0.0),2,1,(2.1)
(0.0),2,2,(2.2)
(0.1),0,0,(0.1)
(0.1),0,1,(0.2)
(0.1),0,2,(0.0)
(0.1),1,0,(1.1)
(0.1),1,1,(1.2)
(0.1),1,2,(1.0)
(0.1),2,0,(2.1)
(0.1),2,1,(2.2)
(0.1),2,2,(2.0)
(0.2),0,0,(0.2)
(0.2),0,1,(0.0)
(0.2),0,2,(0.1)
(0.2),1,0,(1.2)
(0.2),1,1,(1.0)
(0.2),1,2,(1.1)
(0.2),2,0,(2.2)
(0.2),2,1,(2.0)
(0.2),2,2,(2.1)
(0.3),0,0,(0.3)
(0.3),0,1,(0.4)
(0.3),0,2,(0.5)
(0.3),1,0,(1.3)
(0.3),1,1,(1.4)
(0.3),1,2,(1.5)
(0.3),2,0,(2.3)
(0.3),2,1,(2.4)
(0.3),2,2,(2.5)
(0.4),0,0,(0.4)
(0.4),0,1,(0.5)
(0.4),0,2,(0.3)
(0.4),1,0,(1.4)
(0.4),1,1,(1.5)
(0.4),1,2,(1.3)
(0.4),2,0,(2.4)
(0.4),2,1,(2.5)
(0.4),2,2,(2.3)
(0.5),0,0,(0.5)
(0.5),0,1,(0.3)
(0.5),0,2,(0.4)
(0.5),1,0,(1.5)
(0.5),1,1,(1.3)
(0.5),1,2,(1.4)
(0.5),2,0,(2.5)
(0.5),2,1,(2.3)
(0.5),2,2,(2.4)
(0.6),0,0,(0.6)
(0.6),0,1,(0.7)
(0.6),0,2,(0.8)
(0.6),1,0,(1.6)
(0.6),1,1,(1.7)
(0.6),1,2,(1.8)
(0.6),2,0,(2.6)
(0.6),2,1,(2.7)
(0.6),2,2,(2.8)
(0.7),0,0,(0.7)
(0.7),0,1,(0.8)
(0.7),0,2,(0.6)
(0.7),1,0,(1.7)
(0.7),1,1,(1.8)
(0.7),1,2,(1.6)
(0.7),2,0,(2.7)
(0.7),2,1,(2.8)
(0.7),2,2,(2.6)
(0.8),0,0,(0.8)
(0.8),0,1,(0.6)
(0.8),0,2,(0.7)
(0.8),1,0,(1.8)
(0.8),1,1,(1.6)
(0.8),1,2,(1.7)
(0.8),2,0,(2.8)
(0.8),2,1,(2.6)
(0.8),2,2,(2.7)
(1.0),0,0,(1.0)
(1.0),0,1,(1.1)
(1.0),0,2,(1.2)
(1.0),1,0,(2.0)
(1.0),1,1,(2.1)
(1.0),1,2,(2.2)
(1.0),2,0,(0.0)
(1.0),2,1,(0.1)
(1.0),2,2,(0.2)
(1.1),0,0,(1.1)
(1.1),0,1,(1.2)
(1.1),0,2,(1.0)
(1.1),1,0,(2.1)
(1.1),1,1,(2.2)
(1.1),1,2,(2.0)
(1.1),2,0,(0.1)
(1.1),2,1,(0.2)
(1.1),2,2,(0.0)
(1.2),0,0,(1.2)
(1.2),0,1,(1.0)
(1.2),0,2,(1.1)
(1.2),1,0,(2.2)
(1.2),1,1,(2.0)
(1.2),1,2,(2.1)
(1.2),2,0,(0.2)
(1.2),2,1,(0.0)
(1.2),2,2,(0.1)
(1.3),0,0,(1.3)
(1.3),0,1,(1.4)
(1.3),0,2,(1.5)
(1.3),1,0,(2.3)
(1.3),1,1,(2.4)
(1.3),1,2,(2.5)
(1.3),2,0,(0.3)
(1.3),2,1,(0.4)
(1.3),2,2,(0.5)
(1.4),0,0,(1.4)
(1.4),0,1,(1.5)
(1.4),0,2,(1.3)
(1.4),1,0,(2.4)
(1.4),1,1,(2.5)
(1.4),1,2,(2.3)
(1.4),2,0,(0.4)
(1.4),2,1,(0.5)
(1.4),2,2,(0.3)
(1.5),0,0,(1.5)
(1.5),0,1,(1.3)
(1.5),0,2,(1.4)
(1.5),1,0,(2.5)
(1.5),1,1,(2.3)
(1.5),1,2,(2.4)
(1.5),2,0,(0.5)
(1.5),2,1,(0.3)
(1.5),2,2,(0.4)
(1.6),0,0,(1.6)
(1.6),0,1,(1.7)
(1.6),0,2,(1.8)
(1.6),1,0,(2.6)
(1.6),1,1,(2.7)
(1.6),1,2,(2.8)
(1.6),2,0,(0.6)
(1.6),2,1,(0.7)
(1.6),2,2,(0.8)
(1.7),0,0,(1.7)
(1.7),0,1,(1.8)
(1.7),0,2,(1.6)
(1.7),1,0,(2.7)
(1.7),1,1,(2.8)
(1.7),1,2,(2.6)
(1.7),2,0,(0.7)
(1.7),2,1,(0.8)
(1.7),2,2,(0.6)
(1.8),0,0,(1.8)
(1.8),0,1,(1.6)
(1.8),0,2,(1.7)
(1.8),1,0,(2.8)
(1.8),1,1,(2.6)
(1.8),1,2,(2.7)
(1.8),2,0,(0.8)
(1.8),2,1,(0.6)
(1.8),2,2,(0.7)
(2.0),0,0,(2.0)
(2.0),0,1,(2.1)
(2.0),0,2,(2.2)
(2.0),1,0,(0.0)
(2.0),1,1,(0.1)
(2.0),1,2,(0.2)
(2.0),2,0,(1.0)
(2.0),2,1,(1.1)
(2.0),2,2,(1.2)
(2.1),0,0,(2.1)
(2.1),0,1,(2.2)
(2.1),0,2,(2.0)
(2.1),1,0,(0.1)
(2.1),1,1,(0.2)
(2.1),1,2,(0.0)
(2.1),2,0,(1.1)
(2.1),2,1,(1.2)
(2.1),2,2,(1.0)
(2.2),0,0,(2.2)
(2.2),0,1,(2.0)
(2.2),0,2,(2.1)
(2.2),1,0,(0.2)
(2.2),1,1,(0.0)
(2.2),1,2,(0.1)
(2.2),2,0,(1.2)
(2.2),2,1,(1.0)
(2.2),2,2,(1.1)
(2.3),0,0,(2.3)
(2.3),0,1,(2.4)
(2.3),0,2,(2.5)
(2.3),1,0,(0.3)
(2.3),1,1,(0.4)
(2.3),1,2,(0.5)
(2.3),2,0,(1.3)
(2.3),2,1,(1.4)
(2.3),2,2,(1.5)
(2.4),0,0,(2.4)
(2.4),0,1,(2.5)
(2.4),0,2,(2.3)
(2.4),1,0,(0.4)
(2.4),1,1,(0.5)
(2.4),1,2,(0.3)
(2.4),2,0,(1.4)
(2.4),2,1,(1.5)
(2.4),2,2,(1.3)
(2.5),0,0,(2.5)
(2.5),0,1,(2.3)
(2.5),0,2,(2.4)
(2.5),1,0,(0.5)
(2.5),1,1,(0.3)
(2.5),1,2,(0.4)
(2.5),2,0,(1.5)
(2.5),2,1,(1.3)
(2.5),2,2,(1.4)
(2.6),0,0,(2.6)
(2.6),0,1,(2.7)
(2.6),0,2,(2.8)
(2.6),1,0,(0.6)
(2.6),1,1,(0.7)
(2.6),1,2,(0.8)
(2.6),2,0,(1.6)
(2.6),2,1,(1.7)
(2.6),2,2,(1.8)
(2.7),0,0,(2.7)
(2.7),0,1,(2.8)
(2.7),0,2,(2.6)
(2.7),1,0,(0.7)
(2.7),1,1,(0.8)
(2.7),1,2,(0.6)
(2.7),2,0,(1.7)
(2.7),2,1,(1.8)
(2.7),2,2,(1.6)
(2.8),0,0,(2.8)
(2.8),0,1,(2.6)
(2.8),0,2,(2.7)
(2.8),1,0,(0.8)
(2.8),1,1,(0.6)
(2.8),1,2,(0.7)
(2.8),2,0,(1.8)
(2.8),2,1,(1.6)
(2.8),2,2,(1.7)
(3.0),0,0,(3.0)
(3.0),0,1,(3.1)
(3.0),0,2,(3.2)
(3.0),1,0,(4.0)
(3.0),1,1,(4.1)
(3.0),1,2,(4.2)
(3.0),2,0,(5.0)
(3.0),2,1,(5.1)
(3.0),2,2,(5.2)
(3.1),0,0,(3.1)
(3.1),0,1,(3.2)
(3.1),0,2,(3.0)
(3.1),1,0,(4.1)
(3.1),1,1,(4.2)
(3.1),1,2,(4.0)
(3.1),2,0,(5.1)
(3.1),2,1,(5.2)
(3.1),2,2,(5.0)
(3.2),0,0,(3.2)
(3.2),0,1,(3.0)
(3.2),0,2,(3.1)
(3.2),1,0,(4.2)
(3.2),1,1,(4.0)
(3.2),1,2,(4.1)
(3.2),2,0,(5.2)
(3.2),2,1,(5.0)
(3.2),2,2,(5.1)
(3.3),0,0,(3.3)
(3.3),0,1,(3.4)
(3.3),0,2,(3.5)
(3.3),1,0,(4.3)
(3.3),1,1,(4.4)
(3.3),1,2,(4.5)
(3.3),2,0,(5.3)
(3.3),2,1,(5.4)
(3.3),2,2,(5.5)
(3.4),0,0,(3.4)
(3.4),0,1,(3.5)
(3.4),0,2,(3.3)
(3.4),1,0,(4.4)
(3.4),1,1,(4.5)
(3.4),1,2,(4.3)
(3.4),2,0,(5.4)
(3.4),2,1,(5.5)
(3.4),2,2,(5.3)
(3.5),0,0,(3.5)
(3.5),0,1,(3.3)
(3.5),0,2,(3.4)
(3.5),1,0,(4.5)
(3.5),1,1,(4.3)
(3.5),1,2,(4.4)
(3.5),2,0,(5.5)
(3.5),2,1,(5.3)
(3.5),2,2,(5.4)
(3.6),0,0,(3.6)
(3.6),0,1,(3.7)
(3.6),0,2,(3.8)
(3.6),1,0,(4.6)
(3.6),1,1,(4.7)
(3.6),1,2,(4.8)
(3.6),2,0,(5.6)
(3.6),2,1,(5.7)
(3.6),2,2,(5.8)
(3.7),0,0,(3.7)
(3.7),0,1,(3.8)
(3.7),0,2,(3.6)
(3.7),1,0,(4.7)
(3.7),1,1,(4.8)
(3.7),1,2,(4.6)
(3.7),2,0,(5.7)
(3.7),2,1,(5.8)
(3.7),2,2,(5.6)
(3.8),0,0,(3.8)
(3.8),0,1,(3.6)
(3.8),0,2,(3.7)
(3.8),1,0,(4.8)
(3.8),1,1,(4.6)
(3.8),1,2,(4.7)
(3.8),2,0,(5.8)
(3.8),2,1,(5.6)
(3.8),2,2,(5.7)
(4.0),0,0,(4.0)
(4.0),0,1,(4.1)
(4.0),0,2,(4.2)
(4.0),1,0,(5.0)
(4.0),1,1,(5.1)
(4.0),1,2,(5.2)
(4.0),2,0,(3.0)
(4.0),2,1,(3.1)
(4.0),2,2,(3.2)
(4.1),0,0,(4.1)
(4.1),0,1,(4.2)
(4.1),0,2,(4.0)
(4.1),1,0,(5.1)
(4.1),1,1,(5.2)
(4.1),1,2,(5.0)
(4.1),2,0,(3.1)
(4.1),2,1,(3.2)
(4.1),2,2,(3.0)
(4.2),0,0,(4.2)
(4.2),0,1,(4.0)
(4.2),0,2,(4.1)
(4.2),1,0,(5.2)
(4.2),1,1,(5.0)
(4.2),1,2,(5.1)
(4.2),2,0,(3.2)
(4.2),2,1,(3.0)
(4.2),2,2,(3.1)
(4.3),0,0,(4.3)
(4.3),0,1,(4.4)
(4.3),0,2,(4.5)
(4.3),1,0,(5.3)
(4.3),1,1,(5.4)
(4.3),1,2,(5.5)
(4.3),2,0,(3.3)
(4.3),2,1,(3.4)
(4.3),2,2,(3.5)
(4.4),0,0,(4.4)
(4.4),0,1,(4.5)
(4.4),0,2,(4.3)
(4.4),1,0,(5.4)
(4.4),1,1,(5.5)
(4.4),1,2,(5.3)
(4.4),2,0,(3.4)
(4.4),2,1,(3.5)
(4.4),2,2,(3.3)
(4.5),0,0,(4.5)
(4.5),0,1,(4.3)
(4.5),0,2,(4.4)
(4.5),1,0,(5.5)
(4.5),1,1,(5.3)
(4.5),1,2,(5.4)
(4.5),2,0,(3.5)
(4.5),2,1,(3.3)
(4.5),2,2,(3.4)
(4.6),0,0,(4.6)
(4.6),0,1,(4.7)
(4.6),0,2,(4.8)
(4.6),1,0,(5.6)
(4.6),1,1,(5.7)
(4.6),1,2,(5.8)
(4.6),2,0,(3.6)
(4.6),2,1,(3.7)
(4.6),2,2,(3.8)
(4.7),0,0,(4.7)
(4.7),0,1,(4.8)
(4.7),0,2,(4.6)
(4.7),1,0,(5.7)
(4.7),1,1,(5.8)
(4.7),1,2,(5.6)
(4.7),2,0,(3.7)
(4.7),2,1,(3.8)
(4.7),2,2,(3.6)
(4.8),0,0,(4.8)
(4.8),0,1,(4.6)
(4.8),0,2,(4.7)
(4.8),1,0,(5.8)
(4.8),1,1,(5.6)
(4.8),1,2,(5.7)
(4.8),2,0,(3.8)
(4.8),2,1,(3.6)
(4.8),2,2,(3.7)
(5.0),0,0,(5.0)
(5.0),0,1,(5.1)
(5.0),0,2,(5.2)
(5.0),1,0,(3.0)
(5.0),1,1,(3.1)
(5.0),1,2,(3.2)
(5.0),2,0,(4.0)
(5.0),2,1,(4.1)
(5.0),2,2,(4.2)
(5.1),0,0,(5.1)
(5.1),0,1,(5.2)
(5.1),0,2,(5.0)
(5.1),1,0,(3.1)
(5.1),1,1,(3.2)
(5.1),1,2,(3.0)
(5.1),2,0,(4.1)
(5.1),2,1,(4.2)
(5.1),2,2,(4.0)
(5.2),0,0,(5.2)
(5.2),0,1,(5.0)
(5.2),0,2,(5.1)
(5.2),1,0,(3.2)
(5.2),1,1,(3.0)
(5.2),1,2,(3.1)
(5.2),2,0,(4.2)
(5.2),2,1,(4.0)
(5.2),2,2,(4.1)
(5.3),0,0,(5.3)
(5.3),0,1,(5.4)
(5.3),0,2,(5.5)
(5.3),1,0,(3.3)
(5.3),1,1,(3.4)
(5.3),1,2,(3.5)
(5.3),2,0,(4.3)
(5.3),2,1,(4.4)
(5.3),2,2,(4.5)
(5.4),0,0,(5.4)
(5.4),0,1,(5.5)
(5.4),0,2,(5.3)
(5.4),1,0,(3.4)
(5.4),1,1,(3.5)
(5.4),1,2,(3.3)
(5.4),2,0,(4.4)
(5.4),2,1,(4.5)
(5.4),2,2,(4.3)
(5.5),0,0,(5.5)
(5.5),0,1,(5.3)
(5.5),0,2,(5.4)
(5.5),1,0,(3.5)
(5.5),1,1,(3.3)
(5.5),1,2,(3.4)
(5.5),2,0,(4.5)
(5.5),2,1,(4.3)
(5.5),2,2,(4.4)
(5.6),0,0,(5.6)
(5.6),0,1,(5.7)
(5.6),0,2,(5.8)
(5.6),1,0,(3.6)
(5.6),1,1,(3.7)
(5.6),1,2,(3.8)
(5.6),2,0,(4.6)
(5.6),2,1,(4.7)
(5.6),2,2,(4.8)
(5.7),0,0,(5.7)
(5.7),0,1,(5.8)
(5.7),0,2,(5.6)
(5.7),1,0,(3.7)
(5.7),1,1,(3.8)
(5.7),1,2,(3.6)
(5.7),2,0,(4.7)
(5.7),2,1,(4.8)
(5.7),2,2,(4.6)
(5.8),0,0,(5.8)
(5.8),0,1,(5.6)
(5.8),0,2,(5.7)
(5.8),1,0,(3.8)
(5.8),1,1,(3.6)
(5.8),1,2,(3.7)
(5.8),2,0,(4.8)
(5.8),2,1,(4.6)
(5.8),2,2,(4.7)
(6.0),0,0,(6.0)
(6.0),0,1,(6.1)
(6.0),0,2,(6.2)
(6.0),1,0,(7.0)
(6.0),1,1,(7.1)
(6.0),1,2,(7.2)
(6.0),2,0,(8.0)
(6.0),2,1,(8.1)
(6.0),2,2,(8.2)
(6.1),0,0,(6.1)
(6.1),0,1,(6.2)
(6.1),0,2,(6.0)
(6.1),1,0,(7.1)
(6.1),1,1,(7.2)
(6.1),1,2,(7.0)
(6.1),2,0,(8.1)
(6.1),2,1,(8.2)
(6.1),2,2,(8.0)
(6.2),0,0,(6.2)
(6.2),0,1,(6.0)
(6.2),0,2,(6.1)
(6.2),1,0,(7.2)
(6.2),1,1,(7.0)
(6.2),1,2,(7.1)
(6.2),2,0,(8.2)
(6.2),2,1,(8.0)
(6.2),2,2,(8.1)
(6.3),0,0,(6.3)
(6.3),0,1,(6.4)
(6.3),0,2,(6.5)
(6.3),1,0,(7.3)
(6.3),1,1,(7.4)
(6.3),1,2,(7.5)
(6.3),2,0,(8.3)
(6.3),2,1,(8.4)
(6.3),2,2,(8.5)
(6.4),0,0,(6.4)
(6.4),0,1,(6.5)
(6.4),0,2,(6.3)
(6.4),1,0,(7.4)
(6.4),1,1,(7.5)
(6.4),1,2,(7.3)
(6.4),2,0,(8.4)
(6.4),2,1,(8.5)
(6.4),2,2,(8.3)
(6.5),0,0,(6.5)
(6.5),0,1,(6.3)
(6.5),0,2,(6.4)
(6.5),1,0,(7.5)
(6.5),1,1,(7.3)
(6.5),1,2,(7.4)
(6.5),2,0,(8.5)
(6.5),2,1,(8.3)
(6.5),2,2,(8.4)
(6.6),0,0,(6.6)
(6.6),0,1,(6.7)
(6.6),0,2,(6.8)
(6.6),1,0,(7.6)
(6.6),1,1,(7.7)
(6.6),1,2,(7.8)
(6.6),2,0,(8.6)
(6.6),2,1,(8.7)
(6.6),2,2,(8.8)
(6.7),0,0,(6.7)
(6.7),0,1,(6.8)
(6.7),0,2,(6.6)
(6.7),1,0,(7.7)
(6.7),1,1,(7.8)
(6.7),1,2,(7.6)
(6.7),2,0,(8.7)
(6.7),2,1,(8.8)
(6.7),2,2,(8.6)
(6.8),0,0,(6.8)
(6.8),0,1,(6.6)
(6.8),0,2,(6.7)
(6.8),1,0,(7.8)
(6.8),1,1,(7.6)
(6.8),1,2,(7.7)
(6.8),2,0,(8.8)
(6.8),2,1,(8.6)
(6.8),2,2,(8.7)
(7.0),0,0,(7.0)
(7.0),0,1,(7.1)
(7.0),0,2,(7.2)
(7.0),1,0,(8.0)
(7.0),1,1,(8.1)
(7.0),1,2,(8.2)
(7.0),2,0,(6.0)
(7.0),2,1,(6.1)
(7.0),2,2,(6.2)
(7.1),0,0,(7.1)
(7.1),0,1,(7.2)
(7.1),0,2,(7.0)
(7.1),1,0,(8.1)
(7.1),1,1,(8.2)
(7.1),1,2,(8.0)
(7.1),2,0,(6.1)
(7.1),2,1,(6.2)
(7.1),2,2,(6.0)
(7.2),0,0,(7.2)
(7.2),0,1,(7.0)
(7.2),0,2,(7.1)
(7.2),1,0,(8.2)
(7.2),1,1,(8.0)
(7.2),1,2,(8.1)
(7.2),2,0,(6.2)
(7.2),2,1,(6.0)
(7.2),2,2,(6.1)
(7.3),0,0,(7.3)
(7.3),0,1,(7.4)
(7.3),0,2,(7.5)
(7.3),1,0,(8.3)
(7.3),1,1,(8.4)
(7.3),1,2,(8.5)
(7.3),2,0,(6.3)
(7.3),2,1,(6.4)
(7.3),2,2,(6.5)
(7.4),0,0,(7.4)
(7.4),0,1,(7.5)
(7.4),0,2,(7.3)
(7.4),1,0,(8.4)
(7.4),1,1,(8.5)
(7.4),1,2,(8.3)
(7.4),2,0,(6.4)
(7.4),2,1,(6.5)
(7.4),2,2,(6.3)
(7.5),0,0,(7.5)
(7.5),0,1,(7.3)
(7.5),0,2,(7.4)
(7.5),1,0,(8.5)
(7.5),1,1,(8.3)
(7.5),1,2,(8.4)
(7.5),2,0,(6.5)
(7.5),2,1,(6.3)
(7.5),2,2,(6.4)
(7.6),0,0,(7.6)
(7.6),0,1,(7.7)
(7.6),0,2,(7.8)
(7.6),1,0,(8.6)
(7.6),1,1,(8.7)
(7.6),1,2,(8.8)
(7.6),2,0,(6.6)
(7.6),2,1,(6.7)
(7.6),2,2,(6.8)
(7.7),0,0,(7.7)
(7.7),0,1,(7.8)
(7.7),0,2,(7.6)
(7.7),1,0,(8.7)
(7.7),1,1,(8.8)
(7.7),1,2,(8.6)
(7.7),2,0,(6.7)
(7.7),2,1,(6.8)
(7.7),2,2,(6.6)
(7.8),0,0,(7.8)
(7.8),0,1,(7.6)
(7.8),0,2,(7.7)
(7.8),1,0,(8.8)
(7.8),1,1,(8.6)
(7.8),1,2,(8.7)
(7.8),2,0,(6.8)
(7.8),2,1,(6.6)
(7.8),2,2,(6.7)
(8.0),0,0,(8.0)
(8.0),0,1,(8.1)
(8.0),0,2,(8.2)
(8.0),1,0,(6.0)
(8.0),1,1,(6.1)
(8.0),1,2,(6.2)
(8.0),2,0,(7.0)
(8.0),2,1,(7.1)
(8.0),2,2,(7.2)
(8.1),0,0,(8.1)
(8.1),0,1,(8.2)
(8.1),0,2,(8.0)
(8.1),1,0,(6.1)
(8.1),1,1,(6.2)
(8.1),1,2,(6.0)
(8.1),2,0,(7.1)
(8.1),2,1,(7.2)
(8.1),2,2,(7.0)
(8.2),0,0,(8.2)
(8.2),0,1,(8.0)
(8.2),0,2,(8.1)
(8.2),1,0,(6.2)
(8.2),1,1,(6.0)
(8.2),1,2,(6.1)
(8.2),2,0,(7.2)
(8.2),2,1,(7.0)
(8.2),2,2,(7.1)
(8.3),0,0,(8.3)
(8.3),0,1,(8.4)
(8.3),0,2,(8.5)
(8.3),1,0,(6.3)
(8.3),1,1,(6.4)
(8.3),1,2,(6.5)
(8.3),2,0,(7.3)
(8.3),2,1,(7.4)
(8.3),2,2,(7.5)
(8.4),0,0,(8.4)
(8.4),0,1,(8.5)
(8.4),0,2,(8.3)
(8.4),1,0,(6.4)
(8.4),1,1,(6.5)
(8.4),1,2,(6.3)
(8.4),2,0,(7.4)
(8.4),2,1,(7.5)
(8.4),2,2,(7.3)
(8.5),0,0,(8.5)
(8.5),0,1,(8.3)
(8.5),0,2,(8.4)
(8.5),1,0,(6.5)
(8.5),1,1,(6.3)
(8.5),1,2,(6.4)
(8.5),2,0,(7.5)
(8.5),2,1,(7.3)
(8.5),2,2,(7.4)
(8.6),0,0,(8.6)
(8.6),0,1,(8.7)
(8.6),0,2,(8.8)
(8.6),1,0,(6.6)
(8.6),1,1,(6.7)
(8.6),1,2,(6.8)
(8.6),2,0,(7.6)
(8.6),2,1,(7.7)
(8.6),2,2,(7.8)
(8.7),0,0,(8.7)
(8.7),0,1,(8.8)
(8.7),0,2,(8.6)
(8.7),1,0,(6.7)
(8.7),1,1,(6.8)
(8.7),1,2,(6.6)
(8.7),2,0,(7.7)
(8.7),2,1,(7.8)
(8.7),2,2,(7.6)
(8.8),0,0,(8.8)
(8.8),0,1,(8.6)
(8.8),0,2,(8.7)
(8.8),1,0,(6.8)
(8.8),1,1,(6.6)
(8.8),1,2,(6.7)
(8.8),2,0,(7.8)
(8.8),2,1,(7.6)
(8.8),2,2,(7.7)