In [5]:
"""
The Sudoku Problem Formulation for the PuLP Modeller

Authors: Antony Phillips, Dr Stuart Mitchell
"""

# Import PuLP modeler functions
from pulp import *

# A list of strings from "1" to "9" is created
Sequence = ["1", "2", "3", "4", "5", "6", "7", "8", "9"]

# The Vals, Rows and Cols sequences all follow this form
Vals = Sequence
Rows = Sequence
Cols = Sequence

# The boxes list is created, with the row and column index of each square in each box
Boxes =[]
for i in range(3):
    for j in range(3):
        Boxes += [[(Rows[3*i+k],Cols[3*j+l]) for k in range(3) for l in range(3)]]

# The prob variable is created to contain the problem data        
prob = LpProblem("Sudoku Problem",LpMinimize)

# The problem variables are created
choices = LpVariable.dicts("Choice",(Vals,Rows,Cols),0,1,LpInteger)

# The arbitrary objective function is added
prob += 0, "Arbitrary Objective Function"

# A constraint ensuring that only one value can be in each square is created
for r in Rows:
    for c in Cols:
        prob += lpSum([choices[v][r][c] for v in Vals]) == 1, ""

# The row, column and box constraints are added for each value
for v in Vals:
    for r in Rows:
        prob += lpSum([choices[v][r][c] for c in Cols]) == 1,""
        
    for c in Cols:
        prob += lpSum([choices[v][r][c] for r in Rows]) == 1,""

    for b in Boxes:
        prob += lpSum([choices[v][r][c] for (r,c) in b]) == 1,""
                        
# The starting numbers are entered as constraints                
prob += choices["5"]["1"]["1"] == 1,""
prob += choices["6"]["2"]["1"] == 1,""
prob += choices["8"]["4"]["1"] == 1,""
prob += choices["4"]["5"]["1"] == 1,""
prob += choices["7"]["6"]["1"] == 1,""
prob += choices["3"]["1"]["2"] == 1,""
prob += choices["9"]["3"]["2"] == 1,""
prob += choices["6"]["7"]["2"] == 1,""
prob += choices["8"]["3"]["3"] == 1,""
prob += choices["1"]["2"]["4"] == 1,""
prob += choices["8"]["5"]["4"] == 1,""
prob += choices["4"]["8"]["4"] == 1,""
prob += choices["7"]["1"]["5"] == 1,""
prob += choices["9"]["2"]["5"] == 1,""
prob += choices["6"]["4"]["5"] == 1,""
prob += choices["2"]["6"]["5"] == 1,""
prob += choices["1"]["8"]["5"] == 1,""
prob += choices["8"]["9"]["5"] == 1,""
prob += choices["5"]["2"]["6"] == 1,""
prob += choices["3"]["5"]["6"] == 1,""
prob += choices["9"]["8"]["6"] == 1,""
prob += choices["2"]["7"]["7"] == 1,""
prob += choices["6"]["3"]["8"] == 1,""
prob += choices["8"]["7"]["8"] == 1,""
prob += choices["7"]["9"]["8"] == 1,""
prob += choices["3"]["4"]["9"] == 1,""
prob += choices["1"]["5"]["9"] == 1,""
prob += choices["6"]["6"]["9"] == 1,""
prob += choices["5"]["8"]["9"] == 1,""

# The problem data is written to an .lp file
prob.writeLP("Sudoku.lp")

# The problem is solved using PuLP's choice of Solver
prob.solve()

# The status of the solution is printed to the screen
print "Status:", LpStatus[prob.status]

# A file called sudokuout.txt is created/overwritten for writing to
sudokuout = open('sudokuout.txt','w')

# The solution is written to the sudokuout.txt file 
for r in Rows:
    if r == "1" or r == "4" or r == "7":
                    sudokuout.write("+-------+-------+-------+\n")
    for c in Cols:
        for v in Vals:
            if value(choices[v][r][c])==1:
                               
                if c == "1" or c == "4" or c =="7":
                    sudokuout.write("| ")
                    
                sudokuout.write(v + " ")
                
                if c == "9":
                    sudokuout.write("|\n")
sudokuout.write("+-------+-------+-------+")                    
sudokuout.close()

# The location of the solution is give to the user
print "Solution Written to sudokuout.txt"
Status: Optimal
Solution Written to sudokuout.txt
In [6]:
print open("sudokuout.txt").read()
+-------+-------+-------+
| 5 3 4 | 6 7 8 | 9 1 2 |
| 6 7 2 | 1 9 5 | 3 4 8 |
| 1 9 8 | 3 4 2 | 5 6 7 |
+-------+-------+-------+
| 8 5 9 | 7 6 1 | 4 2 3 |
| 4 2 6 | 8 5 3 | 7 9 1 |
| 7 1 3 | 9 2 4 | 8 5 6 |
+-------+-------+-------+
| 9 6 1 | 5 3 7 | 2 8 4 |
| 2 8 7 | 4 1 9 | 6 3 5 |
| 3 4 5 | 2 8 6 | 1 7 9 |
+-------+-------+-------+
In [7]:
prob
Out[7]:
Sudoku Problem:
MINIMIZE
0*__dummy + 0
SUBJECT TO
_C1: Choice_1_1_1 + Choice_2_1_1 + Choice_3_1_1 + Choice_4_1_1 + Choice_5_1_1
 + Choice_6_1_1 + Choice_7_1_1 + Choice_8_1_1 + Choice_9_1_1 = 1

_C2: Choice_1_1_2 + Choice_2_1_2 + Choice_3_1_2 + Choice_4_1_2 + Choice_5_1_2
 + Choice_6_1_2 + Choice_7_1_2 + Choice_8_1_2 + Choice_9_1_2 = 1

_C3: Choice_1_1_3 + Choice_2_1_3 + Choice_3_1_3 + Choice_4_1_3 + Choice_5_1_3
 + Choice_6_1_3 + Choice_7_1_3 + Choice_8_1_3 + Choice_9_1_3 = 1

_C4: Choice_1_1_4 + Choice_2_1_4 + Choice_3_1_4 + Choice_4_1_4 + Choice_5_1_4
 + Choice_6_1_4 + Choice_7_1_4 + Choice_8_1_4 + Choice_9_1_4 = 1

_C5: Choice_1_1_5 + Choice_2_1_5 + Choice_3_1_5 + Choice_4_1_5 + Choice_5_1_5
 + Choice_6_1_5 + Choice_7_1_5 + Choice_8_1_5 + Choice_9_1_5 = 1

_C6: Choice_1_1_6 + Choice_2_1_6 + Choice_3_1_6 + Choice_4_1_6 + Choice_5_1_6
 + Choice_6_1_6 + Choice_7_1_6 + Choice_8_1_6 + Choice_9_1_6 = 1

_C7: Choice_1_1_7 + Choice_2_1_7 + Choice_3_1_7 + Choice_4_1_7 + Choice_5_1_7
 + Choice_6_1_7 + Choice_7_1_7 + Choice_8_1_7 + Choice_9_1_7 = 1

_C8: Choice_1_1_8 + Choice_2_1_8 + Choice_3_1_8 + Choice_4_1_8 + Choice_5_1_8
 + Choice_6_1_8 + Choice_7_1_8 + Choice_8_1_8 + Choice_9_1_8 = 1

_C9: Choice_1_1_9 + Choice_2_1_9 + Choice_3_1_9 + Choice_4_1_9 + Choice_5_1_9
 + Choice_6_1_9 + Choice_7_1_9 + Choice_8_1_9 + Choice_9_1_9 = 1

_C10: Choice_1_2_1 + Choice_2_2_1 + Choice_3_2_1 + Choice_4_2_1 + Choice_5_2_1
 + Choice_6_2_1 + Choice_7_2_1 + Choice_8_2_1 + Choice_9_2_1 = 1

_C11: Choice_1_2_2 + Choice_2_2_2 + Choice_3_2_2 + Choice_4_2_2 + Choice_5_2_2
 + Choice_6_2_2 + Choice_7_2_2 + Choice_8_2_2 + Choice_9_2_2 = 1

_C12: Choice_1_2_3 + Choice_2_2_3 + Choice_3_2_3 + Choice_4_2_3 + Choice_5_2_3
 + Choice_6_2_3 + Choice_7_2_3 + Choice_8_2_3 + Choice_9_2_3 = 1

_C13: Choice_1_2_4 + Choice_2_2_4 + Choice_3_2_4 + Choice_4_2_4 + Choice_5_2_4
 + Choice_6_2_4 + Choice_7_2_4 + Choice_8_2_4 + Choice_9_2_4 = 1

_C14: Choice_1_2_5 + Choice_2_2_5 + Choice_3_2_5 + Choice_4_2_5 + Choice_5_2_5
 + Choice_6_2_5 + Choice_7_2_5 + Choice_8_2_5 + Choice_9_2_5 = 1

_C15: Choice_1_2_6 + Choice_2_2_6 + Choice_3_2_6 + Choice_4_2_6 + Choice_5_2_6
 + Choice_6_2_6 + Choice_7_2_6 + Choice_8_2_6 + Choice_9_2_6 = 1

_C16: Choice_1_2_7 + Choice_2_2_7 + Choice_3_2_7 + Choice_4_2_7 + Choice_5_2_7
 + Choice_6_2_7 + Choice_7_2_7 + Choice_8_2_7 + Choice_9_2_7 = 1

_C17: Choice_1_2_8 + Choice_2_2_8 + Choice_3_2_8 + Choice_4_2_8 + Choice_5_2_8
 + Choice_6_2_8 + Choice_7_2_8 + Choice_8_2_8 + Choice_9_2_8 = 1

_C18: Choice_1_2_9 + Choice_2_2_9 + Choice_3_2_9 + Choice_4_2_9 + Choice_5_2_9
 + Choice_6_2_9 + Choice_7_2_9 + Choice_8_2_9 + Choice_9_2_9 = 1

_C19: Choice_1_3_1 + Choice_2_3_1 + Choice_3_3_1 + Choice_4_3_1 + Choice_5_3_1
 + Choice_6_3_1 + Choice_7_3_1 + Choice_8_3_1 + Choice_9_3_1 = 1

_C20: Choice_1_3_2 + Choice_2_3_2 + Choice_3_3_2 + Choice_4_3_2 + Choice_5_3_2
 + Choice_6_3_2 + Choice_7_3_2 + Choice_8_3_2 + Choice_9_3_2 = 1

_C21: Choice_1_3_3 + Choice_2_3_3 + Choice_3_3_3 + Choice_4_3_3 + Choice_5_3_3
 + Choice_6_3_3 + Choice_7_3_3 + Choice_8_3_3 + Choice_9_3_3 = 1

_C22: Choice_1_3_4 + Choice_2_3_4 + Choice_3_3_4 + Choice_4_3_4 + Choice_5_3_4
 + Choice_6_3_4 + Choice_7_3_4 + Choice_8_3_4 + Choice_9_3_4 = 1

_C23: Choice_1_3_5 + Choice_2_3_5 + Choice_3_3_5 + Choice_4_3_5 + Choice_5_3_5
 + Choice_6_3_5 + Choice_7_3_5 + Choice_8_3_5 + Choice_9_3_5 = 1

_C24: Choice_1_3_6 + Choice_2_3_6 + Choice_3_3_6 + Choice_4_3_6 + Choice_5_3_6
 + Choice_6_3_6 + Choice_7_3_6 + Choice_8_3_6 + Choice_9_3_6 = 1

_C25: Choice_1_3_7 + Choice_2_3_7 + Choice_3_3_7 + Choice_4_3_7 + Choice_5_3_7
 + Choice_6_3_7 + Choice_7_3_7 + Choice_8_3_7 + Choice_9_3_7 = 1

_C26: Choice_1_3_8 + Choice_2_3_8 + Choice_3_3_8 + Choice_4_3_8 + Choice_5_3_8
 + Choice_6_3_8 + Choice_7_3_8 + Choice_8_3_8 + Choice_9_3_8 = 1

_C27: Choice_1_3_9 + Choice_2_3_9 + Choice_3_3_9 + Choice_4_3_9 + Choice_5_3_9
 + Choice_6_3_9 + Choice_7_3_9 + Choice_8_3_9 + Choice_9_3_9 = 1

_C28: Choice_1_4_1 + Choice_2_4_1 + Choice_3_4_1 + Choice_4_4_1 + Choice_5_4_1
 + Choice_6_4_1 + Choice_7_4_1 + Choice_8_4_1 + Choice_9_4_1 = 1

_C29: Choice_1_4_2 + Choice_2_4_2 + Choice_3_4_2 + Choice_4_4_2 + Choice_5_4_2
 + Choice_6_4_2 + Choice_7_4_2 + Choice_8_4_2 + Choice_9_4_2 = 1

_C30: Choice_1_4_3 + Choice_2_4_3 + Choice_3_4_3 + Choice_4_4_3 + Choice_5_4_3
 + Choice_6_4_3 + Choice_7_4_3 + Choice_8_4_3 + Choice_9_4_3 = 1

_C31: Choice_1_4_4 + Choice_2_4_4 + Choice_3_4_4 + Choice_4_4_4 + Choice_5_4_4
 + Choice_6_4_4 + Choice_7_4_4 + Choice_8_4_4 + Choice_9_4_4 = 1

_C32: Choice_1_4_5 + Choice_2_4_5 + Choice_3_4_5 + Choice_4_4_5 + Choice_5_4_5
 + Choice_6_4_5 + Choice_7_4_5 + Choice_8_4_5 + Choice_9_4_5 = 1

_C33: Choice_1_4_6 + Choice_2_4_6 + Choice_3_4_6 + Choice_4_4_6 + Choice_5_4_6
 + Choice_6_4_6 + Choice_7_4_6 + Choice_8_4_6 + Choice_9_4_6 = 1

_C34: Choice_1_4_7 + Choice_2_4_7 + Choice_3_4_7 + Choice_4_4_7 + Choice_5_4_7
 + Choice_6_4_7 + Choice_7_4_7 + Choice_8_4_7 + Choice_9_4_7 = 1

_C35: Choice_1_4_8 + Choice_2_4_8 + Choice_3_4_8 + Choice_4_4_8 + Choice_5_4_8
 + Choice_6_4_8 + Choice_7_4_8 + Choice_8_4_8 + Choice_9_4_8 = 1

_C36: Choice_1_4_9 + Choice_2_4_9 + Choice_3_4_9 + Choice_4_4_9 + Choice_5_4_9
 + Choice_6_4_9 + Choice_7_4_9 + Choice_8_4_9 + Choice_9_4_9 = 1

_C37: Choice_1_5_1 + Choice_2_5_1 + Choice_3_5_1 + Choice_4_5_1 + Choice_5_5_1
 + Choice_6_5_1 + Choice_7_5_1 + Choice_8_5_1 + Choice_9_5_1 = 1

_C38: Choice_1_5_2 + Choice_2_5_2 + Choice_3_5_2 + Choice_4_5_2 + Choice_5_5_2
 + Choice_6_5_2 + Choice_7_5_2 + Choice_8_5_2 + Choice_9_5_2 = 1

_C39: Choice_1_5_3 + Choice_2_5_3 + Choice_3_5_3 + Choice_4_5_3 + Choice_5_5_3
 + Choice_6_5_3 + Choice_7_5_3 + Choice_8_5_3 + Choice_9_5_3 = 1

_C40: Choice_1_5_4 + Choice_2_5_4 + Choice_3_5_4 + Choice_4_5_4 + Choice_5_5_4
 + Choice_6_5_4 + Choice_7_5_4 + Choice_8_5_4 + Choice_9_5_4 = 1

_C41: Choice_1_5_5 + Choice_2_5_5 + Choice_3_5_5 + Choice_4_5_5 + Choice_5_5_5
 + Choice_6_5_5 + Choice_7_5_5 + Choice_8_5_5 + Choice_9_5_5 = 1

_C42: Choice_1_5_6 + Choice_2_5_6 + Choice_3_5_6 + Choice_4_5_6 + Choice_5_5_6
 + Choice_6_5_6 + Choice_7_5_6 + Choice_8_5_6 + Choice_9_5_6 = 1

_C43: Choice_1_5_7 + Choice_2_5_7 + Choice_3_5_7 + Choice_4_5_7 + Choice_5_5_7
 + Choice_6_5_7 + Choice_7_5_7 + Choice_8_5_7 + Choice_9_5_7 = 1

_C44: Choice_1_5_8 + Choice_2_5_8 + Choice_3_5_8 + Choice_4_5_8 + Choice_5_5_8
 + Choice_6_5_8 + Choice_7_5_8 + Choice_8_5_8 + Choice_9_5_8 = 1

_C45: Choice_1_5_9 + Choice_2_5_9 + Choice_3_5_9 + Choice_4_5_9 + Choice_5_5_9
 + Choice_6_5_9 + Choice_7_5_9 + Choice_8_5_9 + Choice_9_5_9 = 1

_C46: Choice_1_6_1 + Choice_2_6_1 + Choice_3_6_1 + Choice_4_6_1 + Choice_5_6_1
 + Choice_6_6_1 + Choice_7_6_1 + Choice_8_6_1 + Choice_9_6_1 = 1

_C47: Choice_1_6_2 + Choice_2_6_2 + Choice_3_6_2 + Choice_4_6_2 + Choice_5_6_2
 + Choice_6_6_2 + Choice_7_6_2 + Choice_8_6_2 + Choice_9_6_2 = 1

_C48: Choice_1_6_3 + Choice_2_6_3 + Choice_3_6_3 + Choice_4_6_3 + Choice_5_6_3
 + Choice_6_6_3 + Choice_7_6_3 + Choice_8_6_3 + Choice_9_6_3 = 1

_C49: Choice_1_6_4 + Choice_2_6_4 + Choice_3_6_4 + Choice_4_6_4 + Choice_5_6_4
 + Choice_6_6_4 + Choice_7_6_4 + Choice_8_6_4 + Choice_9_6_4 = 1

_C50: Choice_1_6_5 + Choice_2_6_5 + Choice_3_6_5 + Choice_4_6_5 + Choice_5_6_5
 + Choice_6_6_5 + Choice_7_6_5 + Choice_8_6_5 + Choice_9_6_5 = 1

_C51: Choice_1_6_6 + Choice_2_6_6 + Choice_3_6_6 + Choice_4_6_6 + Choice_5_6_6
 + Choice_6_6_6 + Choice_7_6_6 + Choice_8_6_6 + Choice_9_6_6 = 1

_C52: Choice_1_6_7 + Choice_2_6_7 + Choice_3_6_7 + Choice_4_6_7 + Choice_5_6_7
 + Choice_6_6_7 + Choice_7_6_7 + Choice_8_6_7 + Choice_9_6_7 = 1

_C53: Choice_1_6_8 + Choice_2_6_8 + Choice_3_6_8 + Choice_4_6_8 + Choice_5_6_8
 + Choice_6_6_8 + Choice_7_6_8 + Choice_8_6_8 + Choice_9_6_8 = 1

_C54: Choice_1_6_9 + Choice_2_6_9 + Choice_3_6_9 + Choice_4_6_9 + Choice_5_6_9
 + Choice_6_6_9 + Choice_7_6_9 + Choice_8_6_9 + Choice_9_6_9 = 1

_C55: Choice_1_7_1 + Choice_2_7_1 + Choice_3_7_1 + Choice_4_7_1 + Choice_5_7_1
 + Choice_6_7_1 + Choice_7_7_1 + Choice_8_7_1 + Choice_9_7_1 = 1

_C56: Choice_1_7_2 + Choice_2_7_2 + Choice_3_7_2 + Choice_4_7_2 + Choice_5_7_2
 + Choice_6_7_2 + Choice_7_7_2 + Choice_8_7_2 + Choice_9_7_2 = 1

_C57: Choice_1_7_3 + Choice_2_7_3 + Choice_3_7_3 + Choice_4_7_3 + Choice_5_7_3
 + Choice_6_7_3 + Choice_7_7_3 + Choice_8_7_3 + Choice_9_7_3 = 1

_C58: Choice_1_7_4 + Choice_2_7_4 + Choice_3_7_4 + Choice_4_7_4 + Choice_5_7_4
 + Choice_6_7_4 + Choice_7_7_4 + Choice_8_7_4 + Choice_9_7_4 = 1

_C59: Choice_1_7_5 + Choice_2_7_5 + Choice_3_7_5 + Choice_4_7_5 + Choice_5_7_5
 + Choice_6_7_5 + Choice_7_7_5 + Choice_8_7_5 + Choice_9_7_5 = 1

_C60: Choice_1_7_6 + Choice_2_7_6 + Choice_3_7_6 + Choice_4_7_6 + Choice_5_7_6
 + Choice_6_7_6 + Choice_7_7_6 + Choice_8_7_6 + Choice_9_7_6 = 1

_C61: Choice_1_7_7 + Choice_2_7_7 + Choice_3_7_7 + Choice_4_7_7 + Choice_5_7_7
 + Choice_6_7_7 + Choice_7_7_7 + Choice_8_7_7 + Choice_9_7_7 = 1

_C62: Choice_1_7_8 + Choice_2_7_8 + Choice_3_7_8 + Choice_4_7_8 + Choice_5_7_8
 + Choice_6_7_8 + Choice_7_7_8 + Choice_8_7_8 + Choice_9_7_8 = 1

_C63: Choice_1_7_9 + Choice_2_7_9 + Choice_3_7_9 + Choice_4_7_9 + Choice_5_7_9
 + Choice_6_7_9 + Choice_7_7_9 + Choice_8_7_9 + Choice_9_7_9 = 1

_C64: Choice_1_8_1 + Choice_2_8_1 + Choice_3_8_1 + Choice_4_8_1 + Choice_5_8_1
 + Choice_6_8_1 + Choice_7_8_1 + Choice_8_8_1 + Choice_9_8_1 = 1

_C65: Choice_1_8_2 + Choice_2_8_2 + Choice_3_8_2 + Choice_4_8_2 + Choice_5_8_2
 + Choice_6_8_2 + Choice_7_8_2 + Choice_8_8_2 + Choice_9_8_2 = 1

_C66: Choice_1_8_3 + Choice_2_8_3 + Choice_3_8_3 + Choice_4_8_3 + Choice_5_8_3
 + Choice_6_8_3 + Choice_7_8_3 + Choice_8_8_3 + Choice_9_8_3 = 1

_C67: Choice_1_8_4 + Choice_2_8_4 + Choice_3_8_4 + Choice_4_8_4 + Choice_5_8_4
 + Choice_6_8_4 + Choice_7_8_4 + Choice_8_8_4 + Choice_9_8_4 = 1

_C68: Choice_1_8_5 + Choice_2_8_5 + Choice_3_8_5 + Choice_4_8_5 + Choice_5_8_5
 + Choice_6_8_5 + Choice_7_8_5 + Choice_8_8_5 + Choice_9_8_5 = 1

_C69: Choice_1_8_6 + Choice_2_8_6 + Choice_3_8_6 + Choice_4_8_6 + Choice_5_8_6
 + Choice_6_8_6 + Choice_7_8_6 + Choice_8_8_6 + Choice_9_8_6 = 1

_C70: Choice_1_8_7 + Choice_2_8_7 + Choice_3_8_7 + Choice_4_8_7 + Choice_5_8_7
 + Choice_6_8_7 + Choice_7_8_7 + Choice_8_8_7 + Choice_9_8_7 = 1

_C71: Choice_1_8_8 + Choice_2_8_8 + Choice_3_8_8 + Choice_4_8_8 + Choice_5_8_8
 + Choice_6_8_8 + Choice_7_8_8 + Choice_8_8_8 + Choice_9_8_8 = 1

_C72: Choice_1_8_9 + Choice_2_8_9 + Choice_3_8_9 + Choice_4_8_9 + Choice_5_8_9
 + Choice_6_8_9 + Choice_7_8_9 + Choice_8_8_9 + Choice_9_8_9 = 1

_C73: Choice_1_9_1 + Choice_2_9_1 + Choice_3_9_1 + Choice_4_9_1 + Choice_5_9_1
 + Choice_6_9_1 + Choice_7_9_1 + Choice_8_9_1 + Choice_9_9_1 = 1

_C74: Choice_1_9_2 + Choice_2_9_2 + Choice_3_9_2 + Choice_4_9_2 + Choice_5_9_2
 + Choice_6_9_2 + Choice_7_9_2 + Choice_8_9_2 + Choice_9_9_2 = 1

_C75: Choice_1_9_3 + Choice_2_9_3 + Choice_3_9_3 + Choice_4_9_3 + Choice_5_9_3
 + Choice_6_9_3 + Choice_7_9_3 + Choice_8_9_3 + Choice_9_9_3 = 1

_C76: Choice_1_9_4 + Choice_2_9_4 + Choice_3_9_4 + Choice_4_9_4 + Choice_5_9_4
 + Choice_6_9_4 + Choice_7_9_4 + Choice_8_9_4 + Choice_9_9_4 = 1

_C77: Choice_1_9_5 + Choice_2_9_5 + Choice_3_9_5 + Choice_4_9_5 + Choice_5_9_5
 + Choice_6_9_5 + Choice_7_9_5 + Choice_8_9_5 + Choice_9_9_5 = 1

_C78: Choice_1_9_6 + Choice_2_9_6 + Choice_3_9_6 + Choice_4_9_6 + Choice_5_9_6
 + Choice_6_9_6 + Choice_7_9_6 + Choice_8_9_6 + Choice_9_9_6 = 1

_C79: Choice_1_9_7 + Choice_2_9_7 + Choice_3_9_7 + Choice_4_9_7 + Choice_5_9_7
 + Choice_6_9_7 + Choice_7_9_7 + Choice_8_9_7 + Choice_9_9_7 = 1

_C80: Choice_1_9_8 + Choice_2_9_8 + Choice_3_9_8 + Choice_4_9_8 + Choice_5_9_8
 + Choice_6_9_8 + Choice_7_9_8 + Choice_8_9_8 + Choice_9_9_8 = 1

_C81: Choice_1_9_9 + Choice_2_9_9 + Choice_3_9_9 + Choice_4_9_9 + Choice_5_9_9
 + Choice_6_9_9 + Choice_7_9_9 + Choice_8_9_9 + Choice_9_9_9 = 1

_C82: Choice_1_1_1 + Choice_1_1_2 + Choice_1_1_3 + Choice_1_1_4 + Choice_1_1_5
 + Choice_1_1_6 + Choice_1_1_7 + Choice_1_1_8 + Choice_1_1_9 = 1

_C83: Choice_1_2_1 + Choice_1_2_2 + Choice_1_2_3 + Choice_1_2_4 + Choice_1_2_5
 + Choice_1_2_6 + Choice_1_2_7 + Choice_1_2_8 + Choice_1_2_9 = 1

_C84: Choice_1_3_1 + Choice_1_3_2 + Choice_1_3_3 + Choice_1_3_4 + Choice_1_3_5
 + Choice_1_3_6 + Choice_1_3_7 + Choice_1_3_8 + Choice_1_3_9 = 1

_C85: Choice_1_4_1 + Choice_1_4_2 + Choice_1_4_3 + Choice_1_4_4 + Choice_1_4_5
 + Choice_1_4_6 + Choice_1_4_7 + Choice_1_4_8 + Choice_1_4_9 = 1

_C86: Choice_1_5_1 + Choice_1_5_2 + Choice_1_5_3 + Choice_1_5_4 + Choice_1_5_5
 + Choice_1_5_6 + Choice_1_5_7 + Choice_1_5_8 + Choice_1_5_9 = 1

_C87: Choice_1_6_1 + Choice_1_6_2 + Choice_1_6_3 + Choice_1_6_4 + Choice_1_6_5
 + Choice_1_6_6 + Choice_1_6_7 + Choice_1_6_8 + Choice_1_6_9 = 1

_C88: Choice_1_7_1 + Choice_1_7_2 + Choice_1_7_3 + Choice_1_7_4 + Choice_1_7_5
 + Choice_1_7_6 + Choice_1_7_7 + Choice_1_7_8 + Choice_1_7_9 = 1

_C89: Choice_1_8_1 + Choice_1_8_2 + Choice_1_8_3 + Choice_1_8_4 + Choice_1_8_5
 + Choice_1_8_6 + Choice_1_8_7 + Choice_1_8_8 + Choice_1_8_9 = 1

_C90: Choice_1_9_1 + Choice_1_9_2 + Choice_1_9_3 + Choice_1_9_4 + Choice_1_9_5
 + Choice_1_9_6 + Choice_1_9_7 + Choice_1_9_8 + Choice_1_9_9 = 1

_C91: Choice_1_1_1 + Choice_1_2_1 + Choice_1_3_1 + Choice_1_4_1 + Choice_1_5_1
 + Choice_1_6_1 + Choice_1_7_1 + Choice_1_8_1 + Choice_1_9_1 = 1

_C92: Choice_1_1_2 + Choice_1_2_2 + Choice_1_3_2 + Choice_1_4_2 + Choice_1_5_2
 + Choice_1_6_2 + Choice_1_7_2 + Choice_1_8_2 + Choice_1_9_2 = 1

_C93: Choice_1_1_3 + Choice_1_2_3 + Choice_1_3_3 + Choice_1_4_3 + Choice_1_5_3
 + Choice_1_6_3 + Choice_1_7_3 + Choice_1_8_3 + Choice_1_9_3 = 1

_C94: Choice_1_1_4 + Choice_1_2_4 + Choice_1_3_4 + Choice_1_4_4 + Choice_1_5_4
 + Choice_1_6_4 + Choice_1_7_4 + Choice_1_8_4 + Choice_1_9_4 = 1

_C95: Choice_1_1_5 + Choice_1_2_5 + Choice_1_3_5 + Choice_1_4_5 + Choice_1_5_5
 + Choice_1_6_5 + Choice_1_7_5 + Choice_1_8_5 + Choice_1_9_5 = 1

_C96: Choice_1_1_6 + Choice_1_2_6 + Choice_1_3_6 + Choice_1_4_6 + Choice_1_5_6
 + Choice_1_6_6 + Choice_1_7_6 + Choice_1_8_6 + Choice_1_9_6 = 1

_C97: Choice_1_1_7 + Choice_1_2_7 + Choice_1_3_7 + Choice_1_4_7 + Choice_1_5_7
 + Choice_1_6_7 + Choice_1_7_7 + Choice_1_8_7 + Choice_1_9_7 = 1

_C98: Choice_1_1_8 + Choice_1_2_8 + Choice_1_3_8 + Choice_1_4_8 + Choice_1_5_8
 + Choice_1_6_8 + Choice_1_7_8 + Choice_1_8_8 + Choice_1_9_8 = 1

_C99: Choice_1_1_9 + Choice_1_2_9 + Choice_1_3_9 + Choice_1_4_9 + Choice_1_5_9
 + Choice_1_6_9 + Choice_1_7_9 + Choice_1_8_9 + Choice_1_9_9 = 1

_C100: Choice_1_1_1 + Choice_1_1_2 + Choice_1_1_3 + Choice_1_2_1
 + Choice_1_2_2 + Choice_1_2_3 + Choice_1_3_1 + Choice_1_3_2 + Choice_1_3_3
 = 1

_C101: Choice_1_1_4 + Choice_1_1_5 + Choice_1_1_6 + Choice_1_2_4
 + Choice_1_2_5 + Choice_1_2_6 + Choice_1_3_4 + Choice_1_3_5 + Choice_1_3_6
 = 1

_C102: Choice_1_1_7 + Choice_1_1_8 + Choice_1_1_9 + Choice_1_2_7
 + Choice_1_2_8 + Choice_1_2_9 + Choice_1_3_7 + Choice_1_3_8 + Choice_1_3_9
 = 1

_C103: Choice_1_4_1 + Choice_1_4_2 + Choice_1_4_3 + Choice_1_5_1
 + Choice_1_5_2 + Choice_1_5_3 + Choice_1_6_1 + Choice_1_6_2 + Choice_1_6_3
 = 1

_C104: Choice_1_4_4 + Choice_1_4_5 + Choice_1_4_6 + Choice_1_5_4
 + Choice_1_5_5 + Choice_1_5_6 + Choice_1_6_4 + Choice_1_6_5 + Choice_1_6_6
 = 1

_C105: Choice_1_4_7 + Choice_1_4_8 + Choice_1_4_9 + Choice_1_5_7
 + Choice_1_5_8 + Choice_1_5_9 + Choice_1_6_7 + Choice_1_6_8 + Choice_1_6_9
 = 1

_C106: Choice_1_7_1 + Choice_1_7_2 + Choice_1_7_3 + Choice_1_8_1
 + Choice_1_8_2 + Choice_1_8_3 + Choice_1_9_1 + Choice_1_9_2 + Choice_1_9_3
 = 1

_C107: Choice_1_7_4 + Choice_1_7_5 + Choice_1_7_6 + Choice_1_8_4
 + Choice_1_8_5 + Choice_1_8_6 + Choice_1_9_4 + Choice_1_9_5 + Choice_1_9_6
 = 1

_C108: Choice_1_7_7 + Choice_1_7_8 + Choice_1_7_9 + Choice_1_8_7
 + Choice_1_8_8 + Choice_1_8_9 + Choice_1_9_7 + Choice_1_9_8 + Choice_1_9_9
 = 1

_C109: Choice_2_1_1 + Choice_2_1_2 + Choice_2_1_3 + Choice_2_1_4
 + Choice_2_1_5 + Choice_2_1_6 + Choice_2_1_7 + Choice_2_1_8 + Choice_2_1_9
 = 1

_C110: Choice_2_2_1 + Choice_2_2_2 + Choice_2_2_3 + Choice_2_2_4
 + Choice_2_2_5 + Choice_2_2_6 + Choice_2_2_7 + Choice_2_2_8 + Choice_2_2_9
 = 1

_C111: Choice_2_3_1 + Choice_2_3_2 + Choice_2_3_3 + Choice_2_3_4
 + Choice_2_3_5 + Choice_2_3_6 + Choice_2_3_7 + Choice_2_3_8 + Choice_2_3_9
 = 1

_C112: Choice_2_4_1 + Choice_2_4_2 + Choice_2_4_3 + Choice_2_4_4
 + Choice_2_4_5 + Choice_2_4_6 + Choice_2_4_7 + Choice_2_4_8 + Choice_2_4_9
 = 1

_C113: Choice_2_5_1 + Choice_2_5_2 + Choice_2_5_3 + Choice_2_5_4
 + Choice_2_5_5 + Choice_2_5_6 + Choice_2_5_7 + Choice_2_5_8 + Choice_2_5_9
 = 1

_C114: Choice_2_6_1 + Choice_2_6_2 + Choice_2_6_3 + Choice_2_6_4
 + Choice_2_6_5 + Choice_2_6_6 + Choice_2_6_7 + Choice_2_6_8 + Choice_2_6_9
 = 1

_C115: Choice_2_7_1 + Choice_2_7_2 + Choice_2_7_3 + Choice_2_7_4
 + Choice_2_7_5 + Choice_2_7_6 + Choice_2_7_7 + Choice_2_7_8 + Choice_2_7_9
 = 1

_C116: Choice_2_8_1 + Choice_2_8_2 + Choice_2_8_3 + Choice_2_8_4
 + Choice_2_8_5 + Choice_2_8_6 + Choice_2_8_7 + Choice_2_8_8 + Choice_2_8_9
 = 1

_C117: Choice_2_9_1 + Choice_2_9_2 + Choice_2_9_3 + Choice_2_9_4
 + Choice_2_9_5 + Choice_2_9_6 + Choice_2_9_7 + Choice_2_9_8 + Choice_2_9_9
 = 1

_C118: Choice_2_1_1 + Choice_2_2_1 + Choice_2_3_1 + Choice_2_4_1
 + Choice_2_5_1 + Choice_2_6_1 + Choice_2_7_1 + Choice_2_8_1 + Choice_2_9_1
 = 1

_C119: Choice_2_1_2 + Choice_2_2_2 + Choice_2_3_2 + Choice_2_4_2
 + Choice_2_5_2 + Choice_2_6_2 + Choice_2_7_2 + Choice_2_8_2 + Choice_2_9_2
 = 1

_C120: Choice_2_1_3 + Choice_2_2_3 + Choice_2_3_3 + Choice_2_4_3
 + Choice_2_5_3 + Choice_2_6_3 + Choice_2_7_3 + Choice_2_8_3 + Choice_2_9_3
 = 1

_C121: Choice_2_1_4 + Choice_2_2_4 + Choice_2_3_4 + Choice_2_4_4
 + Choice_2_5_4 + Choice_2_6_4 + Choice_2_7_4 + Choice_2_8_4 + Choice_2_9_4
 = 1

_C122: Choice_2_1_5 + Choice_2_2_5 + Choice_2_3_5 + Choice_2_4_5
 + Choice_2_5_5 + Choice_2_6_5 + Choice_2_7_5 + Choice_2_8_5 + Choice_2_9_5
 = 1

_C123: Choice_2_1_6 + Choice_2_2_6 + Choice_2_3_6 + Choice_2_4_6
 + Choice_2_5_6 + Choice_2_6_6 + Choice_2_7_6 + Choice_2_8_6 + Choice_2_9_6
 = 1

_C124: Choice_2_1_7 + Choice_2_2_7 + Choice_2_3_7 + Choice_2_4_7
 + Choice_2_5_7 + Choice_2_6_7 + Choice_2_7_7 + Choice_2_8_7 + Choice_2_9_7
 = 1

_C125: Choice_2_1_8 + Choice_2_2_8 + Choice_2_3_8 + Choice_2_4_8
 + Choice_2_5_8 + Choice_2_6_8 + Choice_2_7_8 + Choice_2_8_8 + Choice_2_9_8
 = 1

_C126: Choice_2_1_9 + Choice_2_2_9 + Choice_2_3_9 + Choice_2_4_9
 + Choice_2_5_9 + Choice_2_6_9 + Choice_2_7_9 + Choice_2_8_9 + Choice_2_9_9
 = 1

_C127: Choice_2_1_1 + Choice_2_1_2 + Choice_2_1_3 + Choice_2_2_1
 + Choice_2_2_2 + Choice_2_2_3 + Choice_2_3_1 + Choice_2_3_2 + Choice_2_3_3
 = 1

_C128: Choice_2_1_4 + Choice_2_1_5 + Choice_2_1_6 + Choice_2_2_4
 + Choice_2_2_5 + Choice_2_2_6 + Choice_2_3_4 + Choice_2_3_5 + Choice_2_3_6
 = 1

_C129: Choice_2_1_7 + Choice_2_1_8 + Choice_2_1_9 + Choice_2_2_7
 + Choice_2_2_8 + Choice_2_2_9 + Choice_2_3_7 + Choice_2_3_8 + Choice_2_3_9
 = 1

_C130: Choice_2_4_1 + Choice_2_4_2 + Choice_2_4_3 + Choice_2_5_1
 + Choice_2_5_2 + Choice_2_5_3 + Choice_2_6_1 + Choice_2_6_2 + Choice_2_6_3
 = 1

_C131: Choice_2_4_4 + Choice_2_4_5 + Choice_2_4_6 + Choice_2_5_4
 + Choice_2_5_5 + Choice_2_5_6 + Choice_2_6_4 + Choice_2_6_5 + Choice_2_6_6
 = 1

_C132: Choice_2_4_7 + Choice_2_4_8 + Choice_2_4_9 + Choice_2_5_7
 + Choice_2_5_8 + Choice_2_5_9 + Choice_2_6_7 + Choice_2_6_8 + Choice_2_6_9
 = 1

_C133: Choice_2_7_1 + Choice_2_7_2 + Choice_2_7_3 + Choice_2_8_1
 + Choice_2_8_2 + Choice_2_8_3 + Choice_2_9_1 + Choice_2_9_2 + Choice_2_9_3
 = 1

_C134: Choice_2_7_4 + Choice_2_7_5 + Choice_2_7_6 + Choice_2_8_4
 + Choice_2_8_5 + Choice_2_8_6 + Choice_2_9_4 + Choice_2_9_5 + Choice_2_9_6
 = 1

_C135: Choice_2_7_7 + Choice_2_7_8 + Choice_2_7_9 + Choice_2_8_7
 + Choice_2_8_8 + Choice_2_8_9 + Choice_2_9_7 + Choice_2_9_8 + Choice_2_9_9
 = 1

_C136: Choice_3_1_1 + Choice_3_1_2 + Choice_3_1_3 + Choice_3_1_4
 + Choice_3_1_5 + Choice_3_1_6 + Choice_3_1_7 + Choice_3_1_8 + Choice_3_1_9
 = 1

_C137: Choice_3_2_1 + Choice_3_2_2 + Choice_3_2_3 + Choice_3_2_4
 + Choice_3_2_5 + Choice_3_2_6 + Choice_3_2_7 + Choice_3_2_8 + Choice_3_2_9
 = 1

_C138: Choice_3_3_1 + Choice_3_3_2 + Choice_3_3_3 + Choice_3_3_4
 + Choice_3_3_5 + Choice_3_3_6 + Choice_3_3_7 + Choice_3_3_8 + Choice_3_3_9
 = 1

_C139: Choice_3_4_1 + Choice_3_4_2 + Choice_3_4_3 + Choice_3_4_4
 + Choice_3_4_5 + Choice_3_4_6 + Choice_3_4_7 + Choice_3_4_8 + Choice_3_4_9
 = 1

_C140: Choice_3_5_1 + Choice_3_5_2 + Choice_3_5_3 + Choice_3_5_4
 + Choice_3_5_5 + Choice_3_5_6 + Choice_3_5_7 + Choice_3_5_8 + Choice_3_5_9
 = 1

_C141: Choice_3_6_1 + Choice_3_6_2 + Choice_3_6_3 + Choice_3_6_4
 + Choice_3_6_5 + Choice_3_6_6 + Choice_3_6_7 + Choice_3_6_8 + Choice_3_6_9
 = 1

_C142: Choice_3_7_1 + Choice_3_7_2 + Choice_3_7_3 + Choice_3_7_4
 + Choice_3_7_5 + Choice_3_7_6 + Choice_3_7_7 + Choice_3_7_8 + Choice_3_7_9
 = 1

_C143: Choice_3_8_1 + Choice_3_8_2 + Choice_3_8_3 + Choice_3_8_4
 + Choice_3_8_5 + Choice_3_8_6 + Choice_3_8_7 + Choice_3_8_8 + Choice_3_8_9
 = 1

_C144: Choice_3_9_1 + Choice_3_9_2 + Choice_3_9_3 + Choice_3_9_4
 + Choice_3_9_5 + Choice_3_9_6 + Choice_3_9_7 + Choice_3_9_8 + Choice_3_9_9
 = 1

_C145: Choice_3_1_1 + Choice_3_2_1 + Choice_3_3_1 + Choice_3_4_1
 + Choice_3_5_1 + Choice_3_6_1 + Choice_3_7_1 + Choice_3_8_1 + Choice_3_9_1
 = 1

_C146: Choice_3_1_2 + Choice_3_2_2 + Choice_3_3_2 + Choice_3_4_2
 + Choice_3_5_2 + Choice_3_6_2 + Choice_3_7_2 + Choice_3_8_2 + Choice_3_9_2
 = 1

_C147: Choice_3_1_3 + Choice_3_2_3 + Choice_3_3_3 + Choice_3_4_3
 + Choice_3_5_3 + Choice_3_6_3 + Choice_3_7_3 + Choice_3_8_3 + Choice_3_9_3
 = 1

_C148: Choice_3_1_4 + Choice_3_2_4 + Choice_3_3_4 + Choice_3_4_4
 + Choice_3_5_4 + Choice_3_6_4 + Choice_3_7_4 + Choice_3_8_4 + Choice_3_9_4
 = 1

_C149: Choice_3_1_5 + Choice_3_2_5 + Choice_3_3_5 + Choice_3_4_5
 + Choice_3_5_5 + Choice_3_6_5 + Choice_3_7_5 + Choice_3_8_5 + Choice_3_9_5
 = 1

_C150: Choice_3_1_6 + Choice_3_2_6 + Choice_3_3_6 + Choice_3_4_6
 + Choice_3_5_6 + Choice_3_6_6 + Choice_3_7_6 + Choice_3_8_6 + Choice_3_9_6
 = 1

_C151: Choice_3_1_7 + Choice_3_2_7 + Choice_3_3_7 + Choice_3_4_7
 + Choice_3_5_7 + Choice_3_6_7 + Choice_3_7_7 + Choice_3_8_7 + Choice_3_9_7
 = 1

_C152: Choice_3_1_8 + Choice_3_2_8 + Choice_3_3_8 + Choice_3_4_8
 + Choice_3_5_8 + Choice_3_6_8 + Choice_3_7_8 + Choice_3_8_8 + Choice_3_9_8
 = 1

_C153: Choice_3_1_9 + Choice_3_2_9 + Choice_3_3_9 + Choice_3_4_9
 + Choice_3_5_9 + Choice_3_6_9 + Choice_3_7_9 + Choice_3_8_9 + Choice_3_9_9
 = 1

_C154: Choice_3_1_1 + Choice_3_1_2 + Choice_3_1_3 + Choice_3_2_1
 + Choice_3_2_2 + Choice_3_2_3 + Choice_3_3_1 + Choice_3_3_2 + Choice_3_3_3
 = 1

_C155: Choice_3_1_4 + Choice_3_1_5 + Choice_3_1_6 + Choice_3_2_4
 + Choice_3_2_5 + Choice_3_2_6 + Choice_3_3_4 + Choice_3_3_5 + Choice_3_3_6
 = 1

_C156: Choice_3_1_7 + Choice_3_1_8 + Choice_3_1_9 + Choice_3_2_7
 + Choice_3_2_8 + Choice_3_2_9 + Choice_3_3_7 + Choice_3_3_8 + Choice_3_3_9
 = 1

_C157: Choice_3_4_1 + Choice_3_4_2 + Choice_3_4_3 + Choice_3_5_1
 + Choice_3_5_2 + Choice_3_5_3 + Choice_3_6_1 + Choice_3_6_2 + Choice_3_6_3
 = 1

_C158: Choice_3_4_4 + Choice_3_4_5 + Choice_3_4_6 + Choice_3_5_4
 + Choice_3_5_5 + Choice_3_5_6 + Choice_3_6_4 + Choice_3_6_5 + Choice_3_6_6
 = 1

_C159: Choice_3_4_7 + Choice_3_4_8 + Choice_3_4_9 + Choice_3_5_7
 + Choice_3_5_8 + Choice_3_5_9 + Choice_3_6_7 + Choice_3_6_8 + Choice_3_6_9
 = 1

_C160: Choice_3_7_1 + Choice_3_7_2 + Choice_3_7_3 + Choice_3_8_1
 + Choice_3_8_2 + Choice_3_8_3 + Choice_3_9_1 + Choice_3_9_2 + Choice_3_9_3
 = 1

_C161: Choice_3_7_4 + Choice_3_7_5 + Choice_3_7_6 + Choice_3_8_4
 + Choice_3_8_5 + Choice_3_8_6 + Choice_3_9_4 + Choice_3_9_5 + Choice_3_9_6
 = 1

_C162: Choice_3_7_7 + Choice_3_7_8 + Choice_3_7_9 + Choice_3_8_7
 + Choice_3_8_8 + Choice_3_8_9 + Choice_3_9_7 + Choice_3_9_8 + Choice_3_9_9
 = 1

_C163: Choice_4_1_1 + Choice_4_1_2 + Choice_4_1_3 + Choice_4_1_4
 + Choice_4_1_5 + Choice_4_1_6 + Choice_4_1_7 + Choice_4_1_8 + Choice_4_1_9
 = 1

_C164: Choice_4_2_1 + Choice_4_2_2 + Choice_4_2_3 + Choice_4_2_4
 + Choice_4_2_5 + Choice_4_2_6 + Choice_4_2_7 + Choice_4_2_8 + Choice_4_2_9
 = 1

_C165: Choice_4_3_1 + Choice_4_3_2 + Choice_4_3_3 + Choice_4_3_4
 + Choice_4_3_5 + Choice_4_3_6 + Choice_4_3_7 + Choice_4_3_8 + Choice_4_3_9
 = 1

_C166: Choice_4_4_1 + Choice_4_4_2 + Choice_4_4_3 + Choice_4_4_4
 + Choice_4_4_5 + Choice_4_4_6 + Choice_4_4_7 + Choice_4_4_8 + Choice_4_4_9
 = 1

_C167: Choice_4_5_1 + Choice_4_5_2 + Choice_4_5_3 + Choice_4_5_4
 + Choice_4_5_5 + Choice_4_5_6 + Choice_4_5_7 + Choice_4_5_8 + Choice_4_5_9
 = 1

_C168: Choice_4_6_1 + Choice_4_6_2 + Choice_4_6_3 + Choice_4_6_4
 + Choice_4_6_5 + Choice_4_6_6 + Choice_4_6_7 + Choice_4_6_8 + Choice_4_6_9
 = 1

_C169: Choice_4_7_1 + Choice_4_7_2 + Choice_4_7_3 + Choice_4_7_4
 + Choice_4_7_5 + Choice_4_7_6 + Choice_4_7_7 + Choice_4_7_8 + Choice_4_7_9
 = 1

_C170: Choice_4_8_1 + Choice_4_8_2 + Choice_4_8_3 + Choice_4_8_4
 + Choice_4_8_5 + Choice_4_8_6 + Choice_4_8_7 + Choice_4_8_8 + Choice_4_8_9
 = 1

_C171: Choice_4_9_1 + Choice_4_9_2 + Choice_4_9_3 + Choice_4_9_4
 + Choice_4_9_5 + Choice_4_9_6 + Choice_4_9_7 + Choice_4_9_8 + Choice_4_9_9
 = 1

_C172: Choice_4_1_1 + Choice_4_2_1 + Choice_4_3_1 + Choice_4_4_1
 + Choice_4_5_1 + Choice_4_6_1 + Choice_4_7_1 + Choice_4_8_1 + Choice_4_9_1
 = 1

_C173: Choice_4_1_2 + Choice_4_2_2 + Choice_4_3_2 + Choice_4_4_2
 + Choice_4_5_2 + Choice_4_6_2 + Choice_4_7_2 + Choice_4_8_2 + Choice_4_9_2
 = 1

_C174: Choice_4_1_3 + Choice_4_2_3 + Choice_4_3_3 + Choice_4_4_3
 + Choice_4_5_3 + Choice_4_6_3 + Choice_4_7_3 + Choice_4_8_3 + Choice_4_9_3
 = 1

_C175: Choice_4_1_4 + Choice_4_2_4 + Choice_4_3_4 + Choice_4_4_4
 + Choice_4_5_4 + Choice_4_6_4 + Choice_4_7_4 + Choice_4_8_4 + Choice_4_9_4
 = 1

_C176: Choice_4_1_5 + Choice_4_2_5 + Choice_4_3_5 + Choice_4_4_5
 + Choice_4_5_5 + Choice_4_6_5 + Choice_4_7_5 + Choice_4_8_5 + Choice_4_9_5
 = 1

_C177: Choice_4_1_6 + Choice_4_2_6 + Choice_4_3_6 + Choice_4_4_6
 + Choice_4_5_6 + Choice_4_6_6 + Choice_4_7_6 + Choice_4_8_6 + Choice_4_9_6
 = 1

_C178: Choice_4_1_7 + Choice_4_2_7 + Choice_4_3_7 + Choice_4_4_7
 + Choice_4_5_7 + Choice_4_6_7 + Choice_4_7_7 + Choice_4_8_7 + Choice_4_9_7
 = 1

_C179: Choice_4_1_8 + Choice_4_2_8 + Choice_4_3_8 + Choice_4_4_8
 + Choice_4_5_8 + Choice_4_6_8 + Choice_4_7_8 + Choice_4_8_8 + Choice_4_9_8
 = 1

_C180: Choice_4_1_9 + Choice_4_2_9 + Choice_4_3_9 + Choice_4_4_9
 + Choice_4_5_9 + Choice_4_6_9 + Choice_4_7_9 + Choice_4_8_9 + Choice_4_9_9
 = 1

_C181: Choice_4_1_1 + Choice_4_1_2 + Choice_4_1_3 + Choice_4_2_1
 + Choice_4_2_2 + Choice_4_2_3 + Choice_4_3_1 + Choice_4_3_2 + Choice_4_3_3
 = 1

_C182: Choice_4_1_4 + Choice_4_1_5 + Choice_4_1_6 + Choice_4_2_4
 + Choice_4_2_5 + Choice_4_2_6 + Choice_4_3_4 + Choice_4_3_5 + Choice_4_3_6
 = 1

_C183: Choice_4_1_7 + Choice_4_1_8 + Choice_4_1_9 + Choice_4_2_7
 + Choice_4_2_8 + Choice_4_2_9 + Choice_4_3_7 + Choice_4_3_8 + Choice_4_3_9
 = 1

_C184: Choice_4_4_1 + Choice_4_4_2 + Choice_4_4_3 + Choice_4_5_1
 + Choice_4_5_2 + Choice_4_5_3 + Choice_4_6_1 + Choice_4_6_2 + Choice_4_6_3
 = 1

_C185: Choice_4_4_4 + Choice_4_4_5 + Choice_4_4_6 + Choice_4_5_4
 + Choice_4_5_5 + Choice_4_5_6 + Choice_4_6_4 + Choice_4_6_5 + Choice_4_6_6
 = 1

_C186: Choice_4_4_7 + Choice_4_4_8 + Choice_4_4_9 + Choice_4_5_7
 + Choice_4_5_8 + Choice_4_5_9 + Choice_4_6_7 + Choice_4_6_8 + Choice_4_6_9
 = 1

_C187: Choice_4_7_1 + Choice_4_7_2 + Choice_4_7_3 + Choice_4_8_1
 + Choice_4_8_2 + Choice_4_8_3 + Choice_4_9_1 + Choice_4_9_2 + Choice_4_9_3
 = 1

_C188: Choice_4_7_4 + Choice_4_7_5 + Choice_4_7_6 + Choice_4_8_4
 + Choice_4_8_5 + Choice_4_8_6 + Choice_4_9_4 + Choice_4_9_5 + Choice_4_9_6
 = 1

_C189: Choice_4_7_7 + Choice_4_7_8 + Choice_4_7_9 + Choice_4_8_7
 + Choice_4_8_8 + Choice_4_8_9 + Choice_4_9_7 + Choice_4_9_8 + Choice_4_9_9
 = 1

_C190: Choice_5_1_1 + Choice_5_1_2 + Choice_5_1_3 + Choice_5_1_4
 + Choice_5_1_5 + Choice_5_1_6 + Choice_5_1_7 + Choice_5_1_8 + Choice_5_1_9
 = 1

_C191: Choice_5_2_1 + Choice_5_2_2 + Choice_5_2_3 + Choice_5_2_4
 + Choice_5_2_5 + Choice_5_2_6 + Choice_5_2_7 + Choice_5_2_8 + Choice_5_2_9
 = 1

_C192: Choice_5_3_1 + Choice_5_3_2 + Choice_5_3_3 + Choice_5_3_4
 + Choice_5_3_5 + Choice_5_3_6 + Choice_5_3_7 + Choice_5_3_8 + Choice_5_3_9
 = 1

_C193: Choice_5_4_1 + Choice_5_4_2 + Choice_5_4_3 + Choice_5_4_4
 + Choice_5_4_5 + Choice_5_4_6 + Choice_5_4_7 + Choice_5_4_8 + Choice_5_4_9
 = 1

_C194: Choice_5_5_1 + Choice_5_5_2 + Choice_5_5_3 + Choice_5_5_4
 + Choice_5_5_5 + Choice_5_5_6 + Choice_5_5_7 + Choice_5_5_8 + Choice_5_5_9
 = 1

_C195: Choice_5_6_1 + Choice_5_6_2 + Choice_5_6_3 + Choice_5_6_4
 + Choice_5_6_5 + Choice_5_6_6 + Choice_5_6_7 + Choice_5_6_8 + Choice_5_6_9
 = 1

_C196: Choice_5_7_1 + Choice_5_7_2 + Choice_5_7_3 + Choice_5_7_4
 + Choice_5_7_5 + Choice_5_7_6 + Choice_5_7_7 + Choice_5_7_8 + Choice_5_7_9
 = 1

_C197: Choice_5_8_1 + Choice_5_8_2 + Choice_5_8_3 + Choice_5_8_4
 + Choice_5_8_5 + Choice_5_8_6 + Choice_5_8_7 + Choice_5_8_8 + Choice_5_8_9
 = 1

_C198: Choice_5_9_1 + Choice_5_9_2 + Choice_5_9_3 + Choice_5_9_4
 + Choice_5_9_5 + Choice_5_9_6 + Choice_5_9_7 + Choice_5_9_8 + Choice_5_9_9
 = 1

_C199: Choice_5_1_1 + Choice_5_2_1 + Choice_5_3_1 + Choice_5_4_1
 + Choice_5_5_1 + Choice_5_6_1 + Choice_5_7_1 + Choice_5_8_1 + Choice_5_9_1
 = 1

_C200: Choice_5_1_2 + Choice_5_2_2 + Choice_5_3_2 + Choice_5_4_2
 + Choice_5_5_2 + Choice_5_6_2 + Choice_5_7_2 + Choice_5_8_2 + Choice_5_9_2
 = 1

_C201: Choice_5_1_3 + Choice_5_2_3 + Choice_5_3_3 + Choice_5_4_3
 + Choice_5_5_3 + Choice_5_6_3 + Choice_5_7_3 + Choice_5_8_3 + Choice_5_9_3
 = 1

_C202: Choice_5_1_4 + Choice_5_2_4 + Choice_5_3_4 + Choice_5_4_4
 + Choice_5_5_4 + Choice_5_6_4 + Choice_5_7_4 + Choice_5_8_4 + Choice_5_9_4
 = 1

_C203: Choice_5_1_5 + Choice_5_2_5 + Choice_5_3_5 + Choice_5_4_5
 + Choice_5_5_5 + Choice_5_6_5 + Choice_5_7_5 + Choice_5_8_5 + Choice_5_9_5
 = 1

_C204: Choice_5_1_6 + Choice_5_2_6 + Choice_5_3_6 + Choice_5_4_6
 + Choice_5_5_6 + Choice_5_6_6 + Choice_5_7_6 + Choice_5_8_6 + Choice_5_9_6
 = 1

_C205: Choice_5_1_7 + Choice_5_2_7 + Choice_5_3_7 + Choice_5_4_7
 + Choice_5_5_7 + Choice_5_6_7 + Choice_5_7_7 + Choice_5_8_7 + Choice_5_9_7
 = 1

_C206: Choice_5_1_8 + Choice_5_2_8 + Choice_5_3_8 + Choice_5_4_8
 + Choice_5_5_8 + Choice_5_6_8 + Choice_5_7_8 + Choice_5_8_8 + Choice_5_9_8
 = 1

_C207: Choice_5_1_9 + Choice_5_2_9 + Choice_5_3_9 + Choice_5_4_9
 + Choice_5_5_9 + Choice_5_6_9 + Choice_5_7_9 + Choice_5_8_9 + Choice_5_9_9
 = 1

_C208: Choice_5_1_1 + Choice_5_1_2 + Choice_5_1_3 + Choice_5_2_1
 + Choice_5_2_2 + Choice_5_2_3 + Choice_5_3_1 + Choice_5_3_2 + Choice_5_3_3
 = 1

_C209: Choice_5_1_4 + Choice_5_1_5 + Choice_5_1_6 + Choice_5_2_4
 + Choice_5_2_5 + Choice_5_2_6 + Choice_5_3_4 + Choice_5_3_5 + Choice_5_3_6
 = 1

_C210: Choice_5_1_7 + Choice_5_1_8 + Choice_5_1_9 + Choice_5_2_7
 + Choice_5_2_8 + Choice_5_2_9 + Choice_5_3_7 + Choice_5_3_8 + Choice_5_3_9
 = 1

_C211: Choice_5_4_1 + Choice_5_4_2 + Choice_5_4_3 + Choice_5_5_1
 + Choice_5_5_2 + Choice_5_5_3 + Choice_5_6_1 + Choice_5_6_2 + Choice_5_6_3
 = 1

_C212: Choice_5_4_4 + Choice_5_4_5 + Choice_5_4_6 + Choice_5_5_4
 + Choice_5_5_5 + Choice_5_5_6 + Choice_5_6_4 + Choice_5_6_5 + Choice_5_6_6
 = 1

_C213: Choice_5_4_7 + Choice_5_4_8 + Choice_5_4_9 + Choice_5_5_7
 + Choice_5_5_8 + Choice_5_5_9 + Choice_5_6_7 + Choice_5_6_8 + Choice_5_6_9
 = 1

_C214: Choice_5_7_1 + Choice_5_7_2 + Choice_5_7_3 + Choice_5_8_1
 + Choice_5_8_2 + Choice_5_8_3 + Choice_5_9_1 + Choice_5_9_2 + Choice_5_9_3
 = 1

_C215: Choice_5_7_4 + Choice_5_7_5 + Choice_5_7_6 + Choice_5_8_4
 + Choice_5_8_5 + Choice_5_8_6 + Choice_5_9_4 + Choice_5_9_5 + Choice_5_9_6
 = 1

_C216: Choice_5_7_7 + Choice_5_7_8 + Choice_5_7_9 + Choice_5_8_7
 + Choice_5_8_8 + Choice_5_8_9 + Choice_5_9_7 + Choice_5_9_8 + Choice_5_9_9
 = 1

_C217: Choice_6_1_1 + Choice_6_1_2 + Choice_6_1_3 + Choice_6_1_4
 + Choice_6_1_5 + Choice_6_1_6 + Choice_6_1_7 + Choice_6_1_8 + Choice_6_1_9
 = 1

_C218: Choice_6_2_1 + Choice_6_2_2 + Choice_6_2_3 + Choice_6_2_4
 + Choice_6_2_5 + Choice_6_2_6 + Choice_6_2_7 + Choice_6_2_8 + Choice_6_2_9
 = 1

_C219: Choice_6_3_1 + Choice_6_3_2 + Choice_6_3_3 + Choice_6_3_4
 + Choice_6_3_5 + Choice_6_3_6 + Choice_6_3_7 + Choice_6_3_8 + Choice_6_3_9
 = 1

_C220: Choice_6_4_1 + Choice_6_4_2 + Choice_6_4_3 + Choice_6_4_4
 + Choice_6_4_5 + Choice_6_4_6 + Choice_6_4_7 + Choice_6_4_8 + Choice_6_4_9
 = 1

_C221: Choice_6_5_1 + Choice_6_5_2 + Choice_6_5_3 + Choice_6_5_4
 + Choice_6_5_5 + Choice_6_5_6 + Choice_6_5_7 + Choice_6_5_8 + Choice_6_5_9
 = 1

_C222: Choice_6_6_1 + Choice_6_6_2 + Choice_6_6_3 + Choice_6_6_4
 + Choice_6_6_5 + Choice_6_6_6 + Choice_6_6_7 + Choice_6_6_8 + Choice_6_6_9
 = 1

_C223: Choice_6_7_1 + Choice_6_7_2 + Choice_6_7_3 + Choice_6_7_4
 + Choice_6_7_5 + Choice_6_7_6 + Choice_6_7_7 + Choice_6_7_8 + Choice_6_7_9
 = 1

_C224: Choice_6_8_1 + Choice_6_8_2 + Choice_6_8_3 + Choice_6_8_4
 + Choice_6_8_5 + Choice_6_8_6 + Choice_6_8_7 + Choice_6_8_8 + Choice_6_8_9
 = 1

_C225: Choice_6_9_1 + Choice_6_9_2 + Choice_6_9_3 + Choice_6_9_4
 + Choice_6_9_5 + Choice_6_9_6 + Choice_6_9_7 + Choice_6_9_8 + Choice_6_9_9
 = 1

_C226: Choice_6_1_1 + Choice_6_2_1 + Choice_6_3_1 + Choice_6_4_1
 + Choice_6_5_1 + Choice_6_6_1 + Choice_6_7_1 + Choice_6_8_1 + Choice_6_9_1
 = 1

_C227: Choice_6_1_2 + Choice_6_2_2 + Choice_6_3_2 + Choice_6_4_2
 + Choice_6_5_2 + Choice_6_6_2 + Choice_6_7_2 + Choice_6_8_2 + Choice_6_9_2
 = 1

_C228: Choice_6_1_3 + Choice_6_2_3 + Choice_6_3_3 + Choice_6_4_3
 + Choice_6_5_3 + Choice_6_6_3 + Choice_6_7_3 + Choice_6_8_3 + Choice_6_9_3
 = 1

_C229: Choice_6_1_4 + Choice_6_2_4 + Choice_6_3_4 + Choice_6_4_4
 + Choice_6_5_4 + Choice_6_6_4 + Choice_6_7_4 + Choice_6_8_4 + Choice_6_9_4
 = 1

_C230: Choice_6_1_5 + Choice_6_2_5 + Choice_6_3_5 + Choice_6_4_5
 + Choice_6_5_5 + Choice_6_6_5 + Choice_6_7_5 + Choice_6_8_5 + Choice_6_9_5
 = 1

_C231: Choice_6_1_6 + Choice_6_2_6 + Choice_6_3_6 + Choice_6_4_6
 + Choice_6_5_6 + Choice_6_6_6 + Choice_6_7_6 + Choice_6_8_6 + Choice_6_9_6
 = 1

_C232: Choice_6_1_7 + Choice_6_2_7 + Choice_6_3_7 + Choice_6_4_7
 + Choice_6_5_7 + Choice_6_6_7 + Choice_6_7_7 + Choice_6_8_7 + Choice_6_9_7
 = 1

_C233: Choice_6_1_8 + Choice_6_2_8 + Choice_6_3_8 + Choice_6_4_8
 + Choice_6_5_8 + Choice_6_6_8 + Choice_6_7_8 + Choice_6_8_8 + Choice_6_9_8
 = 1

_C234: Choice_6_1_9 + Choice_6_2_9 + Choice_6_3_9 + Choice_6_4_9
 + Choice_6_5_9 + Choice_6_6_9 + Choice_6_7_9 + Choice_6_8_9 + Choice_6_9_9
 = 1

_C235: Choice_6_1_1 + Choice_6_1_2 + Choice_6_1_3 + Choice_6_2_1
 + Choice_6_2_2 + Choice_6_2_3 + Choice_6_3_1 + Choice_6_3_2 + Choice_6_3_3
 = 1

_C236: Choice_6_1_4 + Choice_6_1_5 + Choice_6_1_6 + Choice_6_2_4
 + Choice_6_2_5 + Choice_6_2_6 + Choice_6_3_4 + Choice_6_3_5 + Choice_6_3_6
 = 1

_C237: Choice_6_1_7 + Choice_6_1_8 + Choice_6_1_9 + Choice_6_2_7
 + Choice_6_2_8 + Choice_6_2_9 + Choice_6_3_7 + Choice_6_3_8 + Choice_6_3_9
 = 1

_C238: Choice_6_4_1 + Choice_6_4_2 + Choice_6_4_3 + Choice_6_5_1
 + Choice_6_5_2 + Choice_6_5_3 + Choice_6_6_1 + Choice_6_6_2 + Choice_6_6_3
 = 1

_C239: Choice_6_4_4 + Choice_6_4_5 + Choice_6_4_6 + Choice_6_5_4
 + Choice_6_5_5 + Choice_6_5_6 + Choice_6_6_4 + Choice_6_6_5 + Choice_6_6_6
 = 1

_C240: Choice_6_4_7 + Choice_6_4_8 + Choice_6_4_9 + Choice_6_5_7
 + Choice_6_5_8 + Choice_6_5_9 + Choice_6_6_7 + Choice_6_6_8 + Choice_6_6_9
 = 1

_C241: Choice_6_7_1 + Choice_6_7_2 + Choice_6_7_3 + Choice_6_8_1
 + Choice_6_8_2 + Choice_6_8_3 + Choice_6_9_1 + Choice_6_9_2 + Choice_6_9_3
 = 1

_C242: Choice_6_7_4 + Choice_6_7_5 + Choice_6_7_6 + Choice_6_8_4
 + Choice_6_8_5 + Choice_6_8_6 + Choice_6_9_4 + Choice_6_9_5 + Choice_6_9_6
 = 1

_C243: Choice_6_7_7 + Choice_6_7_8 + Choice_6_7_9 + Choice_6_8_7
 + Choice_6_8_8 + Choice_6_8_9 + Choice_6_9_7 + Choice_6_9_8 + Choice_6_9_9
 = 1

_C244: Choice_7_1_1 + Choice_7_1_2 + Choice_7_1_3 + Choice_7_1_4
 + Choice_7_1_5 + Choice_7_1_6 + Choice_7_1_7 + Choice_7_1_8 + Choice_7_1_9
 = 1

_C245: Choice_7_2_1 + Choice_7_2_2 + Choice_7_2_3 + Choice_7_2_4
 + Choice_7_2_5 + Choice_7_2_6 + Choice_7_2_7 + Choice_7_2_8 + Choice_7_2_9
 = 1

_C246: Choice_7_3_1 + Choice_7_3_2 + Choice_7_3_3 + Choice_7_3_4
 + Choice_7_3_5 + Choice_7_3_6 + Choice_7_3_7 + Choice_7_3_8 + Choice_7_3_9
 = 1

_C247: Choice_7_4_1 + Choice_7_4_2 + Choice_7_4_3 + Choice_7_4_4
 + Choice_7_4_5 + Choice_7_4_6 + Choice_7_4_7 + Choice_7_4_8 + Choice_7_4_9
 = 1

_C248: Choice_7_5_1 + Choice_7_5_2 + Choice_7_5_3 + Choice_7_5_4
 + Choice_7_5_5 + Choice_7_5_6 + Choice_7_5_7 + Choice_7_5_8 + Choice_7_5_9
 = 1

_C249: Choice_7_6_1 + Choice_7_6_2 + Choice_7_6_3 + Choice_7_6_4
 + Choice_7_6_5 + Choice_7_6_6 + Choice_7_6_7 + Choice_7_6_8 + Choice_7_6_9
 = 1

_C250: Choice_7_7_1 + Choice_7_7_2 + Choice_7_7_3 + Choice_7_7_4
 + Choice_7_7_5 + Choice_7_7_6 + Choice_7_7_7 + Choice_7_7_8 + Choice_7_7_9
 = 1

_C251: Choice_7_8_1 + Choice_7_8_2 + Choice_7_8_3 + Choice_7_8_4
 + Choice_7_8_5 + Choice_7_8_6 + Choice_7_8_7 + Choice_7_8_8 + Choice_7_8_9
 = 1

_C252: Choice_7_9_1 + Choice_7_9_2 + Choice_7_9_3 + Choice_7_9_4
 + Choice_7_9_5 + Choice_7_9_6 + Choice_7_9_7 + Choice_7_9_8 + Choice_7_9_9
 = 1

_C253: Choice_7_1_1 + Choice_7_2_1 + Choice_7_3_1 + Choice_7_4_1
 + Choice_7_5_1 + Choice_7_6_1 + Choice_7_7_1 + Choice_7_8_1 + Choice_7_9_1
 = 1

_C254: Choice_7_1_2 + Choice_7_2_2 + Choice_7_3_2 + Choice_7_4_2
 + Choice_7_5_2 + Choice_7_6_2 + Choice_7_7_2 + Choice_7_8_2 + Choice_7_9_2
 = 1

_C255: Choice_7_1_3 + Choice_7_2_3 + Choice_7_3_3 + Choice_7_4_3
 + Choice_7_5_3 + Choice_7_6_3 + Choice_7_7_3 + Choice_7_8_3 + Choice_7_9_3
 = 1

_C256: Choice_7_1_4 + Choice_7_2_4 + Choice_7_3_4 + Choice_7_4_4
 + Choice_7_5_4 + Choice_7_6_4 + Choice_7_7_4 + Choice_7_8_4 + Choice_7_9_4
 = 1

_C257: Choice_7_1_5 + Choice_7_2_5 + Choice_7_3_5 + Choice_7_4_5
 + Choice_7_5_5 + Choice_7_6_5 + Choice_7_7_5 + Choice_7_8_5 + Choice_7_9_5
 = 1

_C258: Choice_7_1_6 + Choice_7_2_6 + Choice_7_3_6 + Choice_7_4_6
 + Choice_7_5_6 + Choice_7_6_6 + Choice_7_7_6 + Choice_7_8_6 + Choice_7_9_6
 = 1

_C259: Choice_7_1_7 + Choice_7_2_7 + Choice_7_3_7 + Choice_7_4_7
 + Choice_7_5_7 + Choice_7_6_7 + Choice_7_7_7 + Choice_7_8_7 + Choice_7_9_7
 = 1

_C260: Choice_7_1_8 + Choice_7_2_8 + Choice_7_3_8 + Choice_7_4_8
 + Choice_7_5_8 + Choice_7_6_8 + Choice_7_7_8 + Choice_7_8_8 + Choice_7_9_8
 = 1

_C261: Choice_7_1_9 + Choice_7_2_9 + Choice_7_3_9 + Choice_7_4_9
 + Choice_7_5_9 + Choice_7_6_9 + Choice_7_7_9 + Choice_7_8_9 + Choice_7_9_9
 = 1

_C262: Choice_7_1_1 + Choice_7_1_2 + Choice_7_1_3 + Choice_7_2_1
 + Choice_7_2_2 + Choice_7_2_3 + Choice_7_3_1 + Choice_7_3_2 + Choice_7_3_3
 = 1

_C263: Choice_7_1_4 + Choice_7_1_5 + Choice_7_1_6 + Choice_7_2_4
 + Choice_7_2_5 + Choice_7_2_6 + Choice_7_3_4 + Choice_7_3_5 + Choice_7_3_6
 = 1

_C264: Choice_7_1_7 + Choice_7_1_8 + Choice_7_1_9 + Choice_7_2_7
 + Choice_7_2_8 + Choice_7_2_9 + Choice_7_3_7 + Choice_7_3_8 + Choice_7_3_9
 = 1

_C265: Choice_7_4_1 + Choice_7_4_2 + Choice_7_4_3 + Choice_7_5_1
 + Choice_7_5_2 + Choice_7_5_3 + Choice_7_6_1 + Choice_7_6_2 + Choice_7_6_3
 = 1

_C266: Choice_7_4_4 + Choice_7_4_5 + Choice_7_4_6 + Choice_7_5_4
 + Choice_7_5_5 + Choice_7_5_6 + Choice_7_6_4 + Choice_7_6_5 + Choice_7_6_6
 = 1

_C267: Choice_7_4_7 + Choice_7_4_8 + Choice_7_4_9 + Choice_7_5_7
 + Choice_7_5_8 + Choice_7_5_9 + Choice_7_6_7 + Choice_7_6_8 + Choice_7_6_9
 = 1

_C268: Choice_7_7_1 + Choice_7_7_2 + Choice_7_7_3 + Choice_7_8_1
 + Choice_7_8_2 + Choice_7_8_3 + Choice_7_9_1 + Choice_7_9_2 + Choice_7_9_3
 = 1

_C269: Choice_7_7_4 + Choice_7_7_5 + Choice_7_7_6 + Choice_7_8_4
 + Choice_7_8_5 + Choice_7_8_6 + Choice_7_9_4 + Choice_7_9_5 + Choice_7_9_6
 = 1

_C270: Choice_7_7_7 + Choice_7_7_8 + Choice_7_7_9 + Choice_7_8_7
 + Choice_7_8_8 + Choice_7_8_9 + Choice_7_9_7 + Choice_7_9_8 + Choice_7_9_9
 = 1

_C271: Choice_8_1_1 + Choice_8_1_2 + Choice_8_1_3 + Choice_8_1_4
 + Choice_8_1_5 + Choice_8_1_6 + Choice_8_1_7 + Choice_8_1_8 + Choice_8_1_9
 = 1

_C272: Choice_8_2_1 + Choice_8_2_2 + Choice_8_2_3 + Choice_8_2_4
 + Choice_8_2_5 + Choice_8_2_6 + Choice_8_2_7 + Choice_8_2_8 + Choice_8_2_9
 = 1

_C273: Choice_8_3_1 + Choice_8_3_2 + Choice_8_3_3 + Choice_8_3_4
 + Choice_8_3_5 + Choice_8_3_6 + Choice_8_3_7 + Choice_8_3_8 + Choice_8_3_9
 = 1

_C274: Choice_8_4_1 + Choice_8_4_2 + Choice_8_4_3 + Choice_8_4_4
 + Choice_8_4_5 + Choice_8_4_6 + Choice_8_4_7 + Choice_8_4_8 + Choice_8_4_9
 = 1

_C275: Choice_8_5_1 + Choice_8_5_2 + Choice_8_5_3 + Choice_8_5_4
 + Choice_8_5_5 + Choice_8_5_6 + Choice_8_5_7 + Choice_8_5_8 + Choice_8_5_9
 = 1

_C276: Choice_8_6_1 + Choice_8_6_2 + Choice_8_6_3 + Choice_8_6_4
 + Choice_8_6_5 + Choice_8_6_6 + Choice_8_6_7 + Choice_8_6_8 + Choice_8_6_9
 = 1

_C277: Choice_8_7_1 + Choice_8_7_2 + Choice_8_7_3 + Choice_8_7_4
 + Choice_8_7_5 + Choice_8_7_6 + Choice_8_7_7 + Choice_8_7_8 + Choice_8_7_9
 = 1

_C278: Choice_8_8_1 + Choice_8_8_2 + Choice_8_8_3 + Choice_8_8_4
 + Choice_8_8_5 + Choice_8_8_6 + Choice_8_8_7 + Choice_8_8_8 + Choice_8_8_9
 = 1

_C279: Choice_8_9_1 + Choice_8_9_2 + Choice_8_9_3 + Choice_8_9_4
 + Choice_8_9_5 + Choice_8_9_6 + Choice_8_9_7 + Choice_8_9_8 + Choice_8_9_9
 = 1

_C280: Choice_8_1_1 + Choice_8_2_1 + Choice_8_3_1 + Choice_8_4_1
 + Choice_8_5_1 + Choice_8_6_1 + Choice_8_7_1 + Choice_8_8_1 + Choice_8_9_1
 = 1

_C281: Choice_8_1_2 + Choice_8_2_2 + Choice_8_3_2 + Choice_8_4_2
 + Choice_8_5_2 + Choice_8_6_2 + Choice_8_7_2 + Choice_8_8_2 + Choice_8_9_2
 = 1

_C282: Choice_8_1_3 + Choice_8_2_3 + Choice_8_3_3 + Choice_8_4_3
 + Choice_8_5_3 + Choice_8_6_3 + Choice_8_7_3 + Choice_8_8_3 + Choice_8_9_3
 = 1

_C283: Choice_8_1_4 + Choice_8_2_4 + Choice_8_3_4 + Choice_8_4_4
 + Choice_8_5_4 + Choice_8_6_4 + Choice_8_7_4 + Choice_8_8_4 + Choice_8_9_4
 = 1

_C284: Choice_8_1_5 + Choice_8_2_5 + Choice_8_3_5 + Choice_8_4_5
 + Choice_8_5_5 + Choice_8_6_5 + Choice_8_7_5 + Choice_8_8_5 + Choice_8_9_5
 = 1

_C285: Choice_8_1_6 + Choice_8_2_6 + Choice_8_3_6 + Choice_8_4_6
 + Choice_8_5_6 + Choice_8_6_6 + Choice_8_7_6 + Choice_8_8_6 + Choice_8_9_6
 = 1

_C286: Choice_8_1_7 + Choice_8_2_7 + Choice_8_3_7 + Choice_8_4_7
 + Choice_8_5_7 + Choice_8_6_7 + Choice_8_7_7 + Choice_8_8_7 + Choice_8_9_7
 = 1

_C287: Choice_8_1_8 + Choice_8_2_8 + Choice_8_3_8 + Choice_8_4_8
 + Choice_8_5_8 + Choice_8_6_8 + Choice_8_7_8 + Choice_8_8_8 + Choice_8_9_8
 = 1

_C288: Choice_8_1_9 + Choice_8_2_9 + Choice_8_3_9 + Choice_8_4_9
 + Choice_8_5_9 + Choice_8_6_9 + Choice_8_7_9 + Choice_8_8_9 + Choice_8_9_9
 = 1

_C289: Choice_8_1_1 + Choice_8_1_2 + Choice_8_1_3 + Choice_8_2_1
 + Choice_8_2_2 + Choice_8_2_3 + Choice_8_3_1 + Choice_8_3_2 + Choice_8_3_3
 = 1

_C290: Choice_8_1_4 + Choice_8_1_5 + Choice_8_1_6 + Choice_8_2_4
 + Choice_8_2_5 + Choice_8_2_6 + Choice_8_3_4 + Choice_8_3_5 + Choice_8_3_6
 = 1

_C291: Choice_8_1_7 + Choice_8_1_8 + Choice_8_1_9 + Choice_8_2_7
 + Choice_8_2_8 + Choice_8_2_9 + Choice_8_3_7 + Choice_8_3_8 + Choice_8_3_9
 = 1

_C292: Choice_8_4_1 + Choice_8_4_2 + Choice_8_4_3 + Choice_8_5_1
 + Choice_8_5_2 + Choice_8_5_3 + Choice_8_6_1 + Choice_8_6_2 + Choice_8_6_3
 = 1

_C293: Choice_8_4_4 + Choice_8_4_5 + Choice_8_4_6 + Choice_8_5_4
 + Choice_8_5_5 + Choice_8_5_6 + Choice_8_6_4 + Choice_8_6_5 + Choice_8_6_6
 = 1

_C294: Choice_8_4_7 + Choice_8_4_8 + Choice_8_4_9 + Choice_8_5_7
 + Choice_8_5_8 + Choice_8_5_9 + Choice_8_6_7 + Choice_8_6_8 + Choice_8_6_9
 = 1

_C295: Choice_8_7_1 + Choice_8_7_2 + Choice_8_7_3 + Choice_8_8_1
 + Choice_8_8_2 + Choice_8_8_3 + Choice_8_9_1 + Choice_8_9_2 + Choice_8_9_3
 = 1

_C296: Choice_8_7_4 + Choice_8_7_5 + Choice_8_7_6 + Choice_8_8_4
 + Choice_8_8_5 + Choice_8_8_6 + Choice_8_9_4 + Choice_8_9_5 + Choice_8_9_6
 = 1

_C297: Choice_8_7_7 + Choice_8_7_8 + Choice_8_7_9 + Choice_8_8_7
 + Choice_8_8_8 + Choice_8_8_9 + Choice_8_9_7 + Choice_8_9_8 + Choice_8_9_9
 = 1

_C298: Choice_9_1_1 + Choice_9_1_2 + Choice_9_1_3 + Choice_9_1_4
 + Choice_9_1_5 + Choice_9_1_6 + Choice_9_1_7 + Choice_9_1_8 + Choice_9_1_9
 = 1

_C299: Choice_9_2_1 + Choice_9_2_2 + Choice_9_2_3 + Choice_9_2_4
 + Choice_9_2_5 + Choice_9_2_6 + Choice_9_2_7 + Choice_9_2_8 + Choice_9_2_9
 = 1

_C300: Choice_9_3_1 + Choice_9_3_2 + Choice_9_3_3 + Choice_9_3_4
 + Choice_9_3_5 + Choice_9_3_6 + Choice_9_3_7 + Choice_9_3_8 + Choice_9_3_9
 = 1

_C301: Choice_9_4_1 + Choice_9_4_2 + Choice_9_4_3 + Choice_9_4_4
 + Choice_9_4_5 + Choice_9_4_6 + Choice_9_4_7 + Choice_9_4_8 + Choice_9_4_9
 = 1

_C302: Choice_9_5_1 + Choice_9_5_2 + Choice_9_5_3 + Choice_9_5_4
 + Choice_9_5_5 + Choice_9_5_6 + Choice_9_5_7 + Choice_9_5_8 + Choice_9_5_9
 = 1

_C303: Choice_9_6_1 + Choice_9_6_2 + Choice_9_6_3 + Choice_9_6_4
 + Choice_9_6_5 + Choice_9_6_6 + Choice_9_6_7 + Choice_9_6_8 + Choice_9_6_9
 = 1

_C304: Choice_9_7_1 + Choice_9_7_2 + Choice_9_7_3 + Choice_9_7_4
 + Choice_9_7_5 + Choice_9_7_6 + Choice_9_7_7 + Choice_9_7_8 + Choice_9_7_9
 = 1

_C305: Choice_9_8_1 + Choice_9_8_2 + Choice_9_8_3 + Choice_9_8_4
 + Choice_9_8_5 + Choice_9_8_6 + Choice_9_8_7 + Choice_9_8_8 + Choice_9_8_9
 = 1

_C306: Choice_9_9_1 + Choice_9_9_2 + Choice_9_9_3 + Choice_9_9_4
 + Choice_9_9_5 + Choice_9_9_6 + Choice_9_9_7 + Choice_9_9_8 + Choice_9_9_9
 = 1

_C307: Choice_9_1_1 + Choice_9_2_1 + Choice_9_3_1 + Choice_9_4_1
 + Choice_9_5_1 + Choice_9_6_1 + Choice_9_7_1 + Choice_9_8_1 + Choice_9_9_1
 = 1

_C308: Choice_9_1_2 + Choice_9_2_2 + Choice_9_3_2 + Choice_9_4_2
 + Choice_9_5_2 + Choice_9_6_2 + Choice_9_7_2 + Choice_9_8_2 + Choice_9_9_2
 = 1

_C309: Choice_9_1_3 + Choice_9_2_3 + Choice_9_3_3 + Choice_9_4_3
 + Choice_9_5_3 + Choice_9_6_3 + Choice_9_7_3 + Choice_9_8_3 + Choice_9_9_3
 = 1

_C310: Choice_9_1_4 + Choice_9_2_4 + Choice_9_3_4 + Choice_9_4_4
 + Choice_9_5_4 + Choice_9_6_4 + Choice_9_7_4 + Choice_9_8_4 + Choice_9_9_4
 = 1

_C311: Choice_9_1_5 + Choice_9_2_5 + Choice_9_3_5 + Choice_9_4_5
 + Choice_9_5_5 + Choice_9_6_5 + Choice_9_7_5 + Choice_9_8_5 + Choice_9_9_5
 = 1

_C312: Choice_9_1_6 + Choice_9_2_6 + Choice_9_3_6 + Choice_9_4_6
 + Choice_9_5_6 + Choice_9_6_6 + Choice_9_7_6 + Choice_9_8_6 + Choice_9_9_6
 = 1

_C313: Choice_9_1_7 + Choice_9_2_7 + Choice_9_3_7 + Choice_9_4_7
 + Choice_9_5_7 + Choice_9_6_7 + Choice_9_7_7 + Choice_9_8_7 + Choice_9_9_7
 = 1

_C314: Choice_9_1_8 + Choice_9_2_8 + Choice_9_3_8 + Choice_9_4_8
 + Choice_9_5_8 + Choice_9_6_8 + Choice_9_7_8 + Choice_9_8_8 + Choice_9_9_8
 = 1

_C315: Choice_9_1_9 + Choice_9_2_9 + Choice_9_3_9 + Choice_9_4_9
 + Choice_9_5_9 + Choice_9_6_9 + Choice_9_7_9 + Choice_9_8_9 + Choice_9_9_9
 = 1

_C316: Choice_9_1_1 + Choice_9_1_2 + Choice_9_1_3 + Choice_9_2_1
 + Choice_9_2_2 + Choice_9_2_3 + Choice_9_3_1 + Choice_9_3_2 + Choice_9_3_3
 = 1

_C317: Choice_9_1_4 + Choice_9_1_5 + Choice_9_1_6 + Choice_9_2_4
 + Choice_9_2_5 + Choice_9_2_6 + Choice_9_3_4 + Choice_9_3_5 + Choice_9_3_6
 = 1

_C318: Choice_9_1_7 + Choice_9_1_8 + Choice_9_1_9 + Choice_9_2_7
 + Choice_9_2_8 + Choice_9_2_9 + Choice_9_3_7 + Choice_9_3_8 + Choice_9_3_9
 = 1

_C319: Choice_9_4_1 + Choice_9_4_2 + Choice_9_4_3 + Choice_9_5_1
 + Choice_9_5_2 + Choice_9_5_3 + Choice_9_6_1 + Choice_9_6_2 + Choice_9_6_3
 = 1

_C320: Choice_9_4_4 + Choice_9_4_5 + Choice_9_4_6 + Choice_9_5_4
 + Choice_9_5_5 + Choice_9_5_6 + Choice_9_6_4 + Choice_9_6_5 + Choice_9_6_6
 = 1

_C321: Choice_9_4_7 + Choice_9_4_8 + Choice_9_4_9 + Choice_9_5_7
 + Choice_9_5_8 + Choice_9_5_9 + Choice_9_6_7 + Choice_9_6_8 + Choice_9_6_9
 = 1

_C322: Choice_9_7_1 + Choice_9_7_2 + Choice_9_7_3 + Choice_9_8_1
 + Choice_9_8_2 + Choice_9_8_3 + Choice_9_9_1 + Choice_9_9_2 + Choice_9_9_3
 = 1

_C323: Choice_9_7_4 + Choice_9_7_5 + Choice_9_7_6 + Choice_9_8_4
 + Choice_9_8_5 + Choice_9_8_6 + Choice_9_9_4 + Choice_9_9_5 + Choice_9_9_6
 = 1

_C324: Choice_9_7_7 + Choice_9_7_8 + Choice_9_7_9 + Choice_9_8_7
 + Choice_9_8_8 + Choice_9_8_9 + Choice_9_9_7 + Choice_9_9_8 + Choice_9_9_9
 = 1

_C325: Choice_5_1_1 = 1

_C326: Choice_6_2_1 = 1

_C327: Choice_8_4_1 = 1

_C328: Choice_4_5_1 = 1

_C329: Choice_7_6_1 = 1

_C330: Choice_3_1_2 = 1

_C331: Choice_9_3_2 = 1

_C332: Choice_6_7_2 = 1

_C333: Choice_8_3_3 = 1

_C334: Choice_1_2_4 = 1

_C335: Choice_8_5_4 = 1

_C336: Choice_4_8_4 = 1

_C337: Choice_7_1_5 = 1

_C338: Choice_9_2_5 = 1

_C339: Choice_6_4_5 = 1

_C340: Choice_2_6_5 = 1

_C341: Choice_1_8_5 = 1

_C342: Choice_8_9_5 = 1

_C343: Choice_5_2_6 = 1

_C344: Choice_3_5_6 = 1

_C345: Choice_9_8_6 = 1

_C346: Choice_2_7_7 = 1

_C347: Choice_6_3_8 = 1

_C348: Choice_8_7_8 = 1

_C349: Choice_7_9_8 = 1

_C350: Choice_3_4_9 = 1

_C351: Choice_1_5_9 = 1

_C352: Choice_6_6_9 = 1

_C353: Choice_5_8_9 = 1

VARIABLES
0 <= Choice_1_1_1 <= 1 Integer
0 <= Choice_1_1_2 <= 1 Integer
0 <= Choice_1_1_3 <= 1 Integer
0 <= Choice_1_1_4 <= 1 Integer
0 <= Choice_1_1_5 <= 1 Integer
0 <= Choice_1_1_6 <= 1 Integer
0 <= Choice_1_1_7 <= 1 Integer
0 <= Choice_1_1_8 <= 1 Integer
0 <= Choice_1_1_9 <= 1 Integer
0 <= Choice_1_2_1 <= 1 Integer
0 <= Choice_1_2_2 <= 1 Integer
0 <= Choice_1_2_3 <= 1 Integer
0 <= Choice_1_2_4 <= 1 Integer
0 <= Choice_1_2_5 <= 1 Integer
0 <= Choice_1_2_6 <= 1 Integer
0 <= Choice_1_2_7 <= 1 Integer
0 <= Choice_1_2_8 <= 1 Integer
0 <= Choice_1_2_9 <= 1 Integer
0 <= Choice_1_3_1 <= 1 Integer
0 <= Choice_1_3_2 <= 1 Integer
0 <= Choice_1_3_3 <= 1 Integer
0 <= Choice_1_3_4 <= 1 Integer
0 <= Choice_1_3_5 <= 1 Integer
0 <= Choice_1_3_6 <= 1 Integer
0 <= Choice_1_3_7 <= 1 Integer
0 <= Choice_1_3_8 <= 1 Integer
0 <= Choice_1_3_9 <= 1 Integer
0 <= Choice_1_4_1 <= 1 Integer
0 <= Choice_1_4_2 <= 1 Integer
0 <= Choice_1_4_3 <= 1 Integer
0 <= Choice_1_4_4 <= 1 Integer
0 <= Choice_1_4_5 <= 1 Integer
0 <= Choice_1_4_6 <= 1 Integer
0 <= Choice_1_4_7 <= 1 Integer
0 <= Choice_1_4_8 <= 1 Integer
0 <= Choice_1_4_9 <= 1 Integer
0 <= Choice_1_5_1 <= 1 Integer
0 <= Choice_1_5_2 <= 1 Integer
0 <= Choice_1_5_3 <= 1 Integer
0 <= Choice_1_5_4 <= 1 Integer
0 <= Choice_1_5_5 <= 1 Integer
0 <= Choice_1_5_6 <= 1 Integer
0 <= Choice_1_5_7 <= 1 Integer
0 <= Choice_1_5_8 <= 1 Integer
0 <= Choice_1_5_9 <= 1 Integer
0 <= Choice_1_6_1 <= 1 Integer
0 <= Choice_1_6_2 <= 1 Integer
0 <= Choice_1_6_3 <= 1 Integer
0 <= Choice_1_6_4 <= 1 Integer
0 <= Choice_1_6_5 <= 1 Integer
0 <= Choice_1_6_6 <= 1 Integer
0 <= Choice_1_6_7 <= 1 Integer
0 <= Choice_1_6_8 <= 1 Integer
0 <= Choice_1_6_9 <= 1 Integer
0 <= Choice_1_7_1 <= 1 Integer
0 <= Choice_1_7_2 <= 1 Integer
0 <= Choice_1_7_3 <= 1 Integer
0 <= Choice_1_7_4 <= 1 Integer
0 <= Choice_1_7_5 <= 1 Integer
0 <= Choice_1_7_6 <= 1 Integer
0 <= Choice_1_7_7 <= 1 Integer
0 <= Choice_1_7_8 <= 1 Integer
0 <= Choice_1_7_9 <= 1 Integer
0 <= Choice_1_8_1 <= 1 Integer
0 <= Choice_1_8_2 <= 1 Integer
0 <= Choice_1_8_3 <= 1 Integer
0 <= Choice_1_8_4 <= 1 Integer
0 <= Choice_1_8_5 <= 1 Integer
0 <= Choice_1_8_6 <= 1 Integer
0 <= Choice_1_8_7 <= 1 Integer
0 <= Choice_1_8_8 <= 1 Integer
0 <= Choice_1_8_9 <= 1 Integer
0 <= Choice_1_9_1 <= 1 Integer
0 <= Choice_1_9_2 <= 1 Integer
0 <= Choice_1_9_3 <= 1 Integer
0 <= Choice_1_9_4 <= 1 Integer
0 <= Choice_1_9_5 <= 1 Integer
0 <= Choice_1_9_6 <= 1 Integer
0 <= Choice_1_9_7 <= 1 Integer
0 <= Choice_1_9_8 <= 1 Integer
0 <= Choice_1_9_9 <= 1 Integer
0 <= Choice_2_1_1 <= 1 Integer
0 <= Choice_2_1_2 <= 1 Integer
0 <= Choice_2_1_3 <= 1 Integer
0 <= Choice_2_1_4 <= 1 Integer
0 <= Choice_2_1_5 <= 1 Integer
0 <= Choice_2_1_6 <= 1 Integer
0 <= Choice_2_1_7 <= 1 Integer
0 <= Choice_2_1_8 <= 1 Integer
0 <= Choice_2_1_9 <= 1 Integer
0 <= Choice_2_2_1 <= 1 Integer
0 <= Choice_2_2_2 <= 1 Integer
0 <= Choice_2_2_3 <= 1 Integer
0 <= Choice_2_2_4 <= 1 Integer
0 <= Choice_2_2_5 <= 1 Integer
0 <= Choice_2_2_6 <= 1 Integer
0 <= Choice_2_2_7 <= 1 Integer
0 <= Choice_2_2_8 <= 1 Integer
0 <= Choice_2_2_9 <= 1 Integer
0 <= Choice_2_3_1 <= 1 Integer
0 <= Choice_2_3_2 <= 1 Integer
0 <= Choice_2_3_3 <= 1 Integer
0 <= Choice_2_3_4 <= 1 Integer
0 <= Choice_2_3_5 <= 1 Integer
0 <= Choice_2_3_6 <= 1 Integer
0 <= Choice_2_3_7 <= 1 Integer
0 <= Choice_2_3_8 <= 1 Integer
0 <= Choice_2_3_9 <= 1 Integer
0 <= Choice_2_4_1 <= 1 Integer
0 <= Choice_2_4_2 <= 1 Integer
0 <= Choice_2_4_3 <= 1 Integer
0 <= Choice_2_4_4 <= 1 Integer
0 <= Choice_2_4_5 <= 1 Integer
0 <= Choice_2_4_6 <= 1 Integer
0 <= Choice_2_4_7 <= 1 Integer
0 <= Choice_2_4_8 <= 1 Integer
0 <= Choice_2_4_9 <= 1 Integer
0 <= Choice_2_5_1 <= 1 Integer
0 <= Choice_2_5_2 <= 1 Integer
0 <= Choice_2_5_3 <= 1 Integer
0 <= Choice_2_5_4 <= 1 Integer
0 <= Choice_2_5_5 <= 1 Integer
0 <= Choice_2_5_6 <= 1 Integer
0 <= Choice_2_5_7 <= 1 Integer
0 <= Choice_2_5_8 <= 1 Integer
0 <= Choice_2_5_9 <= 1 Integer
0 <= Choice_2_6_1 <= 1 Integer
0 <= Choice_2_6_2 <= 1 Integer
0 <= Choice_2_6_3 <= 1 Integer
0 <= Choice_2_6_4 <= 1 Integer
0 <= Choice_2_6_5 <= 1 Integer
0 <= Choice_2_6_6 <= 1 Integer
0 <= Choice_2_6_7 <= 1 Integer
0 <= Choice_2_6_8 <= 1 Integer
0 <= Choice_2_6_9 <= 1 Integer
0 <= Choice_2_7_1 <= 1 Integer
0 <= Choice_2_7_2 <= 1 Integer
0 <= Choice_2_7_3 <= 1 Integer
0 <= Choice_2_7_4 <= 1 Integer
0 <= Choice_2_7_5 <= 1 Integer
0 <= Choice_2_7_6 <= 1 Integer
0 <= Choice_2_7_7 <= 1 Integer
0 <= Choice_2_7_8 <= 1 Integer
0 <= Choice_2_7_9 <= 1 Integer
0 <= Choice_2_8_1 <= 1 Integer
0 <= Choice_2_8_2 <= 1 Integer
0 <= Choice_2_8_3 <= 1 Integer
0 <= Choice_2_8_4 <= 1 Integer
0 <= Choice_2_8_5 <= 1 Integer
0 <= Choice_2_8_6 <= 1 Integer
0 <= Choice_2_8_7 <= 1 Integer
0 <= Choice_2_8_8 <= 1 Integer
0 <= Choice_2_8_9 <= 1 Integer
0 <= Choice_2_9_1 <= 1 Integer
0 <= Choice_2_9_2 <= 1 Integer
0 <= Choice_2_9_3 <= 1 Integer
0 <= Choice_2_9_4 <= 1 Integer
0 <= Choice_2_9_5 <= 1 Integer
0 <= Choice_2_9_6 <= 1 Integer
0 <= Choice_2_9_7 <= 1 Integer
0 <= Choice_2_9_8 <= 1 Integer
0 <= Choice_2_9_9 <= 1 Integer
0 <= Choice_3_1_1 <= 1 Integer
0 <= Choice_3_1_2 <= 1 Integer
0 <= Choice_3_1_3 <= 1 Integer
0 <= Choice_3_1_4 <= 1 Integer
0 <= Choice_3_1_5 <= 1 Integer
0 <= Choice_3_1_6 <= 1 Integer
0 <= Choice_3_1_7 <= 1 Integer
0 <= Choice_3_1_8 <= 1 Integer
0 <= Choice_3_1_9 <= 1 Integer
0 <= Choice_3_2_1 <= 1 Integer
0 <= Choice_3_2_2 <= 1 Integer
0 <= Choice_3_2_3 <= 1 Integer
0 <= Choice_3_2_4 <= 1 Integer
0 <= Choice_3_2_5 <= 1 Integer
0 <= Choice_3_2_6 <= 1 Integer
0 <= Choice_3_2_7 <= 1 Integer
0 <= Choice_3_2_8 <= 1 Integer
0 <= Choice_3_2_9 <= 1 Integer
0 <= Choice_3_3_1 <= 1 Integer
0 <= Choice_3_3_2 <= 1 Integer
0 <= Choice_3_3_3 <= 1 Integer
0 <= Choice_3_3_4 <= 1 Integer
0 <= Choice_3_3_5 <= 1 Integer
0 <= Choice_3_3_6 <= 1 Integer
0 <= Choice_3_3_7 <= 1 Integer
0 <= Choice_3_3_8 <= 1 Integer
0 <= Choice_3_3_9 <= 1 Integer
0 <= Choice_3_4_1 <= 1 Integer
0 <= Choice_3_4_2 <= 1 Integer
0 <= Choice_3_4_3 <= 1 Integer
0 <= Choice_3_4_4 <= 1 Integer
0 <= Choice_3_4_5 <= 1 Integer
0 <= Choice_3_4_6 <= 1 Integer
0 <= Choice_3_4_7 <= 1 Integer
0 <= Choice_3_4_8 <= 1 Integer
0 <= Choice_3_4_9 <= 1 Integer
0 <= Choice_3_5_1 <= 1 Integer
0 <= Choice_3_5_2 <= 1 Integer
0 <= Choice_3_5_3 <= 1 Integer
0 <= Choice_3_5_4 <= 1 Integer
0 <= Choice_3_5_5 <= 1 Integer
0 <= Choice_3_5_6 <= 1 Integer
0 <= Choice_3_5_7 <= 1 Integer
0 <= Choice_3_5_8 <= 1 Integer
0 <= Choice_3_5_9 <= 1 Integer
0 <= Choice_3_6_1 <= 1 Integer
0 <= Choice_3_6_2 <= 1 Integer
0 <= Choice_3_6_3 <= 1 Integer
0 <= Choice_3_6_4 <= 1 Integer
0 <= Choice_3_6_5 <= 1 Integer
0 <= Choice_3_6_6 <= 1 Integer
0 <= Choice_3_6_7 <= 1 Integer
0 <= Choice_3_6_8 <= 1 Integer
0 <= Choice_3_6_9 <= 1 Integer
0 <= Choice_3_7_1 <= 1 Integer
0 <= Choice_3_7_2 <= 1 Integer
0 <= Choice_3_7_3 <= 1 Integer
0 <= Choice_3_7_4 <= 1 Integer
0 <= Choice_3_7_5 <= 1 Integer
0 <= Choice_3_7_6 <= 1 Integer
0 <= Choice_3_7_7 <= 1 Integer
0 <= Choice_3_7_8 <= 1 Integer
0 <= Choice_3_7_9 <= 1 Integer
0 <= Choice_3_8_1 <= 1 Integer
0 <= Choice_3_8_2 <= 1 Integer
0 <= Choice_3_8_3 <= 1 Integer
0 <= Choice_3_8_4 <= 1 Integer
0 <= Choice_3_8_5 <= 1 Integer
0 <= Choice_3_8_6 <= 1 Integer
0 <= Choice_3_8_7 <= 1 Integer
0 <= Choice_3_8_8 <= 1 Integer
0 <= Choice_3_8_9 <= 1 Integer
0 <= Choice_3_9_1 <= 1 Integer
0 <= Choice_3_9_2 <= 1 Integer
0 <= Choice_3_9_3 <= 1 Integer
0 <= Choice_3_9_4 <= 1 Integer
0 <= Choice_3_9_5 <= 1 Integer
0 <= Choice_3_9_6 <= 1 Integer
0 <= Choice_3_9_7 <= 1 Integer
0 <= Choice_3_9_8 <= 1 Integer
0 <= Choice_3_9_9 <= 1 Integer
0 <= Choice_4_1_1 <= 1 Integer
0 <= Choice_4_1_2 <= 1 Integer
0 <= Choice_4_1_3 <= 1 Integer
0 <= Choice_4_1_4 <= 1 Integer
0 <= Choice_4_1_5 <= 1 Integer
0 <= Choice_4_1_6 <= 1 Integer
0 <= Choice_4_1_7 <= 1 Integer
0 <= Choice_4_1_8 <= 1 Integer
0 <= Choice_4_1_9 <= 1 Integer
0 <= Choice_4_2_1 <= 1 Integer
0 <= Choice_4_2_2 <= 1 Integer
0 <= Choice_4_2_3 <= 1 Integer
0 <= Choice_4_2_4 <= 1 Integer
0 <= Choice_4_2_5 <= 1 Integer
0 <= Choice_4_2_6 <= 1 Integer
0 <= Choice_4_2_7 <= 1 Integer
0 <= Choice_4_2_8 <= 1 Integer
0 <= Choice_4_2_9 <= 1 Integer
0 <= Choice_4_3_1 <= 1 Integer
0 <= Choice_4_3_2 <= 1 Integer
0 <= Choice_4_3_3 <= 1 Integer
0 <= Choice_4_3_4 <= 1 Integer
0 <= Choice_4_3_5 <= 1 Integer
0 <= Choice_4_3_6 <= 1 Integer
0 <= Choice_4_3_7 <= 1 Integer
0 <= Choice_4_3_8 <= 1 Integer
0 <= Choice_4_3_9 <= 1 Integer
0 <= Choice_4_4_1 <= 1 Integer
0 <= Choice_4_4_2 <= 1 Integer
0 <= Choice_4_4_3 <= 1 Integer
0 <= Choice_4_4_4 <= 1 Integer
0 <= Choice_4_4_5 <= 1 Integer
0 <= Choice_4_4_6 <= 1 Integer
0 <= Choice_4_4_7 <= 1 Integer
0 <= Choice_4_4_8 <= 1 Integer
0 <= Choice_4_4_9 <= 1 Integer
0 <= Choice_4_5_1 <= 1 Integer
0 <= Choice_4_5_2 <= 1 Integer
0 <= Choice_4_5_3 <= 1 Integer
0 <= Choice_4_5_4 <= 1 Integer
0 <= Choice_4_5_5 <= 1 Integer
0 <= Choice_4_5_6 <= 1 Integer
0 <= Choice_4_5_7 <= 1 Integer
0 <= Choice_4_5_8 <= 1 Integer
0 <= Choice_4_5_9 <= 1 Integer
0 <= Choice_4_6_1 <= 1 Integer
0 <= Choice_4_6_2 <= 1 Integer
0 <= Choice_4_6_3 <= 1 Integer
0 <= Choice_4_6_4 <= 1 Integer
0 <= Choice_4_6_5 <= 1 Integer
0 <= Choice_4_6_6 <= 1 Integer
0 <= Choice_4_6_7 <= 1 Integer
0 <= Choice_4_6_8 <= 1 Integer
0 <= Choice_4_6_9 <= 1 Integer
0 <= Choice_4_7_1 <= 1 Integer
0 <= Choice_4_7_2 <= 1 Integer
0 <= Choice_4_7_3 <= 1 Integer
0 <= Choice_4_7_4 <= 1 Integer
0 <= Choice_4_7_5 <= 1 Integer
0 <= Choice_4_7_6 <= 1 Integer
0 <= Choice_4_7_7 <= 1 Integer
0 <= Choice_4_7_8 <= 1 Integer
0 <= Choice_4_7_9 <= 1 Integer
0 <= Choice_4_8_1 <= 1 Integer
0 <= Choice_4_8_2 <= 1 Integer
0 <= Choice_4_8_3 <= 1 Integer
0 <= Choice_4_8_4 <= 1 Integer
0 <= Choice_4_8_5 <= 1 Integer
0 <= Choice_4_8_6 <= 1 Integer
0 <= Choice_4_8_7 <= 1 Integer
0 <= Choice_4_8_8 <= 1 Integer
0 <= Choice_4_8_9 <= 1 Integer
0 <= Choice_4_9_1 <= 1 Integer
0 <= Choice_4_9_2 <= 1 Integer
0 <= Choice_4_9_3 <= 1 Integer
0 <= Choice_4_9_4 <= 1 Integer
0 <= Choice_4_9_5 <= 1 Integer
0 <= Choice_4_9_6 <= 1 Integer
0 <= Choice_4_9_7 <= 1 Integer
0 <= Choice_4_9_8 <= 1 Integer
0 <= Choice_4_9_9 <= 1 Integer
0 <= Choice_5_1_1 <= 1 Integer
0 <= Choice_5_1_2 <= 1 Integer
0 <= Choice_5_1_3 <= 1 Integer
0 <= Choice_5_1_4 <= 1 Integer
0 <= Choice_5_1_5 <= 1 Integer
0 <= Choice_5_1_6 <= 1 Integer
0 <= Choice_5_1_7 <= 1 Integer
0 <= Choice_5_1_8 <= 1 Integer
0 <= Choice_5_1_9 <= 1 Integer
0 <= Choice_5_2_1 <= 1 Integer
0 <= Choice_5_2_2 <= 1 Integer
0 <= Choice_5_2_3 <= 1 Integer
0 <= Choice_5_2_4 <= 1 Integer
0 <= Choice_5_2_5 <= 1 Integer
0 <= Choice_5_2_6 <= 1 Integer
0 <= Choice_5_2_7 <= 1 Integer
0 <= Choice_5_2_8 <= 1 Integer
0 <= Choice_5_2_9 <= 1 Integer
0 <= Choice_5_3_1 <= 1 Integer
0 <= Choice_5_3_2 <= 1 Integer
0 <= Choice_5_3_3 <= 1 Integer
0 <= Choice_5_3_4 <= 1 Integer
0 <= Choice_5_3_5 <= 1 Integer
0 <= Choice_5_3_6 <= 1 Integer
0 <= Choice_5_3_7 <= 1 Integer
0 <= Choice_5_3_8 <= 1 Integer
0 <= Choice_5_3_9 <= 1 Integer
0 <= Choice_5_4_1 <= 1 Integer
0 <= Choice_5_4_2 <= 1 Integer
0 <= Choice_5_4_3 <= 1 Integer
0 <= Choice_5_4_4 <= 1 Integer
0 <= Choice_5_4_5 <= 1 Integer
0 <= Choice_5_4_6 <= 1 Integer
0 <= Choice_5_4_7 <= 1 Integer
0 <= Choice_5_4_8 <= 1 Integer
0 <= Choice_5_4_9 <= 1 Integer
0 <= Choice_5_5_1 <= 1 Integer
0 <= Choice_5_5_2 <= 1 Integer
0 <= Choice_5_5_3 <= 1 Integer
0 <= Choice_5_5_4 <= 1 Integer
0 <= Choice_5_5_5 <= 1 Integer
0 <= Choice_5_5_6 <= 1 Integer
0 <= Choice_5_5_7 <= 1 Integer
0 <= Choice_5_5_8 <= 1 Integer
0 <= Choice_5_5_9 <= 1 Integer
0 <= Choice_5_6_1 <= 1 Integer
0 <= Choice_5_6_2 <= 1 Integer
0 <= Choice_5_6_3 <= 1 Integer
0 <= Choice_5_6_4 <= 1 Integer
0 <= Choice_5_6_5 <= 1 Integer
0 <= Choice_5_6_6 <= 1 Integer
0 <= Choice_5_6_7 <= 1 Integer
0 <= Choice_5_6_8 <= 1 Integer
0 <= Choice_5_6_9 <= 1 Integer
0 <= Choice_5_7_1 <= 1 Integer
0 <= Choice_5_7_2 <= 1 Integer
0 <= Choice_5_7_3 <= 1 Integer
0 <= Choice_5_7_4 <= 1 Integer
0 <= Choice_5_7_5 <= 1 Integer
0 <= Choice_5_7_6 <= 1 Integer
0 <= Choice_5_7_7 <= 1 Integer
0 <= Choice_5_7_8 <= 1 Integer
0 <= Choice_5_7_9 <= 1 Integer
0 <= Choice_5_8_1 <= 1 Integer
0 <= Choice_5_8_2 <= 1 Integer
0 <= Choice_5_8_3 <= 1 Integer
0 <= Choice_5_8_4 <= 1 Integer
0 <= Choice_5_8_5 <= 1 Integer
0 <= Choice_5_8_6 <= 1 Integer
0 <= Choice_5_8_7 <= 1 Integer
0 <= Choice_5_8_8 <= 1 Integer
0 <= Choice_5_8_9 <= 1 Integer
0 <= Choice_5_9_1 <= 1 Integer
0 <= Choice_5_9_2 <= 1 Integer
0 <= Choice_5_9_3 <= 1 Integer
0 <= Choice_5_9_4 <= 1 Integer
0 <= Choice_5_9_5 <= 1 Integer
0 <= Choice_5_9_6 <= 1 Integer
0 <= Choice_5_9_7 <= 1 Integer
0 <= Choice_5_9_8 <= 1 Integer
0 <= Choice_5_9_9 <= 1 Integer
0 <= Choice_6_1_1 <= 1 Integer
0 <= Choice_6_1_2 <= 1 Integer
0 <= Choice_6_1_3 <= 1 Integer
0 <= Choice_6_1_4 <= 1 Integer
0 <= Choice_6_1_5 <= 1 Integer
0 <= Choice_6_1_6 <= 1 Integer
0 <= Choice_6_1_7 <= 1 Integer
0 <= Choice_6_1_8 <= 1 Integer
0 <= Choice_6_1_9 <= 1 Integer
0 <= Choice_6_2_1 <= 1 Integer
0 <= Choice_6_2_2 <= 1 Integer
0 <= Choice_6_2_3 <= 1 Integer
0 <= Choice_6_2_4 <= 1 Integer
0 <= Choice_6_2_5 <= 1 Integer
0 <= Choice_6_2_6 <= 1 Integer
0 <= Choice_6_2_7 <= 1 Integer
0 <= Choice_6_2_8 <= 1 Integer
0 <= Choice_6_2_9 <= 1 Integer
0 <= Choice_6_3_1 <= 1 Integer
0 <= Choice_6_3_2 <= 1 Integer
0 <= Choice_6_3_3 <= 1 Integer
0 <= Choice_6_3_4 <= 1 Integer
0 <= Choice_6_3_5 <= 1 Integer
0 <= Choice_6_3_6 <= 1 Integer
0 <= Choice_6_3_7 <= 1 Integer
0 <= Choice_6_3_8 <= 1 Integer
0 <= Choice_6_3_9 <= 1 Integer
0 <= Choice_6_4_1 <= 1 Integer
0 <= Choice_6_4_2 <= 1 Integer
0 <= Choice_6_4_3 <= 1 Integer
0 <= Choice_6_4_4 <= 1 Integer
0 <= Choice_6_4_5 <= 1 Integer
0 <= Choice_6_4_6 <= 1 Integer
0 <= Choice_6_4_7 <= 1 Integer
0 <= Choice_6_4_8 <= 1 Integer
0 <= Choice_6_4_9 <= 1 Integer
0 <= Choice_6_5_1 <= 1 Integer
0 <= Choice_6_5_2 <= 1 Integer
0 <= Choice_6_5_3 <= 1 Integer
0 <= Choice_6_5_4 <= 1 Integer
0 <= Choice_6_5_5 <= 1 Integer
0 <= Choice_6_5_6 <= 1 Integer
0 <= Choice_6_5_7 <= 1 Integer
0 <= Choice_6_5_8 <= 1 Integer
0 <= Choice_6_5_9 <= 1 Integer
0 <= Choice_6_6_1 <= 1 Integer
0 <= Choice_6_6_2 <= 1 Integer
0 <= Choice_6_6_3 <= 1 Integer
0 <= Choice_6_6_4 <= 1 Integer
0 <= Choice_6_6_5 <= 1 Integer
0 <= Choice_6_6_6 <= 1 Integer
0 <= Choice_6_6_7 <= 1 Integer
0 <= Choice_6_6_8 <= 1 Integer
0 <= Choice_6_6_9 <= 1 Integer
0 <= Choice_6_7_1 <= 1 Integer
0 <= Choice_6_7_2 <= 1 Integer
0 <= Choice_6_7_3 <= 1 Integer
0 <= Choice_6_7_4 <= 1 Integer
0 <= Choice_6_7_5 <= 1 Integer
0 <= Choice_6_7_6 <= 1 Integer
0 <= Choice_6_7_7 <= 1 Integer
0 <= Choice_6_7_8 <= 1 Integer
0 <= Choice_6_7_9 <= 1 Integer
0 <= Choice_6_8_1 <= 1 Integer
0 <= Choice_6_8_2 <= 1 Integer
0 <= Choice_6_8_3 <= 1 Integer
0 <= Choice_6_8_4 <= 1 Integer
0 <= Choice_6_8_5 <= 1 Integer
0 <= Choice_6_8_6 <= 1 Integer
0 <= Choice_6_8_7 <= 1 Integer
0 <= Choice_6_8_8 <= 1 Integer
0 <= Choice_6_8_9 <= 1 Integer
0 <= Choice_6_9_1 <= 1 Integer
0 <= Choice_6_9_2 <= 1 Integer
0 <= Choice_6_9_3 <= 1 Integer
0 <= Choice_6_9_4 <= 1 Integer
0 <= Choice_6_9_5 <= 1 Integer
0 <= Choice_6_9_6 <= 1 Integer
0 <= Choice_6_9_7 <= 1 Integer
0 <= Choice_6_9_8 <= 1 Integer
0 <= Choice_6_9_9 <= 1 Integer
0 <= Choice_7_1_1 <= 1 Integer
0 <= Choice_7_1_2 <= 1 Integer
0 <= Choice_7_1_3 <= 1 Integer
0 <= Choice_7_1_4 <= 1 Integer
0 <= Choice_7_1_5 <= 1 Integer
0 <= Choice_7_1_6 <= 1 Integer
0 <= Choice_7_1_7 <= 1 Integer
0 <= Choice_7_1_8 <= 1 Integer
0 <= Choice_7_1_9 <= 1 Integer
0 <= Choice_7_2_1 <= 1 Integer
0 <= Choice_7_2_2 <= 1 Integer
0 <= Choice_7_2_3 <= 1 Integer
0 <= Choice_7_2_4 <= 1 Integer
0 <= Choice_7_2_5 <= 1 Integer
0 <= Choice_7_2_6 <= 1 Integer
0 <= Choice_7_2_7 <= 1 Integer
0 <= Choice_7_2_8 <= 1 Integer
0 <= Choice_7_2_9 <= 1 Integer
0 <= Choice_7_3_1 <= 1 Integer
0 <= Choice_7_3_2 <= 1 Integer
0 <= Choice_7_3_3 <= 1 Integer
0 <= Choice_7_3_4 <= 1 Integer
0 <= Choice_7_3_5 <= 1 Integer
0 <= Choice_7_3_6 <= 1 Integer
0 <= Choice_7_3_7 <= 1 Integer
0 <= Choice_7_3_8 <= 1 Integer
0 <= Choice_7_3_9 <= 1 Integer
0 <= Choice_7_4_1 <= 1 Integer
0 <= Choice_7_4_2 <= 1 Integer
0 <= Choice_7_4_3 <= 1 Integer
0 <= Choice_7_4_4 <= 1 Integer
0 <= Choice_7_4_5 <= 1 Integer
0 <= Choice_7_4_6 <= 1 Integer
0 <= Choice_7_4_7 <= 1 Integer
0 <= Choice_7_4_8 <= 1 Integer
0 <= Choice_7_4_9 <= 1 Integer
0 <= Choice_7_5_1 <= 1 Integer
0 <= Choice_7_5_2 <= 1 Integer
0 <= Choice_7_5_3 <= 1 Integer
0 <= Choice_7_5_4 <= 1 Integer
0 <= Choice_7_5_5 <= 1 Integer
0 <= Choice_7_5_6 <= 1 Integer
0 <= Choice_7_5_7 <= 1 Integer
0 <= Choice_7_5_8 <= 1 Integer
0 <= Choice_7_5_9 <= 1 Integer
0 <= Choice_7_6_1 <= 1 Integer
0 <= Choice_7_6_2 <= 1 Integer
0 <= Choice_7_6_3 <= 1 Integer
0 <= Choice_7_6_4 <= 1 Integer
0 <= Choice_7_6_5 <= 1 Integer
0 <= Choice_7_6_6 <= 1 Integer
0 <= Choice_7_6_7 <= 1 Integer
0 <= Choice_7_6_8 <= 1 Integer
0 <= Choice_7_6_9 <= 1 Integer
0 <= Choice_7_7_1 <= 1 Integer
0 <= Choice_7_7_2 <= 1 Integer
0 <= Choice_7_7_3 <= 1 Integer
0 <= Choice_7_7_4 <= 1 Integer
0 <= Choice_7_7_5 <= 1 Integer
0 <= Choice_7_7_6 <= 1 Integer
0 <= Choice_7_7_7 <= 1 Integer
0 <= Choice_7_7_8 <= 1 Integer
0 <= Choice_7_7_9 <= 1 Integer
0 <= Choice_7_8_1 <= 1 Integer
0 <= Choice_7_8_2 <= 1 Integer
0 <= Choice_7_8_3 <= 1 Integer
0 <= Choice_7_8_4 <= 1 Integer
0 <= Choice_7_8_5 <= 1 Integer
0 <= Choice_7_8_6 <= 1 Integer
0 <= Choice_7_8_7 <= 1 Integer
0 <= Choice_7_8_8 <= 1 Integer
0 <= Choice_7_8_9 <= 1 Integer
0 <= Choice_7_9_1 <= 1 Integer
0 <= Choice_7_9_2 <= 1 Integer
0 <= Choice_7_9_3 <= 1 Integer
0 <= Choice_7_9_4 <= 1 Integer
0 <= Choice_7_9_5 <= 1 Integer
0 <= Choice_7_9_6 <= 1 Integer
0 <= Choice_7_9_7 <= 1 Integer
0 <= Choice_7_9_8 <= 1 Integer
0 <= Choice_7_9_9 <= 1 Integer
0 <= Choice_8_1_1 <= 1 Integer
0 <= Choice_8_1_2 <= 1 Integer
0 <= Choice_8_1_3 <= 1 Integer
0 <= Choice_8_1_4 <= 1 Integer
0 <= Choice_8_1_5 <= 1 Integer
0 <= Choice_8_1_6 <= 1 Integer
0 <= Choice_8_1_7 <= 1 Integer
0 <= Choice_8_1_8 <= 1 Integer
0 <= Choice_8_1_9 <= 1 Integer
0 <= Choice_8_2_1 <= 1 Integer
0 <= Choice_8_2_2 <= 1 Integer
0 <= Choice_8_2_3 <= 1 Integer
0 <= Choice_8_2_4 <= 1 Integer
0 <= Choice_8_2_5 <= 1 Integer
0 <= Choice_8_2_6 <= 1 Integer
0 <= Choice_8_2_7 <= 1 Integer
0 <= Choice_8_2_8 <= 1 Integer
0 <= Choice_8_2_9 <= 1 Integer
0 <= Choice_8_3_1 <= 1 Integer
0 <= Choice_8_3_2 <= 1 Integer
0 <= Choice_8_3_3 <= 1 Integer
0 <= Choice_8_3_4 <= 1 Integer
0 <= Choice_8_3_5 <= 1 Integer
0 <= Choice_8_3_6 <= 1 Integer
0 <= Choice_8_3_7 <= 1 Integer
0 <= Choice_8_3_8 <= 1 Integer
0 <= Choice_8_3_9 <= 1 Integer
0 <= Choice_8_4_1 <= 1 Integer
0 <= Choice_8_4_2 <= 1 Integer
0 <= Choice_8_4_3 <= 1 Integer
0 <= Choice_8_4_4 <= 1 Integer
0 <= Choice_8_4_5 <= 1 Integer
0 <= Choice_8_4_6 <= 1 Integer
0 <= Choice_8_4_7 <= 1 Integer
0 <= Choice_8_4_8 <= 1 Integer
0 <= Choice_8_4_9 <= 1 Integer
0 <= Choice_8_5_1 <= 1 Integer
0 <= Choice_8_5_2 <= 1 Integer
0 <= Choice_8_5_3 <= 1 Integer
0 <= Choice_8_5_4 <= 1 Integer
0 <= Choice_8_5_5 <= 1 Integer
0 <= Choice_8_5_6 <= 1 Integer
0 <= Choice_8_5_7 <= 1 Integer
0 <= Choice_8_5_8 <= 1 Integer
0 <= Choice_8_5_9 <= 1 Integer
0 <= Choice_8_6_1 <= 1 Integer
0 <= Choice_8_6_2 <= 1 Integer
0 <= Choice_8_6_3 <= 1 Integer
0 <= Choice_8_6_4 <= 1 Integer
0 <= Choice_8_6_5 <= 1 Integer
0 <= Choice_8_6_6 <= 1 Integer
0 <= Choice_8_6_7 <= 1 Integer
0 <= Choice_8_6_8 <= 1 Integer
0 <= Choice_8_6_9 <= 1 Integer
0 <= Choice_8_7_1 <= 1 Integer
0 <= Choice_8_7_2 <= 1 Integer
0 <= Choice_8_7_3 <= 1 Integer
0 <= Choice_8_7_4 <= 1 Integer
0 <= Choice_8_7_5 <= 1 Integer
0 <= Choice_8_7_6 <= 1 Integer
0 <= Choice_8_7_7 <= 1 Integer
0 <= Choice_8_7_8 <= 1 Integer
0 <= Choice_8_7_9 <= 1 Integer
0 <= Choice_8_8_1 <= 1 Integer
0 <= Choice_8_8_2 <= 1 Integer
0 <= Choice_8_8_3 <= 1 Integer
0 <= Choice_8_8_4 <= 1 Integer
0 <= Choice_8_8_5 <= 1 Integer
0 <= Choice_8_8_6 <= 1 Integer
0 <= Choice_8_8_7 <= 1 Integer
0 <= Choice_8_8_8 <= 1 Integer
0 <= Choice_8_8_9 <= 1 Integer
0 <= Choice_8_9_1 <= 1 Integer
0 <= Choice_8_9_2 <= 1 Integer
0 <= Choice_8_9_3 <= 1 Integer
0 <= Choice_8_9_4 <= 1 Integer
0 <= Choice_8_9_5 <= 1 Integer
0 <= Choice_8_9_6 <= 1 Integer
0 <= Choice_8_9_7 <= 1 Integer
0 <= Choice_8_9_8 <= 1 Integer
0 <= Choice_8_9_9 <= 1 Integer
0 <= Choice_9_1_1 <= 1 Integer
0 <= Choice_9_1_2 <= 1 Integer
0 <= Choice_9_1_3 <= 1 Integer
0 <= Choice_9_1_4 <= 1 Integer
0 <= Choice_9_1_5 <= 1 Integer
0 <= Choice_9_1_6 <= 1 Integer
0 <= Choice_9_1_7 <= 1 Integer
0 <= Choice_9_1_8 <= 1 Integer
0 <= Choice_9_1_9 <= 1 Integer
0 <= Choice_9_2_1 <= 1 Integer
0 <= Choice_9_2_2 <= 1 Integer
0 <= Choice_9_2_3 <= 1 Integer
0 <= Choice_9_2_4 <= 1 Integer
0 <= Choice_9_2_5 <= 1 Integer
0 <= Choice_9_2_6 <= 1 Integer
0 <= Choice_9_2_7 <= 1 Integer
0 <= Choice_9_2_8 <= 1 Integer
0 <= Choice_9_2_9 <= 1 Integer
0 <= Choice_9_3_1 <= 1 Integer
0 <= Choice_9_3_2 <= 1 Integer
0 <= Choice_9_3_3 <= 1 Integer
0 <= Choice_9_3_4 <= 1 Integer
0 <= Choice_9_3_5 <= 1 Integer
0 <= Choice_9_3_6 <= 1 Integer
0 <= Choice_9_3_7 <= 1 Integer
0 <= Choice_9_3_8 <= 1 Integer
0 <= Choice_9_3_9 <= 1 Integer
0 <= Choice_9_4_1 <= 1 Integer
0 <= Choice_9_4_2 <= 1 Integer
0 <= Choice_9_4_3 <= 1 Integer
0 <= Choice_9_4_4 <= 1 Integer
0 <= Choice_9_4_5 <= 1 Integer
0 <= Choice_9_4_6 <= 1 Integer
0 <= Choice_9_4_7 <= 1 Integer
0 <= Choice_9_4_8 <= 1 Integer
0 <= Choice_9_4_9 <= 1 Integer
0 <= Choice_9_5_1 <= 1 Integer
0 <= Choice_9_5_2 <= 1 Integer
0 <= Choice_9_5_3 <= 1 Integer
0 <= Choice_9_5_4 <= 1 Integer
0 <= Choice_9_5_5 <= 1 Integer
0 <= Choice_9_5_6 <= 1 Integer
0 <= Choice_9_5_7 <= 1 Integer
0 <= Choice_9_5_8 <= 1 Integer
0 <= Choice_9_5_9 <= 1 Integer
0 <= Choice_9_6_1 <= 1 Integer
0 <= Choice_9_6_2 <= 1 Integer
0 <= Choice_9_6_3 <= 1 Integer
0 <= Choice_9_6_4 <= 1 Integer
0 <= Choice_9_6_5 <= 1 Integer
0 <= Choice_9_6_6 <= 1 Integer
0 <= Choice_9_6_7 <= 1 Integer
0 <= Choice_9_6_8 <= 1 Integer
0 <= Choice_9_6_9 <= 1 Integer
0 <= Choice_9_7_1 <= 1 Integer
0 <= Choice_9_7_2 <= 1 Integer
0 <= Choice_9_7_3 <= 1 Integer
0 <= Choice_9_7_4 <= 1 Integer
0 <= Choice_9_7_5 <= 1 Integer
0 <= Choice_9_7_6 <= 1 Integer
0 <= Choice_9_7_7 <= 1 Integer
0 <= Choice_9_7_8 <= 1 Integer
0 <= Choice_9_7_9 <= 1 Integer
0 <= Choice_9_8_1 <= 1 Integer
0 <= Choice_9_8_2 <= 1 Integer
0 <= Choice_9_8_3 <= 1 Integer
0 <= Choice_9_8_4 <= 1 Integer
0 <= Choice_9_8_5 <= 1 Integer
0 <= Choice_9_8_6 <= 1 Integer
0 <= Choice_9_8_7 <= 1 Integer
0 <= Choice_9_8_8 <= 1 Integer
0 <= Choice_9_8_9 <= 1 Integer
0 <= Choice_9_9_1 <= 1 Integer
0 <= Choice_9_9_2 <= 1 Integer
0 <= Choice_9_9_3 <= 1 Integer
0 <= Choice_9_9_4 <= 1 Integer
0 <= Choice_9_9_5 <= 1 Integer
0 <= Choice_9_9_6 <= 1 Integer
0 <= Choice_9_9_7 <= 1 Integer
0 <= Choice_9_9_8 <= 1 Integer
0 <= Choice_9_9_9 <= 1 Integer
__dummy = 0 Continuous
In [16]:
"""
The Sudoku Problem Formulation for the PuLP Modeller

Authors: Antony Phillips, Dr Stuart Mitcehll
"""

# Import PuLP modeler functions
from pulp import *

# A list of strings from "1" to "9" is created
Sequence = ["1", "2", "3", "4", "5", "6", "7", "8", "9"]

# The Vals, Rows and Cols sequences all follow this form
Vals = Sequence
Rows = Sequence
Cols = Sequence

# The boxes list is created, with the row and column index of each square in each box
Boxes =[]
for i in range(3):
    for j in range(3):
        Boxes += [[(Rows[3*i+k],Cols[3*j+l]) for k in range(3) for l in range(3)]]

# The prob variable is created to contain the problem data        
prob = LpProblem("Sudoku Problem",LpMinimize)

# The problem variables are created
choices = LpVariable.dicts("Choice",(Vals,Rows,Cols),0,1)

# Minimum L1 norm
#prob += lpSum([choices[v][r][c] for v in Vals for r in Rows for c in Cols])
prob += 0
# A constraint ensuring that only one value can be in each square is created
for r in Rows:
    for c in Cols:
        prob += lpSum([choices[v][r][c] for v in Vals]) == 1, ""

# The row, column and box constraints are added for each value
for v in Vals:
    for r in Rows:
        prob += lpSum([choices[v][r][c] for c in Cols]) == 1,""
        
    for c in Cols:
        prob += lpSum([choices[v][r][c] for r in Rows]) == 1,""

    for b in Boxes:
        prob += lpSum([choices[v][r][c] for (r,c) in b]) == 1,""
                        
# The starting numbers are entered as constraints                
prob += choices["5"]["1"]["1"] == 1,""
prob += choices["6"]["2"]["1"] == 1,""
prob += choices["8"]["4"]["1"] == 1,""
prob += choices["4"]["5"]["1"] == 1,""
prob += choices["7"]["6"]["1"] == 1,""
prob += choices["3"]["1"]["2"] == 1,""
prob += choices["9"]["3"]["2"] == 1,""
prob += choices["6"]["7"]["2"] == 1,""
prob += choices["8"]["3"]["3"] == 1,""
prob += choices["1"]["2"]["4"] == 1,""
prob += choices["8"]["5"]["4"] == 1,""
prob += choices["4"]["8"]["4"] == 1,""
prob += choices["7"]["1"]["5"] == 1,""
prob += choices["9"]["2"]["5"] == 1,""
prob += choices["6"]["4"]["5"] == 1,""
prob += choices["2"]["6"]["5"] == 1,""
prob += choices["1"]["8"]["5"] == 1,""
prob += choices["8"]["9"]["5"] == 1,""
prob += choices["5"]["2"]["6"] == 1,""
prob += choices["3"]["5"]["6"] == 1,""
prob += choices["9"]["8"]["6"] == 1,""
prob += choices["2"]["7"]["7"] == 1,""
prob += choices["6"]["3"]["8"] == 1,""
prob += choices["8"]["7"]["8"] == 1,""
prob += choices["7"]["9"]["8"] == 1,""
#prob += choices["3"]["4"]["9"] == 1,""
#prob += choices["1"]["5"]["9"] == 1,""
#prob += choices["6"]["6"]["9"] == 1,""
#prob += choices["5"]["8"]["9"] == 1,""

# The problem data is written to an .lp file
prob.writeLP("Sudoku.lp")

# The problem is solved using PuLP's choice of Solver
prob.solve()

# The status of the solution is printed to the screen
print "Status:", LpStatus[prob.status]

# A file called sudokuout.txt is created/overwritten for writing to
sudokuout = open('sudokuout2.txt','w')

# The solution is written to the sudokuout.txt file 
for r in Rows:
    if r == "1" or r == "4" or r == "7":
                    sudokuout.write("+-------+-------+-------+\n")
    for c in Cols:
        for v in Vals:
            if value(choices[v][r][c])==1:
                               
                if c == "1" or c == "4" or c =="7":
                    sudokuout.write("| ")
                    
                sudokuout.write(v + " ")
                
                if c == "9":
                    sudokuout.write("|\n")
sudokuout.write("+-------+-------+-------+")                    
sudokuout.close()

# The location of the solution is give to the user
print "Solution Written to sudokuout2.txt"
Status: Optimal
Solution Written to sudokuout2.txt
In [17]:
value(choices['2']['2']['1'])
Out[17]:
$$0.0$$
In [18]:
prob
Out[18]:
Sudoku Problem:
MINIMIZE
0*__dummy + 0
SUBJECT TO
_C1: Choice_1_1_1 + Choice_2_1_1 + Choice_3_1_1 + Choice_4_1_1 + Choice_5_1_1
 + Choice_6_1_1 + Choice_7_1_1 + Choice_8_1_1 + Choice_9_1_1 = 1

_C2: Choice_1_1_2 + Choice_2_1_2 + Choice_3_1_2 + Choice_4_1_2 + Choice_5_1_2
 + Choice_6_1_2 + Choice_7_1_2 + Choice_8_1_2 + Choice_9_1_2 = 1

_C3: Choice_1_1_3 + Choice_2_1_3 + Choice_3_1_3 + Choice_4_1_3 + Choice_5_1_3
 + Choice_6_1_3 + Choice_7_1_3 + Choice_8_1_3 + Choice_9_1_3 = 1

_C4: Choice_1_1_4 + Choice_2_1_4 + Choice_3_1_4 + Choice_4_1_4 + Choice_5_1_4
 + Choice_6_1_4 + Choice_7_1_4 + Choice_8_1_4 + Choice_9_1_4 = 1

_C5: Choice_1_1_5 + Choice_2_1_5 + Choice_3_1_5 + Choice_4_1_5 + Choice_5_1_5
 + Choice_6_1_5 + Choice_7_1_5 + Choice_8_1_5 + Choice_9_1_5 = 1

_C6: Choice_1_1_6 + Choice_2_1_6 + Choice_3_1_6 + Choice_4_1_6 + Choice_5_1_6
 + Choice_6_1_6 + Choice_7_1_6 + Choice_8_1_6 + Choice_9_1_6 = 1

_C7: Choice_1_1_7 + Choice_2_1_7 + Choice_3_1_7 + Choice_4_1_7 + Choice_5_1_7
 + Choice_6_1_7 + Choice_7_1_7 + Choice_8_1_7 + Choice_9_1_7 = 1

_C8: Choice_1_1_8 + Choice_2_1_8 + Choice_3_1_8 + Choice_4_1_8 + Choice_5_1_8
 + Choice_6_1_8 + Choice_7_1_8 + Choice_8_1_8 + Choice_9_1_8 = 1

_C9: Choice_1_1_9 + Choice_2_1_9 + Choice_3_1_9 + Choice_4_1_9 + Choice_5_1_9
 + Choice_6_1_9 + Choice_7_1_9 + Choice_8_1_9 + Choice_9_1_9 = 1

_C10: Choice_1_2_1 + Choice_2_2_1 + Choice_3_2_1 + Choice_4_2_1 + Choice_5_2_1
 + Choice_6_2_1 + Choice_7_2_1 + Choice_8_2_1 + Choice_9_2_1 = 1

_C11: Choice_1_2_2 + Choice_2_2_2 + Choice_3_2_2 + Choice_4_2_2 + Choice_5_2_2
 + Choice_6_2_2 + Choice_7_2_2 + Choice_8_2_2 + Choice_9_2_2 = 1

_C12: Choice_1_2_3 + Choice_2_2_3 + Choice_3_2_3 + Choice_4_2_3 + Choice_5_2_3
 + Choice_6_2_3 + Choice_7_2_3 + Choice_8_2_3 + Choice_9_2_3 = 1

_C13: Choice_1_2_4 + Choice_2_2_4 + Choice_3_2_4 + Choice_4_2_4 + Choice_5_2_4
 + Choice_6_2_4 + Choice_7_2_4 + Choice_8_2_4 + Choice_9_2_4 = 1

_C14: Choice_1_2_5 + Choice_2_2_5 + Choice_3_2_5 + Choice_4_2_5 + Choice_5_2_5
 + Choice_6_2_5 + Choice_7_2_5 + Choice_8_2_5 + Choice_9_2_5 = 1

_C15: Choice_1_2_6 + Choice_2_2_6 + Choice_3_2_6 + Choice_4_2_6 + Choice_5_2_6
 + Choice_6_2_6 + Choice_7_2_6 + Choice_8_2_6 + Choice_9_2_6 = 1

_C16: Choice_1_2_7 + Choice_2_2_7 + Choice_3_2_7 + Choice_4_2_7 + Choice_5_2_7
 + Choice_6_2_7 + Choice_7_2_7 + Choice_8_2_7 + Choice_9_2_7 = 1

_C17: Choice_1_2_8 + Choice_2_2_8 + Choice_3_2_8 + Choice_4_2_8 + Choice_5_2_8
 + Choice_6_2_8 + Choice_7_2_8 + Choice_8_2_8 + Choice_9_2_8 = 1

_C18: Choice_1_2_9 + Choice_2_2_9 + Choice_3_2_9 + Choice_4_2_9 + Choice_5_2_9
 + Choice_6_2_9 + Choice_7_2_9 + Choice_8_2_9 + Choice_9_2_9 = 1

_C19: Choice_1_3_1 + Choice_2_3_1 + Choice_3_3_1 + Choice_4_3_1 + Choice_5_3_1
 + Choice_6_3_1 + Choice_7_3_1 + Choice_8_3_1 + Choice_9_3_1 = 1

_C20: Choice_1_3_2 + Choice_2_3_2 + Choice_3_3_2 + Choice_4_3_2 + Choice_5_3_2
 + Choice_6_3_2 + Choice_7_3_2 + Choice_8_3_2 + Choice_9_3_2 = 1

_C21: Choice_1_3_3 + Choice_2_3_3 + Choice_3_3_3 + Choice_4_3_3 + Choice_5_3_3
 + Choice_6_3_3 + Choice_7_3_3 + Choice_8_3_3 + Choice_9_3_3 = 1

_C22: Choice_1_3_4 + Choice_2_3_4 + Choice_3_3_4 + Choice_4_3_4 + Choice_5_3_4
 + Choice_6_3_4 + Choice_7_3_4 + Choice_8_3_4 + Choice_9_3_4 = 1

_C23: Choice_1_3_5 + Choice_2_3_5 + Choice_3_3_5 + Choice_4_3_5 + Choice_5_3_5
 + Choice_6_3_5 + Choice_7_3_5 + Choice_8_3_5 + Choice_9_3_5 = 1

_C24: Choice_1_3_6 + Choice_2_3_6 + Choice_3_3_6 + Choice_4_3_6 + Choice_5_3_6
 + Choice_6_3_6 + Choice_7_3_6 + Choice_8_3_6 + Choice_9_3_6 = 1

_C25: Choice_1_3_7 + Choice_2_3_7 + Choice_3_3_7 + Choice_4_3_7 + Choice_5_3_7
 + Choice_6_3_7 + Choice_7_3_7 + Choice_8_3_7 + Choice_9_3_7 = 1

_C26: Choice_1_3_8 + Choice_2_3_8 + Choice_3_3_8 + Choice_4_3_8 + Choice_5_3_8
 + Choice_6_3_8 + Choice_7_3_8 + Choice_8_3_8 + Choice_9_3_8 = 1

_C27: Choice_1_3_9 + Choice_2_3_9 + Choice_3_3_9 + Choice_4_3_9 + Choice_5_3_9
 + Choice_6_3_9 + Choice_7_3_9 + Choice_8_3_9 + Choice_9_3_9 = 1

_C28: Choice_1_4_1 + Choice_2_4_1 + Choice_3_4_1 + Choice_4_4_1 + Choice_5_4_1
 + Choice_6_4_1 + Choice_7_4_1 + Choice_8_4_1 + Choice_9_4_1 = 1

_C29: Choice_1_4_2 + Choice_2_4_2 + Choice_3_4_2 + Choice_4_4_2 + Choice_5_4_2
 + Choice_6_4_2 + Choice_7_4_2 + Choice_8_4_2 + Choice_9_4_2 = 1

_C30: Choice_1_4_3 + Choice_2_4_3 + Choice_3_4_3 + Choice_4_4_3 + Choice_5_4_3
 + Choice_6_4_3 + Choice_7_4_3 + Choice_8_4_3 + Choice_9_4_3 = 1

_C31: Choice_1_4_4 + Choice_2_4_4 + Choice_3_4_4 + Choice_4_4_4 + Choice_5_4_4
 + Choice_6_4_4 + Choice_7_4_4 + Choice_8_4_4 + Choice_9_4_4 = 1

_C32: Choice_1_4_5 + Choice_2_4_5 + Choice_3_4_5 + Choice_4_4_5 + Choice_5_4_5
 + Choice_6_4_5 + Choice_7_4_5 + Choice_8_4_5 + Choice_9_4_5 = 1

_C33: Choice_1_4_6 + Choice_2_4_6 + Choice_3_4_6 + Choice_4_4_6 + Choice_5_4_6
 + Choice_6_4_6 + Choice_7_4_6 + Choice_8_4_6 + Choice_9_4_6 = 1

_C34: Choice_1_4_7 + Choice_2_4_7 + Choice_3_4_7 + Choice_4_4_7 + Choice_5_4_7
 + Choice_6_4_7 + Choice_7_4_7 + Choice_8_4_7 + Choice_9_4_7 = 1

_C35: Choice_1_4_8 + Choice_2_4_8 + Choice_3_4_8 + Choice_4_4_8 + Choice_5_4_8
 + Choice_6_4_8 + Choice_7_4_8 + Choice_8_4_8 + Choice_9_4_8 = 1

_C36: Choice_1_4_9 + Choice_2_4_9 + Choice_3_4_9 + Choice_4_4_9 + Choice_5_4_9
 + Choice_6_4_9 + Choice_7_4_9 + Choice_8_4_9 + Choice_9_4_9 = 1

_C37: Choice_1_5_1 + Choice_2_5_1 + Choice_3_5_1 + Choice_4_5_1 + Choice_5_5_1
 + Choice_6_5_1 + Choice_7_5_1 + Choice_8_5_1 + Choice_9_5_1 = 1

_C38: Choice_1_5_2 + Choice_2_5_2 + Choice_3_5_2 + Choice_4_5_2 + Choice_5_5_2
 + Choice_6_5_2 + Choice_7_5_2 + Choice_8_5_2 + Choice_9_5_2 = 1

_C39: Choice_1_5_3 + Choice_2_5_3 + Choice_3_5_3 + Choice_4_5_3 + Choice_5_5_3
 + Choice_6_5_3 + Choice_7_5_3 + Choice_8_5_3 + Choice_9_5_3 = 1

_C40: Choice_1_5_4 + Choice_2_5_4 + Choice_3_5_4 + Choice_4_5_4 + Choice_5_5_4
 + Choice_6_5_4 + Choice_7_5_4 + Choice_8_5_4 + Choice_9_5_4 = 1

_C41: Choice_1_5_5 + Choice_2_5_5 + Choice_3_5_5 + Choice_4_5_5 + Choice_5_5_5
 + Choice_6_5_5 + Choice_7_5_5 + Choice_8_5_5 + Choice_9_5_5 = 1

_C42: Choice_1_5_6 + Choice_2_5_6 + Choice_3_5_6 + Choice_4_5_6 + Choice_5_5_6
 + Choice_6_5_6 + Choice_7_5_6 + Choice_8_5_6 + Choice_9_5_6 = 1

_C43: Choice_1_5_7 + Choice_2_5_7 + Choice_3_5_7 + Choice_4_5_7 + Choice_5_5_7
 + Choice_6_5_7 + Choice_7_5_7 + Choice_8_5_7 + Choice_9_5_7 = 1

_C44: Choice_1_5_8 + Choice_2_5_8 + Choice_3_5_8 + Choice_4_5_8 + Choice_5_5_8
 + Choice_6_5_8 + Choice_7_5_8 + Choice_8_5_8 + Choice_9_5_8 = 1

_C45: Choice_1_5_9 + Choice_2_5_9 + Choice_3_5_9 + Choice_4_5_9 + Choice_5_5_9
 + Choice_6_5_9 + Choice_7_5_9 + Choice_8_5_9 + Choice_9_5_9 = 1

_C46: Choice_1_6_1 + Choice_2_6_1 + Choice_3_6_1 + Choice_4_6_1 + Choice_5_6_1
 + Choice_6_6_1 + Choice_7_6_1 + Choice_8_6_1 + Choice_9_6_1 = 1

_C47: Choice_1_6_2 + Choice_2_6_2 + Choice_3_6_2 + Choice_4_6_2 + Choice_5_6_2
 + Choice_6_6_2 + Choice_7_6_2 + Choice_8_6_2 + Choice_9_6_2 = 1

_C48: Choice_1_6_3 + Choice_2_6_3 + Choice_3_6_3 + Choice_4_6_3 + Choice_5_6_3
 + Choice_6_6_3 + Choice_7_6_3 + Choice_8_6_3 + Choice_9_6_3 = 1

_C49: Choice_1_6_4 + Choice_2_6_4 + Choice_3_6_4 + Choice_4_6_4 + Choice_5_6_4
 + Choice_6_6_4 + Choice_7_6_4 + Choice_8_6_4 + Choice_9_6_4 = 1

_C50: Choice_1_6_5 + Choice_2_6_5 + Choice_3_6_5 + Choice_4_6_5 + Choice_5_6_5
 + Choice_6_6_5 + Choice_7_6_5 + Choice_8_6_5 + Choice_9_6_5 = 1

_C51: Choice_1_6_6 + Choice_2_6_6 + Choice_3_6_6 + Choice_4_6_6 + Choice_5_6_6
 + Choice_6_6_6 + Choice_7_6_6 + Choice_8_6_6 + Choice_9_6_6 = 1

_C52: Choice_1_6_7 + Choice_2_6_7 + Choice_3_6_7 + Choice_4_6_7 + Choice_5_6_7
 + Choice_6_6_7 + Choice_7_6_7 + Choice_8_6_7 + Choice_9_6_7 = 1

_C53: Choice_1_6_8 + Choice_2_6_8 + Choice_3_6_8 + Choice_4_6_8 + Choice_5_6_8
 + Choice_6_6_8 + Choice_7_6_8 + Choice_8_6_8 + Choice_9_6_8 = 1

_C54: Choice_1_6_9 + Choice_2_6_9 + Choice_3_6_9 + Choice_4_6_9 + Choice_5_6_9
 + Choice_6_6_9 + Choice_7_6_9 + Choice_8_6_9 + Choice_9_6_9 = 1

_C55: Choice_1_7_1 + Choice_2_7_1 + Choice_3_7_1 + Choice_4_7_1 + Choice_5_7_1
 + Choice_6_7_1 + Choice_7_7_1 + Choice_8_7_1 + Choice_9_7_1 = 1

_C56: Choice_1_7_2 + Choice_2_7_2 + Choice_3_7_2 + Choice_4_7_2 + Choice_5_7_2
 + Choice_6_7_2 + Choice_7_7_2 + Choice_8_7_2 + Choice_9_7_2 = 1

_C57: Choice_1_7_3 + Choice_2_7_3 + Choice_3_7_3 + Choice_4_7_3 + Choice_5_7_3
 + Choice_6_7_3 + Choice_7_7_3 + Choice_8_7_3 + Choice_9_7_3 = 1

_C58: Choice_1_7_4 + Choice_2_7_4 + Choice_3_7_4 + Choice_4_7_4 + Choice_5_7_4
 + Choice_6_7_4 + Choice_7_7_4 + Choice_8_7_4 + Choice_9_7_4 = 1

_C59: Choice_1_7_5 + Choice_2_7_5 + Choice_3_7_5 + Choice_4_7_5 + Choice_5_7_5
 + Choice_6_7_5 + Choice_7_7_5 + Choice_8_7_5 + Choice_9_7_5 = 1

_C60: Choice_1_7_6 + Choice_2_7_6 + Choice_3_7_6 + Choice_4_7_6 + Choice_5_7_6
 + Choice_6_7_6 + Choice_7_7_6 + Choice_8_7_6 + Choice_9_7_6 = 1

_C61: Choice_1_7_7 + Choice_2_7_7 + Choice_3_7_7 + Choice_4_7_7 + Choice_5_7_7
 + Choice_6_7_7 + Choice_7_7_7 + Choice_8_7_7 + Choice_9_7_7 = 1

_C62: Choice_1_7_8 + Choice_2_7_8 + Choice_3_7_8 + Choice_4_7_8 + Choice_5_7_8
 + Choice_6_7_8 + Choice_7_7_8 + Choice_8_7_8 + Choice_9_7_8 = 1

_C63: Choice_1_7_9 + Choice_2_7_9 + Choice_3_7_9 + Choice_4_7_9 + Choice_5_7_9
 + Choice_6_7_9 + Choice_7_7_9 + Choice_8_7_9 + Choice_9_7_9 = 1

_C64: Choice_1_8_1 + Choice_2_8_1 + Choice_3_8_1 + Choice_4_8_1 + Choice_5_8_1
 + Choice_6_8_1 + Choice_7_8_1 + Choice_8_8_1 + Choice_9_8_1 = 1

_C65: Choice_1_8_2 + Choice_2_8_2 + Choice_3_8_2 + Choice_4_8_2 + Choice_5_8_2
 + Choice_6_8_2 + Choice_7_8_2 + Choice_8_8_2 + Choice_9_8_2 = 1

_C66: Choice_1_8_3 + Choice_2_8_3 + Choice_3_8_3 + Choice_4_8_3 + Choice_5_8_3
 + Choice_6_8_3 + Choice_7_8_3 + Choice_8_8_3 + Choice_9_8_3 = 1

_C67: Choice_1_8_4 + Choice_2_8_4 + Choice_3_8_4 + Choice_4_8_4 + Choice_5_8_4
 + Choice_6_8_4 + Choice_7_8_4 + Choice_8_8_4 + Choice_9_8_4 = 1

_C68: Choice_1_8_5 + Choice_2_8_5 + Choice_3_8_5 + Choice_4_8_5 + Choice_5_8_5
 + Choice_6_8_5 + Choice_7_8_5 + Choice_8_8_5 + Choice_9_8_5 = 1

_C69: Choice_1_8_6 + Choice_2_8_6 + Choice_3_8_6 + Choice_4_8_6 + Choice_5_8_6
 + Choice_6_8_6 + Choice_7_8_6 + Choice_8_8_6 + Choice_9_8_6 = 1

_C70: Choice_1_8_7 + Choice_2_8_7 + Choice_3_8_7 + Choice_4_8_7 + Choice_5_8_7
 + Choice_6_8_7 + Choice_7_8_7 + Choice_8_8_7 + Choice_9_8_7 = 1

_C71: Choice_1_8_8 + Choice_2_8_8 + Choice_3_8_8 + Choice_4_8_8 + Choice_5_8_8
 + Choice_6_8_8 + Choice_7_8_8 + Choice_8_8_8 + Choice_9_8_8 = 1

_C72: Choice_1_8_9 + Choice_2_8_9 + Choice_3_8_9 + Choice_4_8_9 + Choice_5_8_9
 + Choice_6_8_9 + Choice_7_8_9 + Choice_8_8_9 + Choice_9_8_9 = 1

_C73: Choice_1_9_1 + Choice_2_9_1 + Choice_3_9_1 + Choice_4_9_1 + Choice_5_9_1
 + Choice_6_9_1 + Choice_7_9_1 + Choice_8_9_1 + Choice_9_9_1 = 1

_C74: Choice_1_9_2 + Choice_2_9_2 + Choice_3_9_2 + Choice_4_9_2 + Choice_5_9_2
 + Choice_6_9_2 + Choice_7_9_2 + Choice_8_9_2 + Choice_9_9_2 = 1

_C75: Choice_1_9_3 + Choice_2_9_3 + Choice_3_9_3 + Choice_4_9_3 + Choice_5_9_3
 + Choice_6_9_3 + Choice_7_9_3 + Choice_8_9_3 + Choice_9_9_3 = 1

_C76: Choice_1_9_4 + Choice_2_9_4 + Choice_3_9_4 + Choice_4_9_4 + Choice_5_9_4
 + Choice_6_9_4 + Choice_7_9_4 + Choice_8_9_4 + Choice_9_9_4 = 1

_C77: Choice_1_9_5 + Choice_2_9_5 + Choice_3_9_5 + Choice_4_9_5 + Choice_5_9_5
 + Choice_6_9_5 + Choice_7_9_5 + Choice_8_9_5 + Choice_9_9_5 = 1

_C78: Choice_1_9_6 + Choice_2_9_6 + Choice_3_9_6 + Choice_4_9_6 + Choice_5_9_6
 + Choice_6_9_6 + Choice_7_9_6 + Choice_8_9_6 + Choice_9_9_6 = 1

_C79: Choice_1_9_7 + Choice_2_9_7 + Choice_3_9_7 + Choice_4_9_7 + Choice_5_9_7
 + Choice_6_9_7 + Choice_7_9_7 + Choice_8_9_7 + Choice_9_9_7 = 1

_C80: Choice_1_9_8 + Choice_2_9_8 + Choice_3_9_8 + Choice_4_9_8 + Choice_5_9_8
 + Choice_6_9_8 + Choice_7_9_8 + Choice_8_9_8 + Choice_9_9_8 = 1

_C81: Choice_1_9_9 + Choice_2_9_9 + Choice_3_9_9 + Choice_4_9_9 + Choice_5_9_9
 + Choice_6_9_9 + Choice_7_9_9 + Choice_8_9_9 + Choice_9_9_9 = 1

_C82: Choice_1_1_1 + Choice_1_1_2 + Choice_1_1_3 + Choice_1_1_4 + Choice_1_1_5
 + Choice_1_1_6 + Choice_1_1_7 + Choice_1_1_8 + Choice_1_1_9 = 1

_C83: Choice_1_2_1 + Choice_1_2_2 + Choice_1_2_3 + Choice_1_2_4 + Choice_1_2_5
 + Choice_1_2_6 + Choice_1_2_7 + Choice_1_2_8 + Choice_1_2_9 = 1

_C84: Choice_1_3_1 + Choice_1_3_2 + Choice_1_3_3 + Choice_1_3_4 + Choice_1_3_5
 + Choice_1_3_6 + Choice_1_3_7 + Choice_1_3_8 + Choice_1_3_9 = 1

_C85: Choice_1_4_1 + Choice_1_4_2 + Choice_1_4_3 + Choice_1_4_4 + Choice_1_4_5
 + Choice_1_4_6 + Choice_1_4_7 + Choice_1_4_8 + Choice_1_4_9 = 1

_C86: Choice_1_5_1 + Choice_1_5_2 + Choice_1_5_3 + Choice_1_5_4 + Choice_1_5_5
 + Choice_1_5_6 + Choice_1_5_7 + Choice_1_5_8 + Choice_1_5_9 = 1

_C87: Choice_1_6_1 + Choice_1_6_2 + Choice_1_6_3 + Choice_1_6_4 + Choice_1_6_5
 + Choice_1_6_6 + Choice_1_6_7 + Choice_1_6_8 + Choice_1_6_9 = 1

_C88: Choice_1_7_1 + Choice_1_7_2 + Choice_1_7_3 + Choice_1_7_4 + Choice_1_7_5
 + Choice_1_7_6 + Choice_1_7_7 + Choice_1_7_8 + Choice_1_7_9 = 1

_C89: Choice_1_8_1 + Choice_1_8_2 + Choice_1_8_3 + Choice_1_8_4 + Choice_1_8_5
 + Choice_1_8_6 + Choice_1_8_7 + Choice_1_8_8 + Choice_1_8_9 = 1

_C90: Choice_1_9_1 + Choice_1_9_2 + Choice_1_9_3 + Choice_1_9_4 + Choice_1_9_5
 + Choice_1_9_6 + Choice_1_9_7 + Choice_1_9_8 + Choice_1_9_9 = 1

_C91: Choice_1_1_1 + Choice_1_2_1 + Choice_1_3_1 + Choice_1_4_1 + Choice_1_5_1
 + Choice_1_6_1 + Choice_1_7_1 + Choice_1_8_1 + Choice_1_9_1 = 1

_C92: Choice_1_1_2 + Choice_1_2_2 + Choice_1_3_2 + Choice_1_4_2 + Choice_1_5_2
 + Choice_1_6_2 + Choice_1_7_2 + Choice_1_8_2 + Choice_1_9_2 = 1

_C93: Choice_1_1_3 + Choice_1_2_3 + Choice_1_3_3 + Choice_1_4_3 + Choice_1_5_3
 + Choice_1_6_3 + Choice_1_7_3 + Choice_1_8_3 + Choice_1_9_3 = 1

_C94: Choice_1_1_4 + Choice_1_2_4 + Choice_1_3_4 + Choice_1_4_4 + Choice_1_5_4
 + Choice_1_6_4 + Choice_1_7_4 + Choice_1_8_4 + Choice_1_9_4 = 1

_C95: Choice_1_1_5 + Choice_1_2_5 + Choice_1_3_5 + Choice_1_4_5 + Choice_1_5_5
 + Choice_1_6_5 + Choice_1_7_5 + Choice_1_8_5 + Choice_1_9_5 = 1

_C96: Choice_1_1_6 + Choice_1_2_6 + Choice_1_3_6 + Choice_1_4_6 + Choice_1_5_6
 + Choice_1_6_6 + Choice_1_7_6 + Choice_1_8_6 + Choice_1_9_6 = 1

_C97: Choice_1_1_7 + Choice_1_2_7 + Choice_1_3_7 + Choice_1_4_7 + Choice_1_5_7
 + Choice_1_6_7 + Choice_1_7_7 + Choice_1_8_7 + Choice_1_9_7 = 1

_C98: Choice_1_1_8 + Choice_1_2_8 + Choice_1_3_8 + Choice_1_4_8 + Choice_1_5_8
 + Choice_1_6_8 + Choice_1_7_8 + Choice_1_8_8 + Choice_1_9_8 = 1

_C99: Choice_1_1_9 + Choice_1_2_9 + Choice_1_3_9 + Choice_1_4_9 + Choice_1_5_9
 + Choice_1_6_9 + Choice_1_7_9 + Choice_1_8_9 + Choice_1_9_9 = 1

_C100: Choice_1_1_1 + Choice_1_1_2 + Choice_1_1_3 + Choice_1_2_1
 + Choice_1_2_2 + Choice_1_2_3 + Choice_1_3_1 + Choice_1_3_2 + Choice_1_3_3
 = 1

_C101: Choice_1_1_4 + Choice_1_1_5 + Choice_1_1_6 + Choice_1_2_4
 + Choice_1_2_5 + Choice_1_2_6 + Choice_1_3_4 + Choice_1_3_5 + Choice_1_3_6
 = 1

_C102: Choice_1_1_7 + Choice_1_1_8 + Choice_1_1_9 + Choice_1_2_7
 + Choice_1_2_8 + Choice_1_2_9 + Choice_1_3_7 + Choice_1_3_8 + Choice_1_3_9
 = 1

_C103: Choice_1_4_1 + Choice_1_4_2 + Choice_1_4_3 + Choice_1_5_1
 + Choice_1_5_2 + Choice_1_5_3 + Choice_1_6_1 + Choice_1_6_2 + Choice_1_6_3
 = 1

_C104: Choice_1_4_4 + Choice_1_4_5 + Choice_1_4_6 + Choice_1_5_4
 + Choice_1_5_5 + Choice_1_5_6 + Choice_1_6_4 + Choice_1_6_5 + Choice_1_6_6
 = 1

_C105: Choice_1_4_7 + Choice_1_4_8 + Choice_1_4_9 + Choice_1_5_7
 + Choice_1_5_8 + Choice_1_5_9 + Choice_1_6_7 + Choice_1_6_8 + Choice_1_6_9
 = 1

_C106: Choice_1_7_1 + Choice_1_7_2 + Choice_1_7_3 + Choice_1_8_1
 + Choice_1_8_2 + Choice_1_8_3 + Choice_1_9_1 + Choice_1_9_2 + Choice_1_9_3
 = 1

_C107: Choice_1_7_4 + Choice_1_7_5 + Choice_1_7_6 + Choice_1_8_4
 + Choice_1_8_5 + Choice_1_8_6 + Choice_1_9_4 + Choice_1_9_5 + Choice_1_9_6
 = 1

_C108: Choice_1_7_7 + Choice_1_7_8 + Choice_1_7_9 + Choice_1_8_7
 + Choice_1_8_8 + Choice_1_8_9 + Choice_1_9_7 + Choice_1_9_8 + Choice_1_9_9
 = 1

_C109: Choice_2_1_1 + Choice_2_1_2 + Choice_2_1_3 + Choice_2_1_4
 + Choice_2_1_5 + Choice_2_1_6 + Choice_2_1_7 + Choice_2_1_8 + Choice_2_1_9
 = 1

_C110: Choice_2_2_1 + Choice_2_2_2 + Choice_2_2_3 + Choice_2_2_4
 + Choice_2_2_5 + Choice_2_2_6 + Choice_2_2_7 + Choice_2_2_8 + Choice_2_2_9
 = 1

_C111: Choice_2_3_1 + Choice_2_3_2 + Choice_2_3_3 + Choice_2_3_4
 + Choice_2_3_5 + Choice_2_3_6 + Choice_2_3_7 + Choice_2_3_8 + Choice_2_3_9
 = 1

_C112: Choice_2_4_1 + Choice_2_4_2 + Choice_2_4_3 + Choice_2_4_4
 + Choice_2_4_5 + Choice_2_4_6 + Choice_2_4_7 + Choice_2_4_8 + Choice_2_4_9
 = 1

_C113: Choice_2_5_1 + Choice_2_5_2 + Choice_2_5_3 + Choice_2_5_4
 + Choice_2_5_5 + Choice_2_5_6 + Choice_2_5_7 + Choice_2_5_8 + Choice_2_5_9
 = 1

_C114: Choice_2_6_1 + Choice_2_6_2 + Choice_2_6_3 + Choice_2_6_4
 + Choice_2_6_5 + Choice_2_6_6 + Choice_2_6_7 + Choice_2_6_8 + Choice_2_6_9
 = 1

_C115: Choice_2_7_1 + Choice_2_7_2 + Choice_2_7_3 + Choice_2_7_4
 + Choice_2_7_5 + Choice_2_7_6 + Choice_2_7_7 + Choice_2_7_8 + Choice_2_7_9
 = 1

_C116: Choice_2_8_1 + Choice_2_8_2 + Choice_2_8_3 + Choice_2_8_4
 + Choice_2_8_5 + Choice_2_8_6 + Choice_2_8_7 + Choice_2_8_8 + Choice_2_8_9
 = 1

_C117: Choice_2_9_1 + Choice_2_9_2 + Choice_2_9_3 + Choice_2_9_4
 + Choice_2_9_5 + Choice_2_9_6 + Choice_2_9_7 + Choice_2_9_8 + Choice_2_9_9
 = 1

_C118: Choice_2_1_1 + Choice_2_2_1 + Choice_2_3_1 + Choice_2_4_1
 + Choice_2_5_1 + Choice_2_6_1 + Choice_2_7_1 + Choice_2_8_1 + Choice_2_9_1
 = 1

_C119: Choice_2_1_2 + Choice_2_2_2 + Choice_2_3_2 + Choice_2_4_2
 + Choice_2_5_2 + Choice_2_6_2 + Choice_2_7_2 + Choice_2_8_2 + Choice_2_9_2
 = 1

_C120: Choice_2_1_3 + Choice_2_2_3 + Choice_2_3_3 + Choice_2_4_3
 + Choice_2_5_3 + Choice_2_6_3 + Choice_2_7_3 + Choice_2_8_3 + Choice_2_9_3
 = 1

_C121: Choice_2_1_4 + Choice_2_2_4 + Choice_2_3_4 + Choice_2_4_4
 + Choice_2_5_4 + Choice_2_6_4 + Choice_2_7_4 + Choice_2_8_4 + Choice_2_9_4
 = 1

_C122: Choice_2_1_5 + Choice_2_2_5 + Choice_2_3_5 + Choice_2_4_5
 + Choice_2_5_5 + Choice_2_6_5 + Choice_2_7_5 + Choice_2_8_5 + Choice_2_9_5
 = 1

_C123: Choice_2_1_6 + Choice_2_2_6 + Choice_2_3_6 + Choice_2_4_6
 + Choice_2_5_6 + Choice_2_6_6 + Choice_2_7_6 + Choice_2_8_6 + Choice_2_9_6
 = 1

_C124: Choice_2_1_7 + Choice_2_2_7 + Choice_2_3_7 + Choice_2_4_7
 + Choice_2_5_7 + Choice_2_6_7 + Choice_2_7_7 + Choice_2_8_7 + Choice_2_9_7
 = 1

_C125: Choice_2_1_8 + Choice_2_2_8 + Choice_2_3_8 + Choice_2_4_8
 + Choice_2_5_8 + Choice_2_6_8 + Choice_2_7_8 + Choice_2_8_8 + Choice_2_9_8
 = 1

_C126: Choice_2_1_9 + Choice_2_2_9 + Choice_2_3_9 + Choice_2_4_9
 + Choice_2_5_9 + Choice_2_6_9 + Choice_2_7_9 + Choice_2_8_9 + Choice_2_9_9
 = 1

_C127: Choice_2_1_1 + Choice_2_1_2 + Choice_2_1_3 + Choice_2_2_1
 + Choice_2_2_2 + Choice_2_2_3 + Choice_2_3_1 + Choice_2_3_2 + Choice_2_3_3
 = 1

_C128: Choice_2_1_4 + Choice_2_1_5 + Choice_2_1_6 + Choice_2_2_4
 + Choice_2_2_5 + Choice_2_2_6 + Choice_2_3_4 + Choice_2_3_5 + Choice_2_3_6
 = 1

_C129: Choice_2_1_7 + Choice_2_1_8 + Choice_2_1_9 + Choice_2_2_7
 + Choice_2_2_8 + Choice_2_2_9 + Choice_2_3_7 + Choice_2_3_8 + Choice_2_3_9
 = 1

_C130: Choice_2_4_1 + Choice_2_4_2 + Choice_2_4_3 + Choice_2_5_1
 + Choice_2_5_2 + Choice_2_5_3 + Choice_2_6_1 + Choice_2_6_2 + Choice_2_6_3
 = 1

_C131: Choice_2_4_4 + Choice_2_4_5 + Choice_2_4_6 + Choice_2_5_4
 + Choice_2_5_5 + Choice_2_5_6 + Choice_2_6_4 + Choice_2_6_5 + Choice_2_6_6
 = 1

_C132: Choice_2_4_7 + Choice_2_4_8 + Choice_2_4_9 + Choice_2_5_7
 + Choice_2_5_8 + Choice_2_5_9 + Choice_2_6_7 + Choice_2_6_8 + Choice_2_6_9
 = 1

_C133: Choice_2_7_1 + Choice_2_7_2 + Choice_2_7_3 + Choice_2_8_1
 + Choice_2_8_2 + Choice_2_8_3 + Choice_2_9_1 + Choice_2_9_2 + Choice_2_9_3
 = 1

_C134: Choice_2_7_4 + Choice_2_7_5 + Choice_2_7_6 + Choice_2_8_4
 + Choice_2_8_5 + Choice_2_8_6 + Choice_2_9_4 + Choice_2_9_5 + Choice_2_9_6
 = 1

_C135: Choice_2_7_7 + Choice_2_7_8 + Choice_2_7_9 + Choice_2_8_7
 + Choice_2_8_8 + Choice_2_8_9 + Choice_2_9_7 + Choice_2_9_8 + Choice_2_9_9
 = 1

_C136: Choice_3_1_1 + Choice_3_1_2 + Choice_3_1_3 + Choice_3_1_4
 + Choice_3_1_5 + Choice_3_1_6 + Choice_3_1_7 + Choice_3_1_8 + Choice_3_1_9
 = 1

_C137: Choice_3_2_1 + Choice_3_2_2 + Choice_3_2_3 + Choice_3_2_4
 + Choice_3_2_5 + Choice_3_2_6 + Choice_3_2_7 + Choice_3_2_8 + Choice_3_2_9
 = 1

_C138: Choice_3_3_1 + Choice_3_3_2 + Choice_3_3_3 + Choice_3_3_4
 + Choice_3_3_5 + Choice_3_3_6 + Choice_3_3_7 + Choice_3_3_8 + Choice_3_3_9
 = 1

_C139: Choice_3_4_1 + Choice_3_4_2 + Choice_3_4_3 + Choice_3_4_4
 + Choice_3_4_5 + Choice_3_4_6 + Choice_3_4_7 + Choice_3_4_8 + Choice_3_4_9
 = 1

_C140: Choice_3_5_1 + Choice_3_5_2 + Choice_3_5_3 + Choice_3_5_4
 + Choice_3_5_5 + Choice_3_5_6 + Choice_3_5_7 + Choice_3_5_8 + Choice_3_5_9
 = 1

_C141: Choice_3_6_1 + Choice_3_6_2 + Choice_3_6_3 + Choice_3_6_4
 + Choice_3_6_5 + Choice_3_6_6 + Choice_3_6_7 + Choice_3_6_8 + Choice_3_6_9
 = 1

_C142: Choice_3_7_1 + Choice_3_7_2 + Choice_3_7_3 + Choice_3_7_4
 + Choice_3_7_5 + Choice_3_7_6 + Choice_3_7_7 + Choice_3_7_8 + Choice_3_7_9
 = 1

_C143: Choice_3_8_1 + Choice_3_8_2 + Choice_3_8_3 + Choice_3_8_4
 + Choice_3_8_5 + Choice_3_8_6 + Choice_3_8_7 + Choice_3_8_8 + Choice_3_8_9
 = 1

_C144: Choice_3_9_1 + Choice_3_9_2 + Choice_3_9_3 + Choice_3_9_4
 + Choice_3_9_5 + Choice_3_9_6 + Choice_3_9_7 + Choice_3_9_8 + Choice_3_9_9
 = 1

_C145: Choice_3_1_1 + Choice_3_2_1 + Choice_3_3_1 + Choice_3_4_1
 + Choice_3_5_1 + Choice_3_6_1 + Choice_3_7_1 + Choice_3_8_1 + Choice_3_9_1
 = 1

_C146: Choice_3_1_2 + Choice_3_2_2 + Choice_3_3_2 + Choice_3_4_2
 + Choice_3_5_2 + Choice_3_6_2 + Choice_3_7_2 + Choice_3_8_2 + Choice_3_9_2
 = 1

_C147: Choice_3_1_3 + Choice_3_2_3 + Choice_3_3_3 + Choice_3_4_3
 + Choice_3_5_3 + Choice_3_6_3 + Choice_3_7_3 + Choice_3_8_3 + Choice_3_9_3
 = 1

_C148: Choice_3_1_4 + Choice_3_2_4 + Choice_3_3_4 + Choice_3_4_4
 + Choice_3_5_4 + Choice_3_6_4 + Choice_3_7_4 + Choice_3_8_4 + Choice_3_9_4
 = 1

_C149: Choice_3_1_5 + Choice_3_2_5 + Choice_3_3_5 + Choice_3_4_5
 + Choice_3_5_5 + Choice_3_6_5 + Choice_3_7_5 + Choice_3_8_5 + Choice_3_9_5
 = 1

_C150: Choice_3_1_6 + Choice_3_2_6 + Choice_3_3_6 + Choice_3_4_6
 + Choice_3_5_6 + Choice_3_6_6 + Choice_3_7_6 + Choice_3_8_6 + Choice_3_9_6
 = 1

_C151: Choice_3_1_7 + Choice_3_2_7 + Choice_3_3_7 + Choice_3_4_7
 + Choice_3_5_7 + Choice_3_6_7 + Choice_3_7_7 + Choice_3_8_7 + Choice_3_9_7
 = 1

_C152: Choice_3_1_8 + Choice_3_2_8 + Choice_3_3_8 + Choice_3_4_8
 + Choice_3_5_8 + Choice_3_6_8 + Choice_3_7_8 + Choice_3_8_8 + Choice_3_9_8
 = 1

_C153: Choice_3_1_9 + Choice_3_2_9 + Choice_3_3_9 + Choice_3_4_9
 + Choice_3_5_9 + Choice_3_6_9 + Choice_3_7_9 + Choice_3_8_9 + Choice_3_9_9
 = 1

_C154: Choice_3_1_1 + Choice_3_1_2 + Choice_3_1_3 + Choice_3_2_1
 + Choice_3_2_2 + Choice_3_2_3 + Choice_3_3_1 + Choice_3_3_2 + Choice_3_3_3
 = 1

_C155: Choice_3_1_4 + Choice_3_1_5 + Choice_3_1_6 + Choice_3_2_4
 + Choice_3_2_5 + Choice_3_2_6 + Choice_3_3_4 + Choice_3_3_5 + Choice_3_3_6
 = 1

_C156: Choice_3_1_7 + Choice_3_1_8 + Choice_3_1_9 + Choice_3_2_7
 + Choice_3_2_8 + Choice_3_2_9 + Choice_3_3_7 + Choice_3_3_8 + Choice_3_3_9
 = 1

_C157: Choice_3_4_1 + Choice_3_4_2 + Choice_3_4_3 + Choice_3_5_1
 + Choice_3_5_2 + Choice_3_5_3 + Choice_3_6_1 + Choice_3_6_2 + Choice_3_6_3
 = 1

_C158: Choice_3_4_4 + Choice_3_4_5 + Choice_3_4_6 + Choice_3_5_4
 + Choice_3_5_5 + Choice_3_5_6 + Choice_3_6_4 + Choice_3_6_5 + Choice_3_6_6
 = 1

_C159: Choice_3_4_7 + Choice_3_4_8 + Choice_3_4_9 + Choice_3_5_7
 + Choice_3_5_8 + Choice_3_5_9 + Choice_3_6_7 + Choice_3_6_8 + Choice_3_6_9
 = 1

_C160: Choice_3_7_1 + Choice_3_7_2 + Choice_3_7_3 + Choice_3_8_1
 + Choice_3_8_2 + Choice_3_8_3 + Choice_3_9_1 + Choice_3_9_2 + Choice_3_9_3
 = 1

_C161: Choice_3_7_4 + Choice_3_7_5 + Choice_3_7_6 + Choice_3_8_4
 + Choice_3_8_5 + Choice_3_8_6 + Choice_3_9_4 + Choice_3_9_5 + Choice_3_9_6
 = 1

_C162: Choice_3_7_7 + Choice_3_7_8 + Choice_3_7_9 + Choice_3_8_7
 + Choice_3_8_8 + Choice_3_8_9 + Choice_3_9_7 + Choice_3_9_8 + Choice_3_9_9
 = 1

_C163: Choice_4_1_1 + Choice_4_1_2 + Choice_4_1_3 + Choice_4_1_4
 + Choice_4_1_5 + Choice_4_1_6 + Choice_4_1_7 + Choice_4_1_8 + Choice_4_1_9
 = 1

_C164: Choice_4_2_1 + Choice_4_2_2 + Choice_4_2_3 + Choice_4_2_4
 + Choice_4_2_5 + Choice_4_2_6 + Choice_4_2_7 + Choice_4_2_8 + Choice_4_2_9
 = 1

_C165: Choice_4_3_1 + Choice_4_3_2 + Choice_4_3_3 + Choice_4_3_4
 + Choice_4_3_5 + Choice_4_3_6 + Choice_4_3_7 + Choice_4_3_8 + Choice_4_3_9
 = 1

_C166: Choice_4_4_1 + Choice_4_4_2 + Choice_4_4_3 + Choice_4_4_4
 + Choice_4_4_5 + Choice_4_4_6 + Choice_4_4_7 + Choice_4_4_8 + Choice_4_4_9
 = 1

_C167: Choice_4_5_1 + Choice_4_5_2 + Choice_4_5_3 + Choice_4_5_4
 + Choice_4_5_5 + Choice_4_5_6 + Choice_4_5_7 + Choice_4_5_8 + Choice_4_5_9
 = 1

_C168: Choice_4_6_1 + Choice_4_6_2 + Choice_4_6_3 + Choice_4_6_4
 + Choice_4_6_5 + Choice_4_6_6 + Choice_4_6_7 + Choice_4_6_8 + Choice_4_6_9
 = 1

_C169: Choice_4_7_1 + Choice_4_7_2 + Choice_4_7_3 + Choice_4_7_4
 + Choice_4_7_5 + Choice_4_7_6 + Choice_4_7_7 + Choice_4_7_8 + Choice_4_7_9
 = 1

_C170: Choice_4_8_1 + Choice_4_8_2 + Choice_4_8_3 + Choice_4_8_4
 + Choice_4_8_5 + Choice_4_8_6 + Choice_4_8_7 + Choice_4_8_8 + Choice_4_8_9
 = 1

_C171: Choice_4_9_1 + Choice_4_9_2 + Choice_4_9_3 + Choice_4_9_4
 + Choice_4_9_5 + Choice_4_9_6 + Choice_4_9_7 + Choice_4_9_8 + Choice_4_9_9
 = 1

_C172: Choice_4_1_1 + Choice_4_2_1 + Choice_4_3_1 + Choice_4_4_1
 + Choice_4_5_1 + Choice_4_6_1 + Choice_4_7_1 + Choice_4_8_1 + Choice_4_9_1
 = 1

_C173: Choice_4_1_2 + Choice_4_2_2 + Choice_4_3_2 + Choice_4_4_2
 + Choice_4_5_2 + Choice_4_6_2 + Choice_4_7_2 + Choice_4_8_2 + Choice_4_9_2
 = 1

_C174: Choice_4_1_3 + Choice_4_2_3 + Choice_4_3_3 + Choice_4_4_3
 + Choice_4_5_3 + Choice_4_6_3 + Choice_4_7_3 + Choice_4_8_3 + Choice_4_9_3
 = 1

_C175: Choice_4_1_4 + Choice_4_2_4 + Choice_4_3_4 + Choice_4_4_4
 + Choice_4_5_4 + Choice_4_6_4 + Choice_4_7_4 + Choice_4_8_4 + Choice_4_9_4
 = 1

_C176: Choice_4_1_5 + Choice_4_2_5 + Choice_4_3_5 + Choice_4_4_5
 + Choice_4_5_5 + Choice_4_6_5 + Choice_4_7_5 + Choice_4_8_5 + Choice_4_9_5
 = 1

_C177: Choice_4_1_6 + Choice_4_2_6 + Choice_4_3_6 + Choice_4_4_6
 + Choice_4_5_6 + Choice_4_6_6 + Choice_4_7_6 + Choice_4_8_6 + Choice_4_9_6
 = 1

_C178: Choice_4_1_7 + Choice_4_2_7 + Choice_4_3_7 + Choice_4_4_7
 + Choice_4_5_7 + Choice_4_6_7 + Choice_4_7_7 + Choice_4_8_7 + Choice_4_9_7
 = 1

_C179: Choice_4_1_8 + Choice_4_2_8 + Choice_4_3_8 + Choice_4_4_8
 + Choice_4_5_8 + Choice_4_6_8 + Choice_4_7_8 + Choice_4_8_8 + Choice_4_9_8
 = 1

_C180: Choice_4_1_9 + Choice_4_2_9 + Choice_4_3_9 + Choice_4_4_9
 + Choice_4_5_9 + Choice_4_6_9 + Choice_4_7_9 + Choice_4_8_9 + Choice_4_9_9
 = 1

_C181: Choice_4_1_1 + Choice_4_1_2 + Choice_4_1_3 + Choice_4_2_1
 + Choice_4_2_2 + Choice_4_2_3 + Choice_4_3_1 + Choice_4_3_2 + Choice_4_3_3
 = 1

_C182: Choice_4_1_4 + Choice_4_1_5 + Choice_4_1_6 + Choice_4_2_4
 + Choice_4_2_5 + Choice_4_2_6 + Choice_4_3_4 + Choice_4_3_5 + Choice_4_3_6
 = 1

_C183: Choice_4_1_7 + Choice_4_1_8 + Choice_4_1_9 + Choice_4_2_7
 + Choice_4_2_8 + Choice_4_2_9 + Choice_4_3_7 + Choice_4_3_8 + Choice_4_3_9
 = 1

_C184: Choice_4_4_1 + Choice_4_4_2 + Choice_4_4_3 + Choice_4_5_1
 + Choice_4_5_2 + Choice_4_5_3 + Choice_4_6_1 + Choice_4_6_2 + Choice_4_6_3
 = 1

_C185: Choice_4_4_4 + Choice_4_4_5 + Choice_4_4_6 + Choice_4_5_4
 + Choice_4_5_5 + Choice_4_5_6 + Choice_4_6_4 + Choice_4_6_5 + Choice_4_6_6
 = 1

_C186: Choice_4_4_7 + Choice_4_4_8 + Choice_4_4_9 + Choice_4_5_7
 + Choice_4_5_8 + Choice_4_5_9 + Choice_4_6_7 + Choice_4_6_8 + Choice_4_6_9
 = 1

_C187: Choice_4_7_1 + Choice_4_7_2 + Choice_4_7_3 + Choice_4_8_1
 + Choice_4_8_2 + Choice_4_8_3 + Choice_4_9_1 + Choice_4_9_2 + Choice_4_9_3
 = 1

_C188: Choice_4_7_4 + Choice_4_7_5 + Choice_4_7_6 + Choice_4_8_4
 + Choice_4_8_5 + Choice_4_8_6 + Choice_4_9_4 + Choice_4_9_5 + Choice_4_9_6
 = 1

_C189: Choice_4_7_7 + Choice_4_7_8 + Choice_4_7_9 + Choice_4_8_7
 + Choice_4_8_8 + Choice_4_8_9 + Choice_4_9_7 + Choice_4_9_8 + Choice_4_9_9
 = 1

_C190: Choice_5_1_1 + Choice_5_1_2 + Choice_5_1_3 + Choice_5_1_4
 + Choice_5_1_5 + Choice_5_1_6 + Choice_5_1_7 + Choice_5_1_8 + Choice_5_1_9
 = 1

_C191: Choice_5_2_1 + Choice_5_2_2 + Choice_5_2_3 + Choice_5_2_4
 + Choice_5_2_5 + Choice_5_2_6 + Choice_5_2_7 + Choice_5_2_8 + Choice_5_2_9
 = 1

_C192: Choice_5_3_1 + Choice_5_3_2 + Choice_5_3_3 + Choice_5_3_4
 + Choice_5_3_5 + Choice_5_3_6 + Choice_5_3_7 + Choice_5_3_8 + Choice_5_3_9
 = 1

_C193: Choice_5_4_1 + Choice_5_4_2 + Choice_5_4_3 + Choice_5_4_4
 + Choice_5_4_5 + Choice_5_4_6 + Choice_5_4_7 + Choice_5_4_8 + Choice_5_4_9
 = 1

_C194: Choice_5_5_1 + Choice_5_5_2 + Choice_5_5_3 + Choice_5_5_4
 + Choice_5_5_5 + Choice_5_5_6 + Choice_5_5_7 + Choice_5_5_8 + Choice_5_5_9
 = 1

_C195: Choice_5_6_1 + Choice_5_6_2 + Choice_5_6_3 + Choice_5_6_4
 + Choice_5_6_5 + Choice_5_6_6 + Choice_5_6_7 + Choice_5_6_8 + Choice_5_6_9
 = 1

_C196: Choice_5_7_1 + Choice_5_7_2 + Choice_5_7_3 + Choice_5_7_4
 + Choice_5_7_5 + Choice_5_7_6 + Choice_5_7_7 + Choice_5_7_8 + Choice_5_7_9
 = 1

_C197: Choice_5_8_1 + Choice_5_8_2 + Choice_5_8_3 + Choice_5_8_4
 + Choice_5_8_5 + Choice_5_8_6 + Choice_5_8_7 + Choice_5_8_8 + Choice_5_8_9
 = 1

_C198: Choice_5_9_1 + Choice_5_9_2 + Choice_5_9_3 + Choice_5_9_4
 + Choice_5_9_5 + Choice_5_9_6 + Choice_5_9_7 + Choice_5_9_8 + Choice_5_9_9
 = 1

_C199: Choice_5_1_1 + Choice_5_2_1 + Choice_5_3_1 + Choice_5_4_1
 + Choice_5_5_1 + Choice_5_6_1 + Choice_5_7_1 + Choice_5_8_1 + Choice_5_9_1
 = 1

_C200: Choice_5_1_2 + Choice_5_2_2 + Choice_5_3_2 + Choice_5_4_2
 + Choice_5_5_2 + Choice_5_6_2 + Choice_5_7_2 + Choice_5_8_2 + Choice_5_9_2
 = 1

_C201: Choice_5_1_3 + Choice_5_2_3 + Choice_5_3_3 + Choice_5_4_3
 + Choice_5_5_3 + Choice_5_6_3 + Choice_5_7_3 + Choice_5_8_3 + Choice_5_9_3
 = 1

_C202: Choice_5_1_4 + Choice_5_2_4 + Choice_5_3_4 + Choice_5_4_4
 + Choice_5_5_4 + Choice_5_6_4 + Choice_5_7_4 + Choice_5_8_4 + Choice_5_9_4
 = 1

_C203: Choice_5_1_5 + Choice_5_2_5 + Choice_5_3_5 + Choice_5_4_5
 + Choice_5_5_5 + Choice_5_6_5 + Choice_5_7_5 + Choice_5_8_5 + Choice_5_9_5
 = 1

_C204: Choice_5_1_6 + Choice_5_2_6 + Choice_5_3_6 + Choice_5_4_6
 + Choice_5_5_6 + Choice_5_6_6 + Choice_5_7_6 + Choice_5_8_6 + Choice_5_9_6
 = 1

_C205: Choice_5_1_7 + Choice_5_2_7 + Choice_5_3_7 + Choice_5_4_7
 + Choice_5_5_7 + Choice_5_6_7 + Choice_5_7_7 + Choice_5_8_7 + Choice_5_9_7
 = 1

_C206: Choice_5_1_8 + Choice_5_2_8 + Choice_5_3_8 + Choice_5_4_8
 + Choice_5_5_8 + Choice_5_6_8 + Choice_5_7_8 + Choice_5_8_8 + Choice_5_9_8
 = 1

_C207: Choice_5_1_9 + Choice_5_2_9 + Choice_5_3_9 + Choice_5_4_9
 + Choice_5_5_9 + Choice_5_6_9 + Choice_5_7_9 + Choice_5_8_9 + Choice_5_9_9
 = 1

_C208: Choice_5_1_1 + Choice_5_1_2 + Choice_5_1_3 + Choice_5_2_1
 + Choice_5_2_2 + Choice_5_2_3 + Choice_5_3_1 + Choice_5_3_2 + Choice_5_3_3
 = 1

_C209: Choice_5_1_4 + Choice_5_1_5 + Choice_5_1_6 + Choice_5_2_4
 + Choice_5_2_5 + Choice_5_2_6 + Choice_5_3_4 + Choice_5_3_5 + Choice_5_3_6
 = 1

_C210: Choice_5_1_7 + Choice_5_1_8 + Choice_5_1_9 + Choice_5_2_7
 + Choice_5_2_8 + Choice_5_2_9 + Choice_5_3_7 + Choice_5_3_8 + Choice_5_3_9
 = 1

_C211: Choice_5_4_1 + Choice_5_4_2 + Choice_5_4_3 + Choice_5_5_1
 + Choice_5_5_2 + Choice_5_5_3 + Choice_5_6_1 + Choice_5_6_2 + Choice_5_6_3
 = 1

_C212: Choice_5_4_4 + Choice_5_4_5 + Choice_5_4_6 + Choice_5_5_4
 + Choice_5_5_5 + Choice_5_5_6 + Choice_5_6_4 + Choice_5_6_5 + Choice_5_6_6
 = 1

_C213: Choice_5_4_7 + Choice_5_4_8 + Choice_5_4_9 + Choice_5_5_7
 + Choice_5_5_8 + Choice_5_5_9 + Choice_5_6_7 + Choice_5_6_8 + Choice_5_6_9
 = 1

_C214: Choice_5_7_1 + Choice_5_7_2 + Choice_5_7_3 + Choice_5_8_1
 + Choice_5_8_2 + Choice_5_8_3 + Choice_5_9_1 + Choice_5_9_2 + Choice_5_9_3
 = 1

_C215: Choice_5_7_4 + Choice_5_7_5 + Choice_5_7_6 + Choice_5_8_4
 + Choice_5_8_5 + Choice_5_8_6 + Choice_5_9_4 + Choice_5_9_5 + Choice_5_9_6
 = 1

_C216: Choice_5_7_7 + Choice_5_7_8 + Choice_5_7_9 + Choice_5_8_7
 + Choice_5_8_8 + Choice_5_8_9 + Choice_5_9_7 + Choice_5_9_8 + Choice_5_9_9
 = 1

_C217: Choice_6_1_1 + Choice_6_1_2 + Choice_6_1_3 + Choice_6_1_4
 + Choice_6_1_5 + Choice_6_1_6 + Choice_6_1_7 + Choice_6_1_8 + Choice_6_1_9
 = 1

_C218: Choice_6_2_1 + Choice_6_2_2 + Choice_6_2_3 + Choice_6_2_4
 + Choice_6_2_5 + Choice_6_2_6 + Choice_6_2_7 + Choice_6_2_8 + Choice_6_2_9
 = 1

_C219: Choice_6_3_1 + Choice_6_3_2 + Choice_6_3_3 + Choice_6_3_4
 + Choice_6_3_5 + Choice_6_3_6 + Choice_6_3_7 + Choice_6_3_8 + Choice_6_3_9
 = 1

_C220: Choice_6_4_1 + Choice_6_4_2 + Choice_6_4_3 + Choice_6_4_4
 + Choice_6_4_5 + Choice_6_4_6 + Choice_6_4_7 + Choice_6_4_8 + Choice_6_4_9
 = 1

_C221: Choice_6_5_1 + Choice_6_5_2 + Choice_6_5_3 + Choice_6_5_4
 + Choice_6_5_5 + Choice_6_5_6 + Choice_6_5_7 + Choice_6_5_8 + Choice_6_5_9
 = 1

_C222: Choice_6_6_1 + Choice_6_6_2 + Choice_6_6_3 + Choice_6_6_4
 + Choice_6_6_5 + Choice_6_6_6 + Choice_6_6_7 + Choice_6_6_8 + Choice_6_6_9
 = 1

_C223: Choice_6_7_1 + Choice_6_7_2 + Choice_6_7_3 + Choice_6_7_4
 + Choice_6_7_5 + Choice_6_7_6 + Choice_6_7_7 + Choice_6_7_8 + Choice_6_7_9
 = 1

_C224: Choice_6_8_1 + Choice_6_8_2 + Choice_6_8_3 + Choice_6_8_4
 + Choice_6_8_5 + Choice_6_8_6 + Choice_6_8_7 + Choice_6_8_8 + Choice_6_8_9
 = 1

_C225: Choice_6_9_1 + Choice_6_9_2 + Choice_6_9_3 + Choice_6_9_4
 + Choice_6_9_5 + Choice_6_9_6 + Choice_6_9_7 + Choice_6_9_8 + Choice_6_9_9
 = 1

_C226: Choice_6_1_1 + Choice_6_2_1 + Choice_6_3_1 + Choice_6_4_1
 + Choice_6_5_1 + Choice_6_6_1 + Choice_6_7_1 + Choice_6_8_1 + Choice_6_9_1
 = 1

_C227: Choice_6_1_2 + Choice_6_2_2 + Choice_6_3_2 + Choice_6_4_2
 + Choice_6_5_2 + Choice_6_6_2 + Choice_6_7_2 + Choice_6_8_2 + Choice_6_9_2
 = 1

_C228: Choice_6_1_3 + Choice_6_2_3 + Choice_6_3_3 + Choice_6_4_3
 + Choice_6_5_3 + Choice_6_6_3 + Choice_6_7_3 + Choice_6_8_3 + Choice_6_9_3
 = 1

_C229: Choice_6_1_4 + Choice_6_2_4 + Choice_6_3_4 + Choice_6_4_4
 + Choice_6_5_4 + Choice_6_6_4 + Choice_6_7_4 + Choice_6_8_4 + Choice_6_9_4
 = 1

_C230: Choice_6_1_5 + Choice_6_2_5 + Choice_6_3_5 + Choice_6_4_5
 + Choice_6_5_5 + Choice_6_6_5 + Choice_6_7_5 + Choice_6_8_5 + Choice_6_9_5
 = 1

_C231: Choice_6_1_6 + Choice_6_2_6 + Choice_6_3_6 + Choice_6_4_6
 + Choice_6_5_6 + Choice_6_6_6 + Choice_6_7_6 + Choice_6_8_6 + Choice_6_9_6
 = 1

_C232: Choice_6_1_7 + Choice_6_2_7 + Choice_6_3_7 + Choice_6_4_7
 + Choice_6_5_7 + Choice_6_6_7 + Choice_6_7_7 + Choice_6_8_7 + Choice_6_9_7
 = 1

_C233: Choice_6_1_8 + Choice_6_2_8 + Choice_6_3_8 + Choice_6_4_8
 + Choice_6_5_8 + Choice_6_6_8 + Choice_6_7_8 + Choice_6_8_8 + Choice_6_9_8
 = 1

_C234: Choice_6_1_9 + Choice_6_2_9 + Choice_6_3_9 + Choice_6_4_9
 + Choice_6_5_9 + Choice_6_6_9 + Choice_6_7_9 + Choice_6_8_9 + Choice_6_9_9
 = 1

_C235: Choice_6_1_1 + Choice_6_1_2 + Choice_6_1_3 + Choice_6_2_1
 + Choice_6_2_2 + Choice_6_2_3 + Choice_6_3_1 + Choice_6_3_2 + Choice_6_3_3
 = 1

_C236: Choice_6_1_4 + Choice_6_1_5 + Choice_6_1_6 + Choice_6_2_4
 + Choice_6_2_5 + Choice_6_2_6 + Choice_6_3_4 + Choice_6_3_5 + Choice_6_3_6
 = 1

_C237: Choice_6_1_7 + Choice_6_1_8 + Choice_6_1_9 + Choice_6_2_7
 + Choice_6_2_8 + Choice_6_2_9 + Choice_6_3_7 + Choice_6_3_8 + Choice_6_3_9
 = 1

_C238: Choice_6_4_1 + Choice_6_4_2 + Choice_6_4_3 + Choice_6_5_1
 + Choice_6_5_2 + Choice_6_5_3 + Choice_6_6_1 + Choice_6_6_2 + Choice_6_6_3
 = 1

_C239: Choice_6_4_4 + Choice_6_4_5 + Choice_6_4_6 + Choice_6_5_4
 + Choice_6_5_5 + Choice_6_5_6 + Choice_6_6_4 + Choice_6_6_5 + Choice_6_6_6
 = 1

_C240: Choice_6_4_7 + Choice_6_4_8 + Choice_6_4_9 + Choice_6_5_7
 + Choice_6_5_8 + Choice_6_5_9 + Choice_6_6_7 + Choice_6_6_8 + Choice_6_6_9
 = 1

_C241: Choice_6_7_1 + Choice_6_7_2 + Choice_6_7_3 + Choice_6_8_1
 + Choice_6_8_2 + Choice_6_8_3 + Choice_6_9_1 + Choice_6_9_2 + Choice_6_9_3
 = 1

_C242: Choice_6_7_4 + Choice_6_7_5 + Choice_6_7_6 + Choice_6_8_4
 + Choice_6_8_5 + Choice_6_8_6 + Choice_6_9_4 + Choice_6_9_5 + Choice_6_9_6
 = 1

_C243: Choice_6_7_7 + Choice_6_7_8 + Choice_6_7_9 + Choice_6_8_7
 + Choice_6_8_8 + Choice_6_8_9 + Choice_6_9_7 + Choice_6_9_8 + Choice_6_9_9
 = 1

_C244: Choice_7_1_1 + Choice_7_1_2 + Choice_7_1_3 + Choice_7_1_4
 + Choice_7_1_5 + Choice_7_1_6 + Choice_7_1_7 + Choice_7_1_8 + Choice_7_1_9
 = 1

_C245: Choice_7_2_1 + Choice_7_2_2 + Choice_7_2_3 + Choice_7_2_4
 + Choice_7_2_5 + Choice_7_2_6 + Choice_7_2_7 + Choice_7_2_8 + Choice_7_2_9
 = 1

_C246: Choice_7_3_1 + Choice_7_3_2 + Choice_7_3_3 + Choice_7_3_4
 + Choice_7_3_5 + Choice_7_3_6 + Choice_7_3_7 + Choice_7_3_8 + Choice_7_3_9
 = 1

_C247: Choice_7_4_1 + Choice_7_4_2 + Choice_7_4_3 + Choice_7_4_4
 + Choice_7_4_5 + Choice_7_4_6 + Choice_7_4_7 + Choice_7_4_8 + Choice_7_4_9
 = 1

_C248: Choice_7_5_1 + Choice_7_5_2 + Choice_7_5_3 + Choice_7_5_4
 + Choice_7_5_5 + Choice_7_5_6 + Choice_7_5_7 + Choice_7_5_8 + Choice_7_5_9
 = 1

_C249: Choice_7_6_1 + Choice_7_6_2 + Choice_7_6_3 + Choice_7_6_4
 + Choice_7_6_5 + Choice_7_6_6 + Choice_7_6_7 + Choice_7_6_8 + Choice_7_6_9
 = 1

_C250: Choice_7_7_1 + Choice_7_7_2 + Choice_7_7_3 + Choice_7_7_4
 + Choice_7_7_5 + Choice_7_7_6 + Choice_7_7_7 + Choice_7_7_8 + Choice_7_7_9
 = 1

_C251: Choice_7_8_1 + Choice_7_8_2 + Choice_7_8_3 + Choice_7_8_4
 + Choice_7_8_5 + Choice_7_8_6 + Choice_7_8_7 + Choice_7_8_8 + Choice_7_8_9
 = 1

_C252: Choice_7_9_1 + Choice_7_9_2 + Choice_7_9_3 + Choice_7_9_4
 + Choice_7_9_5 + Choice_7_9_6 + Choice_7_9_7 + Choice_7_9_8 + Choice_7_9_9
 = 1

_C253: Choice_7_1_1 + Choice_7_2_1 + Choice_7_3_1 + Choice_7_4_1
 + Choice_7_5_1 + Choice_7_6_1 + Choice_7_7_1 + Choice_7_8_1 + Choice_7_9_1
 = 1

_C254: Choice_7_1_2 + Choice_7_2_2 + Choice_7_3_2 + Choice_7_4_2
 + Choice_7_5_2 + Choice_7_6_2 + Choice_7_7_2 + Choice_7_8_2 + Choice_7_9_2
 = 1

_C255: Choice_7_1_3 + Choice_7_2_3 + Choice_7_3_3 + Choice_7_4_3
 + Choice_7_5_3 + Choice_7_6_3 + Choice_7_7_3 + Choice_7_8_3 + Choice_7_9_3
 = 1

_C256: Choice_7_1_4 + Choice_7_2_4 + Choice_7_3_4 + Choice_7_4_4
 + Choice_7_5_4 + Choice_7_6_4 + Choice_7_7_4 + Choice_7_8_4 + Choice_7_9_4
 = 1

_C257: Choice_7_1_5 + Choice_7_2_5 + Choice_7_3_5 + Choice_7_4_5
 + Choice_7_5_5 + Choice_7_6_5 + Choice_7_7_5 + Choice_7_8_5 + Choice_7_9_5
 = 1

_C258: Choice_7_1_6 + Choice_7_2_6 + Choice_7_3_6 + Choice_7_4_6
 + Choice_7_5_6 + Choice_7_6_6 + Choice_7_7_6 + Choice_7_8_6 + Choice_7_9_6
 = 1

_C259: Choice_7_1_7 + Choice_7_2_7 + Choice_7_3_7 + Choice_7_4_7
 + Choice_7_5_7 + Choice_7_6_7 + Choice_7_7_7 + Choice_7_8_7 + Choice_7_9_7
 = 1

_C260: Choice_7_1_8 + Choice_7_2_8 + Choice_7_3_8 + Choice_7_4_8
 + Choice_7_5_8 + Choice_7_6_8 + Choice_7_7_8 + Choice_7_8_8 + Choice_7_9_8
 = 1

_C261: Choice_7_1_9 + Choice_7_2_9 + Choice_7_3_9 + Choice_7_4_9
 + Choice_7_5_9 + Choice_7_6_9 + Choice_7_7_9 + Choice_7_8_9 + Choice_7_9_9
 = 1

_C262: Choice_7_1_1 + Choice_7_1_2 + Choice_7_1_3 + Choice_7_2_1
 + Choice_7_2_2 + Choice_7_2_3 + Choice_7_3_1 + Choice_7_3_2 + Choice_7_3_3
 = 1

_C263: Choice_7_1_4 + Choice_7_1_5 + Choice_7_1_6 + Choice_7_2_4
 + Choice_7_2_5 + Choice_7_2_6 + Choice_7_3_4 + Choice_7_3_5 + Choice_7_3_6
 = 1

_C264: Choice_7_1_7 + Choice_7_1_8 + Choice_7_1_9 + Choice_7_2_7
 + Choice_7_2_8 + Choice_7_2_9 + Choice_7_3_7 + Choice_7_3_8 + Choice_7_3_9
 = 1

_C265: Choice_7_4_1 + Choice_7_4_2 + Choice_7_4_3 + Choice_7_5_1
 + Choice_7_5_2 + Choice_7_5_3 + Choice_7_6_1 + Choice_7_6_2 + Choice_7_6_3
 = 1

_C266: Choice_7_4_4 + Choice_7_4_5 + Choice_7_4_6 + Choice_7_5_4
 + Choice_7_5_5 + Choice_7_5_6 + Choice_7_6_4 + Choice_7_6_5 + Choice_7_6_6
 = 1

_C267: Choice_7_4_7 + Choice_7_4_8 + Choice_7_4_9 + Choice_7_5_7
 + Choice_7_5_8 + Choice_7_5_9 + Choice_7_6_7 + Choice_7_6_8 + Choice_7_6_9
 = 1

_C268: Choice_7_7_1 + Choice_7_7_2 + Choice_7_7_3 + Choice_7_8_1
 + Choice_7_8_2 + Choice_7_8_3 + Choice_7_9_1 + Choice_7_9_2 + Choice_7_9_3
 = 1

_C269: Choice_7_7_4 + Choice_7_7_5 + Choice_7_7_6 + Choice_7_8_4
 + Choice_7_8_5 + Choice_7_8_6 + Choice_7_9_4 + Choice_7_9_5 + Choice_7_9_6
 = 1

_C270: Choice_7_7_7 + Choice_7_7_8 + Choice_7_7_9 + Choice_7_8_7
 + Choice_7_8_8 + Choice_7_8_9 + Choice_7_9_7 + Choice_7_9_8 + Choice_7_9_9
 = 1

_C271: Choice_8_1_1 + Choice_8_1_2 + Choice_8_1_3 + Choice_8_1_4
 + Choice_8_1_5 + Choice_8_1_6 + Choice_8_1_7 + Choice_8_1_8 + Choice_8_1_9
 = 1

_C272: Choice_8_2_1 + Choice_8_2_2 + Choice_8_2_3 + Choice_8_2_4
 + Choice_8_2_5 + Choice_8_2_6 + Choice_8_2_7 + Choice_8_2_8 + Choice_8_2_9
 = 1

_C273: Choice_8_3_1 + Choice_8_3_2 + Choice_8_3_3 + Choice_8_3_4
 + Choice_8_3_5 + Choice_8_3_6 + Choice_8_3_7 + Choice_8_3_8 + Choice_8_3_9
 = 1

_C274: Choice_8_4_1 + Choice_8_4_2 + Choice_8_4_3 + Choice_8_4_4
 + Choice_8_4_5 + Choice_8_4_6 + Choice_8_4_7 + Choice_8_4_8 + Choice_8_4_9
 = 1

_C275: Choice_8_5_1 + Choice_8_5_2 + Choice_8_5_3 + Choice_8_5_4
 + Choice_8_5_5 + Choice_8_5_6 + Choice_8_5_7 + Choice_8_5_8 + Choice_8_5_9
 = 1

_C276: Choice_8_6_1 + Choice_8_6_2 + Choice_8_6_3 + Choice_8_6_4
 + Choice_8_6_5 + Choice_8_6_6 + Choice_8_6_7 + Choice_8_6_8 + Choice_8_6_9
 = 1

_C277: Choice_8_7_1 + Choice_8_7_2 + Choice_8_7_3 + Choice_8_7_4
 + Choice_8_7_5 + Choice_8_7_6 + Choice_8_7_7 + Choice_8_7_8 + Choice_8_7_9
 = 1

_C278: Choice_8_8_1 + Choice_8_8_2 + Choice_8_8_3 + Choice_8_8_4
 + Choice_8_8_5 + Choice_8_8_6 + Choice_8_8_7 + Choice_8_8_8 + Choice_8_8_9
 = 1

_C279: Choice_8_9_1 + Choice_8_9_2 + Choice_8_9_3 + Choice_8_9_4
 + Choice_8_9_5 + Choice_8_9_6 + Choice_8_9_7 + Choice_8_9_8 + Choice_8_9_9
 = 1

_C280: Choice_8_1_1 + Choice_8_2_1 + Choice_8_3_1 + Choice_8_4_1
 + Choice_8_5_1 + Choice_8_6_1 + Choice_8_7_1 + Choice_8_8_1 + Choice_8_9_1
 = 1

_C281: Choice_8_1_2 + Choice_8_2_2 + Choice_8_3_2 + Choice_8_4_2
 + Choice_8_5_2 + Choice_8_6_2 + Choice_8_7_2 + Choice_8_8_2 + Choice_8_9_2
 = 1

_C282: Choice_8_1_3 + Choice_8_2_3 + Choice_8_3_3 + Choice_8_4_3
 + Choice_8_5_3 + Choice_8_6_3 + Choice_8_7_3 + Choice_8_8_3 + Choice_8_9_3
 = 1

_C283: Choice_8_1_4 + Choice_8_2_4 + Choice_8_3_4 + Choice_8_4_4
 + Choice_8_5_4 + Choice_8_6_4 + Choice_8_7_4 + Choice_8_8_4 + Choice_8_9_4
 = 1

_C284: Choice_8_1_5 + Choice_8_2_5 + Choice_8_3_5 + Choice_8_4_5
 + Choice_8_5_5 + Choice_8_6_5 + Choice_8_7_5 + Choice_8_8_5 + Choice_8_9_5
 = 1

_C285: Choice_8_1_6 + Choice_8_2_6 + Choice_8_3_6 + Choice_8_4_6
 + Choice_8_5_6 + Choice_8_6_6 + Choice_8_7_6 + Choice_8_8_6 + Choice_8_9_6
 = 1

_C286: Choice_8_1_7 + Choice_8_2_7 + Choice_8_3_7 + Choice_8_4_7
 + Choice_8_5_7 + Choice_8_6_7 + Choice_8_7_7 + Choice_8_8_7 + Choice_8_9_7
 = 1

_C287: Choice_8_1_8 + Choice_8_2_8 + Choice_8_3_8 + Choice_8_4_8
 + Choice_8_5_8 + Choice_8_6_8 + Choice_8_7_8 + Choice_8_8_8 + Choice_8_9_8
 = 1

_C288: Choice_8_1_9 + Choice_8_2_9 + Choice_8_3_9 + Choice_8_4_9
 + Choice_8_5_9 + Choice_8_6_9 + Choice_8_7_9 + Choice_8_8_9 + Choice_8_9_9
 = 1

_C289: Choice_8_1_1 + Choice_8_1_2 + Choice_8_1_3 + Choice_8_2_1
 + Choice_8_2_2 + Choice_8_2_3 + Choice_8_3_1 + Choice_8_3_2 + Choice_8_3_3
 = 1

_C290: Choice_8_1_4 + Choice_8_1_5 + Choice_8_1_6 + Choice_8_2_4
 + Choice_8_2_5 + Choice_8_2_6 + Choice_8_3_4 + Choice_8_3_5 + Choice_8_3_6
 = 1

_C291: Choice_8_1_7 + Choice_8_1_8 + Choice_8_1_9 + Choice_8_2_7
 + Choice_8_2_8 + Choice_8_2_9 + Choice_8_3_7 + Choice_8_3_8 + Choice_8_3_9
 = 1

_C292: Choice_8_4_1 + Choice_8_4_2 + Choice_8_4_3 + Choice_8_5_1
 + Choice_8_5_2 + Choice_8_5_3 + Choice_8_6_1 + Choice_8_6_2 + Choice_8_6_3
 = 1

_C293: Choice_8_4_4 + Choice_8_4_5 + Choice_8_4_6 + Choice_8_5_4
 + Choice_8_5_5 + Choice_8_5_6 + Choice_8_6_4 + Choice_8_6_5 + Choice_8_6_6
 = 1

_C294: Choice_8_4_7 + Choice_8_4_8 + Choice_8_4_9 + Choice_8_5_7
 + Choice_8_5_8 + Choice_8_5_9 + Choice_8_6_7 + Choice_8_6_8 + Choice_8_6_9
 = 1

_C295: Choice_8_7_1 + Choice_8_7_2 + Choice_8_7_3 + Choice_8_8_1
 + Choice_8_8_2 + Choice_8_8_3 + Choice_8_9_1 + Choice_8_9_2 + Choice_8_9_3
 = 1

_C296: Choice_8_7_4 + Choice_8_7_5 + Choice_8_7_6 + Choice_8_8_4
 + Choice_8_8_5 + Choice_8_8_6 + Choice_8_9_4 + Choice_8_9_5 + Choice_8_9_6
 = 1

_C297: Choice_8_7_7 + Choice_8_7_8 + Choice_8_7_9 + Choice_8_8_7
 + Choice_8_8_8 + Choice_8_8_9 + Choice_8_9_7 + Choice_8_9_8 + Choice_8_9_9
 = 1

_C298: Choice_9_1_1 + Choice_9_1_2 + Choice_9_1_3 + Choice_9_1_4
 + Choice_9_1_5 + Choice_9_1_6 + Choice_9_1_7 + Choice_9_1_8 + Choice_9_1_9
 = 1

_C299: Choice_9_2_1 + Choice_9_2_2 + Choice_9_2_3 + Choice_9_2_4
 + Choice_9_2_5 + Choice_9_2_6 + Choice_9_2_7 + Choice_9_2_8 + Choice_9_2_9
 = 1

_C300: Choice_9_3_1 + Choice_9_3_2 + Choice_9_3_3 + Choice_9_3_4
 + Choice_9_3_5 + Choice_9_3_6 + Choice_9_3_7 + Choice_9_3_8 + Choice_9_3_9
 = 1

_C301: Choice_9_4_1 + Choice_9_4_2 + Choice_9_4_3 + Choice_9_4_4
 + Choice_9_4_5 + Choice_9_4_6 + Choice_9_4_7 + Choice_9_4_8 + Choice_9_4_9
 = 1

_C302: Choice_9_5_1 + Choice_9_5_2 + Choice_9_5_3 + Choice_9_5_4
 + Choice_9_5_5 + Choice_9_5_6 + Choice_9_5_7 + Choice_9_5_8 + Choice_9_5_9
 = 1

_C303: Choice_9_6_1 + Choice_9_6_2 + Choice_9_6_3 + Choice_9_6_4
 + Choice_9_6_5 + Choice_9_6_6 + Choice_9_6_7 + Choice_9_6_8 + Choice_9_6_9
 = 1

_C304: Choice_9_7_1 + Choice_9_7_2 + Choice_9_7_3 + Choice_9_7_4
 + Choice_9_7_5 + Choice_9_7_6 + Choice_9_7_7 + Choice_9_7_8 + Choice_9_7_9
 = 1

_C305: Choice_9_8_1 + Choice_9_8_2 + Choice_9_8_3 + Choice_9_8_4
 + Choice_9_8_5 + Choice_9_8_6 + Choice_9_8_7 + Choice_9_8_8 + Choice_9_8_9
 = 1

_C306: Choice_9_9_1 + Choice_9_9_2 + Choice_9_9_3 + Choice_9_9_4
 + Choice_9_9_5 + Choice_9_9_6 + Choice_9_9_7 + Choice_9_9_8 + Choice_9_9_9
 = 1

_C307: Choice_9_1_1 + Choice_9_2_1 + Choice_9_3_1 + Choice_9_4_1
 + Choice_9_5_1 + Choice_9_6_1 + Choice_9_7_1 + Choice_9_8_1 + Choice_9_9_1
 = 1

_C308: Choice_9_1_2 + Choice_9_2_2 + Choice_9_3_2 + Choice_9_4_2
 + Choice_9_5_2 + Choice_9_6_2 + Choice_9_7_2 + Choice_9_8_2 + Choice_9_9_2
 = 1

_C309: Choice_9_1_3 + Choice_9_2_3 + Choice_9_3_3 + Choice_9_4_3
 + Choice_9_5_3 + Choice_9_6_3 + Choice_9_7_3 + Choice_9_8_3 + Choice_9_9_3
 = 1

_C310: Choice_9_1_4 + Choice_9_2_4 + Choice_9_3_4 + Choice_9_4_4
 + Choice_9_5_4 + Choice_9_6_4 + Choice_9_7_4 + Choice_9_8_4 + Choice_9_9_4
 = 1

_C311: Choice_9_1_5 + Choice_9_2_5 + Choice_9_3_5 + Choice_9_4_5
 + Choice_9_5_5 + Choice_9_6_5 + Choice_9_7_5 + Choice_9_8_5 + Choice_9_9_5
 = 1

_C312: Choice_9_1_6 + Choice_9_2_6 + Choice_9_3_6 + Choice_9_4_6
 + Choice_9_5_6 + Choice_9_6_6 + Choice_9_7_6 + Choice_9_8_6 + Choice_9_9_6
 = 1

_C313: Choice_9_1_7 + Choice_9_2_7 + Choice_9_3_7 + Choice_9_4_7
 + Choice_9_5_7 + Choice_9_6_7 + Choice_9_7_7 + Choice_9_8_7 + Choice_9_9_7
 = 1

_C314: Choice_9_1_8 + Choice_9_2_8 + Choice_9_3_8 + Choice_9_4_8
 + Choice_9_5_8 + Choice_9_6_8 + Choice_9_7_8 + Choice_9_8_8 + Choice_9_9_8
 = 1

_C315: Choice_9_1_9 + Choice_9_2_9 + Choice_9_3_9 + Choice_9_4_9
 + Choice_9_5_9 + Choice_9_6_9 + Choice_9_7_9 + Choice_9_8_9 + Choice_9_9_9
 = 1

_C316: Choice_9_1_1 + Choice_9_1_2 + Choice_9_1_3 + Choice_9_2_1
 + Choice_9_2_2 + Choice_9_2_3 + Choice_9_3_1 + Choice_9_3_2 + Choice_9_3_3
 = 1

_C317: Choice_9_1_4 + Choice_9_1_5 + Choice_9_1_6 + Choice_9_2_4
 + Choice_9_2_5 + Choice_9_2_6 + Choice_9_3_4 + Choice_9_3_5 + Choice_9_3_6
 = 1

_C318: Choice_9_1_7 + Choice_9_1_8 + Choice_9_1_9 + Choice_9_2_7
 + Choice_9_2_8 + Choice_9_2_9 + Choice_9_3_7 + Choice_9_3_8 + Choice_9_3_9
 = 1

_C319: Choice_9_4_1 + Choice_9_4_2 + Choice_9_4_3 + Choice_9_5_1
 + Choice_9_5_2 + Choice_9_5_3 + Choice_9_6_1 + Choice_9_6_2 + Choice_9_6_3
 = 1

_C320: Choice_9_4_4 + Choice_9_4_5 + Choice_9_4_6 + Choice_9_5_4
 + Choice_9_5_5 + Choice_9_5_6 + Choice_9_6_4 + Choice_9_6_5 + Choice_9_6_6
 = 1

_C321: Choice_9_4_7 + Choice_9_4_8 + Choice_9_4_9 + Choice_9_5_7
 + Choice_9_5_8 + Choice_9_5_9 + Choice_9_6_7 + Choice_9_6_8 + Choice_9_6_9
 = 1

_C322: Choice_9_7_1 + Choice_9_7_2 + Choice_9_7_3 + Choice_9_8_1
 + Choice_9_8_2 + Choice_9_8_3 + Choice_9_9_1 + Choice_9_9_2 + Choice_9_9_3
 = 1

_C323: Choice_9_7_4 + Choice_9_7_5 + Choice_9_7_6 + Choice_9_8_4
 + Choice_9_8_5 + Choice_9_8_6 + Choice_9_9_4 + Choice_9_9_5 + Choice_9_9_6
 = 1

_C324: Choice_9_7_7 + Choice_9_7_8 + Choice_9_7_9 + Choice_9_8_7
 + Choice_9_8_8 + Choice_9_8_9 + Choice_9_9_7 + Choice_9_9_8 + Choice_9_9_9
 = 1

VARIABLES
Choice_1_1_1 <= 1 Continuous
Choice_1_1_2 <= 1 Continuous
Choice_1_1_3 <= 1 Continuous
Choice_1_1_4 <= 1 Continuous
Choice_1_1_5 <= 1 Continuous
Choice_1_1_6 <= 1 Continuous
Choice_1_1_7 <= 1 Continuous
Choice_1_1_8 <= 1 Continuous
Choice_1_1_9 <= 1 Continuous
Choice_1_2_1 <= 1 Continuous
Choice_1_2_2 <= 1 Continuous
Choice_1_2_3 <= 1 Continuous
Choice_1_2_4 <= 1 Continuous
Choice_1_2_5 <= 1 Continuous
Choice_1_2_6 <= 1 Continuous
Choice_1_2_7 <= 1 Continuous
Choice_1_2_8 <= 1 Continuous
Choice_1_2_9 <= 1 Continuous
Choice_1_3_1 <= 1 Continuous
Choice_1_3_2 <= 1 Continuous
Choice_1_3_3 <= 1 Continuous
Choice_1_3_4 <= 1 Continuous
Choice_1_3_5 <= 1 Continuous
Choice_1_3_6 <= 1 Continuous
Choice_1_3_7 <= 1 Continuous
Choice_1_3_8 <= 1 Continuous
Choice_1_3_9 <= 1 Continuous
Choice_1_4_1 <= 1 Continuous
Choice_1_4_2 <= 1 Continuous
Choice_1_4_3 <= 1 Continuous
Choice_1_4_4 <= 1 Continuous
Choice_1_4_5 <= 1 Continuous
Choice_1_4_6 <= 1 Continuous
Choice_1_4_7 <= 1 Continuous
Choice_1_4_8 <= 1 Continuous
Choice_1_4_9 <= 1 Continuous
Choice_1_5_1 <= 1 Continuous
Choice_1_5_2 <= 1 Continuous
Choice_1_5_3 <= 1 Continuous
Choice_1_5_4 <= 1 Continuous
Choice_1_5_5 <= 1 Continuous
Choice_1_5_6 <= 1 Continuous
Choice_1_5_7 <= 1 Continuous
Choice_1_5_8 <= 1 Continuous
Choice_1_5_9 <= 1 Continuous
Choice_1_6_1 <= 1 Continuous
Choice_1_6_2 <= 1 Continuous
Choice_1_6_3 <= 1 Continuous
Choice_1_6_4 <= 1 Continuous
Choice_1_6_5 <= 1 Continuous
Choice_1_6_6 <= 1 Continuous
Choice_1_6_7 <= 1 Continuous
Choice_1_6_8 <= 1 Continuous
Choice_1_6_9 <= 1 Continuous
Choice_1_7_1 <= 1 Continuous
Choice_1_7_2 <= 1 Continuous
Choice_1_7_3 <= 1 Continuous
Choice_1_7_4 <= 1 Continuous
Choice_1_7_5 <= 1 Continuous
Choice_1_7_6 <= 1 Continuous
Choice_1_7_7 <= 1 Continuous
Choice_1_7_8 <= 1 Continuous
Choice_1_7_9 <= 1 Continuous
Choice_1_8_1 <= 1 Continuous
Choice_1_8_2 <= 1 Continuous
Choice_1_8_3 <= 1 Continuous
Choice_1_8_4 <= 1 Continuous
Choice_1_8_5 <= 1 Continuous
Choice_1_8_6 <= 1 Continuous
Choice_1_8_7 <= 1 Continuous
Choice_1_8_8 <= 1 Continuous
Choice_1_8_9 <= 1 Continuous
Choice_1_9_1 <= 1 Continuous
Choice_1_9_2 <= 1 Continuous
Choice_1_9_3 <= 1 Continuous
Choice_1_9_4 <= 1 Continuous
Choice_1_9_5 <= 1 Continuous
Choice_1_9_6 <= 1 Continuous
Choice_1_9_7 <= 1 Continuous
Choice_1_9_8 <= 1 Continuous
Choice_1_9_9 <= 1 Continuous
Choice_2_1_1 <= 1 Continuous
Choice_2_1_2 <= 1 Continuous
Choice_2_1_3 <= 1 Continuous
Choice_2_1_4 <= 1 Continuous
Choice_2_1_5 <= 1 Continuous
Choice_2_1_6 <= 1 Continuous
Choice_2_1_7 <= 1 Continuous
Choice_2_1_8 <= 1 Continuous
Choice_2_1_9 <= 1 Continuous
Choice_2_2_1 <= 1 Continuous
Choice_2_2_2 <= 1 Continuous
Choice_2_2_3 <= 1 Continuous
Choice_2_2_4 <= 1 Continuous
Choice_2_2_5 <= 1 Continuous
Choice_2_2_6 <= 1 Continuous
Choice_2_2_7 <= 1 Continuous
Choice_2_2_8 <= 1 Continuous
Choice_2_2_9 <= 1 Continuous
Choice_2_3_1 <= 1 Continuous
Choice_2_3_2 <= 1 Continuous
Choice_2_3_3 <= 1 Continuous
Choice_2_3_4 <= 1 Continuous
Choice_2_3_5 <= 1 Continuous
Choice_2_3_6 <= 1 Continuous
Choice_2_3_7 <= 1 Continuous
Choice_2_3_8 <= 1 Continuous
Choice_2_3_9 <= 1 Continuous
Choice_2_4_1 <= 1 Continuous
Choice_2_4_2 <= 1 Continuous
Choice_2_4_3 <= 1 Continuous
Choice_2_4_4 <= 1 Continuous
Choice_2_4_5 <= 1 Continuous
Choice_2_4_6 <= 1 Continuous
Choice_2_4_7 <= 1 Continuous
Choice_2_4_8 <= 1 Continuous
Choice_2_4_9 <= 1 Continuous
Choice_2_5_1 <= 1 Continuous
Choice_2_5_2 <= 1 Continuous
Choice_2_5_3 <= 1 Continuous
Choice_2_5_4 <= 1 Continuous
Choice_2_5_5 <= 1 Continuous
Choice_2_5_6 <= 1 Continuous
Choice_2_5_7 <= 1 Continuous
Choice_2_5_8 <= 1 Continuous
Choice_2_5_9 <= 1 Continuous
Choice_2_6_1 <= 1 Continuous
Choice_2_6_2 <= 1 Continuous
Choice_2_6_3 <= 1 Continuous
Choice_2_6_4 <= 1 Continuous
Choice_2_6_5 <= 1 Continuous
Choice_2_6_6 <= 1 Continuous
Choice_2_6_7 <= 1 Continuous
Choice_2_6_8 <= 1 Continuous
Choice_2_6_9 <= 1 Continuous
Choice_2_7_1 <= 1 Continuous
Choice_2_7_2 <= 1 Continuous
Choice_2_7_3 <= 1 Continuous
Choice_2_7_4 <= 1 Continuous
Choice_2_7_5 <= 1 Continuous
Choice_2_7_6 <= 1 Continuous
Choice_2_7_7 <= 1 Continuous
Choice_2_7_8 <= 1 Continuous
Choice_2_7_9 <= 1 Continuous
Choice_2_8_1 <= 1 Continuous
Choice_2_8_2 <= 1 Continuous
Choice_2_8_3 <= 1 Continuous
Choice_2_8_4 <= 1 Continuous
Choice_2_8_5 <= 1 Continuous
Choice_2_8_6 <= 1 Continuous
Choice_2_8_7 <= 1 Continuous
Choice_2_8_8 <= 1 Continuous
Choice_2_8_9 <= 1 Continuous
Choice_2_9_1 <= 1 Continuous
Choice_2_9_2 <= 1 Continuous
Choice_2_9_3 <= 1 Continuous
Choice_2_9_4 <= 1 Continuous
Choice_2_9_5 <= 1 Continuous
Choice_2_9_6 <= 1 Continuous
Choice_2_9_7 <= 1 Continuous
Choice_2_9_8 <= 1 Continuous
Choice_2_9_9 <= 1 Continuous
Choice_3_1_1 <= 1 Continuous
Choice_3_1_2 <= 1 Continuous
Choice_3_1_3 <= 1 Continuous
Choice_3_1_4 <= 1 Continuous
Choice_3_1_5 <= 1 Continuous
Choice_3_1_6 <= 1 Continuous
Choice_3_1_7 <= 1 Continuous
Choice_3_1_8 <= 1 Continuous
Choice_3_1_9 <= 1 Continuous
Choice_3_2_1 <= 1 Continuous
Choice_3_2_2 <= 1 Continuous
Choice_3_2_3 <= 1 Continuous
Choice_3_2_4 <= 1 Continuous
Choice_3_2_5 <= 1 Continuous
Choice_3_2_6 <= 1 Continuous
Choice_3_2_7 <= 1 Continuous
Choice_3_2_8 <= 1 Continuous
Choice_3_2_9 <= 1 Continuous
Choice_3_3_1 <= 1 Continuous
Choice_3_3_2 <= 1 Continuous
Choice_3_3_3 <= 1 Continuous
Choice_3_3_4 <= 1 Continuous
Choice_3_3_5 <= 1 Continuous
Choice_3_3_6 <= 1 Continuous
Choice_3_3_7 <= 1 Continuous
Choice_3_3_8 <= 1 Continuous
Choice_3_3_9 <= 1 Continuous
Choice_3_4_1 <= 1 Continuous
Choice_3_4_2 <= 1 Continuous
Choice_3_4_3 <= 1 Continuous
Choice_3_4_4 <= 1 Continuous
Choice_3_4_5 <= 1 Continuous
Choice_3_4_6 <= 1 Continuous
Choice_3_4_7 <= 1 Continuous
Choice_3_4_8 <= 1 Continuous
Choice_3_4_9 <= 1 Continuous
Choice_3_5_1 <= 1 Continuous
Choice_3_5_2 <= 1 Continuous
Choice_3_5_3 <= 1 Continuous
Choice_3_5_4 <= 1 Continuous
Choice_3_5_5 <= 1 Continuous
Choice_3_5_6 <= 1 Continuous
Choice_3_5_7 <= 1 Continuous
Choice_3_5_8 <= 1 Continuous
Choice_3_5_9 <= 1 Continuous
Choice_3_6_1 <= 1 Continuous
Choice_3_6_2 <= 1 Continuous
Choice_3_6_3 <= 1 Continuous
Choice_3_6_4 <= 1 Continuous
Choice_3_6_5 <= 1 Continuous
Choice_3_6_6 <= 1 Continuous
Choice_3_6_7 <= 1 Continuous
Choice_3_6_8 <= 1 Continuous
Choice_3_6_9 <= 1 Continuous
Choice_3_7_1 <= 1 Continuous
Choice_3_7_2 <= 1 Continuous
Choice_3_7_3 <= 1 Continuous
Choice_3_7_4 <= 1 Continuous
Choice_3_7_5 <= 1 Continuous
Choice_3_7_6 <= 1 Continuous
Choice_3_7_7 <= 1 Continuous
Choice_3_7_8 <= 1 Continuous
Choice_3_7_9 <= 1 Continuous
Choice_3_8_1 <= 1 Continuous
Choice_3_8_2 <= 1 Continuous
Choice_3_8_3 <= 1 Continuous
Choice_3_8_4 <= 1 Continuous
Choice_3_8_5 <= 1 Continuous
Choice_3_8_6 <= 1 Continuous
Choice_3_8_7 <= 1 Continuous
Choice_3_8_8 <= 1 Continuous
Choice_3_8_9 <= 1 Continuous
Choice_3_9_1 <= 1 Continuous
Choice_3_9_2 <= 1 Continuous
Choice_3_9_3 <= 1 Continuous
Choice_3_9_4 <= 1 Continuous
Choice_3_9_5 <= 1 Continuous
Choice_3_9_6 <= 1 Continuous
Choice_3_9_7 <= 1 Continuous
Choice_3_9_8 <= 1 Continuous
Choice_3_9_9 <= 1 Continuous
Choice_4_1_1 <= 1 Continuous
Choice_4_1_2 <= 1 Continuous
Choice_4_1_3 <= 1 Continuous
Choice_4_1_4 <= 1 Continuous
Choice_4_1_5 <= 1 Continuous
Choice_4_1_6 <= 1 Continuous
Choice_4_1_7 <= 1 Continuous
Choice_4_1_8 <= 1 Continuous
Choice_4_1_9 <= 1 Continuous
Choice_4_2_1 <= 1 Continuous
Choice_4_2_2 <= 1 Continuous
Choice_4_2_3 <= 1 Continuous
Choice_4_2_4 <= 1 Continuous
Choice_4_2_5 <= 1 Continuous
Choice_4_2_6 <= 1 Continuous
Choice_4_2_7 <= 1 Continuous
Choice_4_2_8 <= 1 Continuous
Choice_4_2_9 <= 1 Continuous
Choice_4_3_1 <= 1 Continuous
Choice_4_3_2 <= 1 Continuous
Choice_4_3_3 <= 1 Continuous
Choice_4_3_4 <= 1 Continuous
Choice_4_3_5 <= 1 Continuous
Choice_4_3_6 <= 1 Continuous
Choice_4_3_7 <= 1 Continuous
Choice_4_3_8 <= 1 Continuous
Choice_4_3_9 <= 1 Continuous
Choice_4_4_1 <= 1 Continuous
Choice_4_4_2 <= 1 Continuous
Choice_4_4_3 <= 1 Continuous
Choice_4_4_4 <= 1 Continuous
Choice_4_4_5 <= 1 Continuous
Choice_4_4_6 <= 1 Continuous
Choice_4_4_7 <= 1 Continuous
Choice_4_4_8 <= 1 Continuous
Choice_4_4_9 <= 1 Continuous
Choice_4_5_1 <= 1 Continuous
Choice_4_5_2 <= 1 Continuous
Choice_4_5_3 <= 1 Continuous
Choice_4_5_4 <= 1 Continuous
Choice_4_5_5 <= 1 Continuous
Choice_4_5_6 <= 1 Continuous
Choice_4_5_7 <= 1 Continuous
Choice_4_5_8 <= 1 Continuous
Choice_4_5_9 <= 1 Continuous
Choice_4_6_1 <= 1 Continuous
Choice_4_6_2 <= 1 Continuous
Choice_4_6_3 <= 1 Continuous
Choice_4_6_4 <= 1 Continuous
Choice_4_6_5 <= 1 Continuous
Choice_4_6_6 <= 1 Continuous
Choice_4_6_7 <= 1 Continuous
Choice_4_6_8 <= 1 Continuous
Choice_4_6_9 <= 1 Continuous
Choice_4_7_1 <= 1 Continuous
Choice_4_7_2 <= 1 Continuous
Choice_4_7_3 <= 1 Continuous
Choice_4_7_4 <= 1 Continuous
Choice_4_7_5 <= 1 Continuous
Choice_4_7_6 <= 1 Continuous
Choice_4_7_7 <= 1 Continuous
Choice_4_7_8 <= 1 Continuous
Choice_4_7_9 <= 1 Continuous
Choice_4_8_1 <= 1 Continuous
Choice_4_8_2 <= 1 Continuous
Choice_4_8_3 <= 1 Continuous
Choice_4_8_4 <= 1 Continuous
Choice_4_8_5 <= 1 Continuous
Choice_4_8_6 <= 1 Continuous
Choice_4_8_7 <= 1 Continuous
Choice_4_8_8 <= 1 Continuous
Choice_4_8_9 <= 1 Continuous
Choice_4_9_1 <= 1 Continuous
Choice_4_9_2 <= 1 Continuous
Choice_4_9_3 <= 1 Continuous
Choice_4_9_4 <= 1 Continuous
Choice_4_9_5 <= 1 Continuous
Choice_4_9_6 <= 1 Continuous
Choice_4_9_7 <= 1 Continuous
Choice_4_9_8 <= 1 Continuous
Choice_4_9_9 <= 1 Continuous
Choice_5_1_1 <= 1 Continuous
Choice_5_1_2 <= 1 Continuous
Choice_5_1_3 <= 1 Continuous
Choice_5_1_4 <= 1 Continuous
Choice_5_1_5 <= 1 Continuous
Choice_5_1_6 <= 1 Continuous
Choice_5_1_7 <= 1 Continuous
Choice_5_1_8 <= 1 Continuous
Choice_5_1_9 <= 1 Continuous
Choice_5_2_1 <= 1 Continuous
Choice_5_2_2 <= 1 Continuous
Choice_5_2_3 <= 1 Continuous
Choice_5_2_4 <= 1 Continuous
Choice_5_2_5 <= 1 Continuous
Choice_5_2_6 <= 1 Continuous
Choice_5_2_7 <= 1 Continuous
Choice_5_2_8 <= 1 Continuous
Choice_5_2_9 <= 1 Continuous
Choice_5_3_1 <= 1 Continuous
Choice_5_3_2 <= 1 Continuous
Choice_5_3_3 <= 1 Continuous
Choice_5_3_4 <= 1 Continuous
Choice_5_3_5 <= 1 Continuous
Choice_5_3_6 <= 1 Continuous
Choice_5_3_7 <= 1 Continuous
Choice_5_3_8 <= 1 Continuous
Choice_5_3_9 <= 1 Continuous
Choice_5_4_1 <= 1 Continuous
Choice_5_4_2 <= 1 Continuous
Choice_5_4_3 <= 1 Continuous
Choice_5_4_4 <= 1 Continuous
Choice_5_4_5 <= 1 Continuous
Choice_5_4_6 <= 1 Continuous
Choice_5_4_7 <= 1 Continuous
Choice_5_4_8 <= 1 Continuous
Choice_5_4_9 <= 1 Continuous
Choice_5_5_1 <= 1 Continuous
Choice_5_5_2 <= 1 Continuous
Choice_5_5_3 <= 1 Continuous
Choice_5_5_4 <= 1 Continuous
Choice_5_5_5 <= 1 Continuous
Choice_5_5_6 <= 1 Continuous
Choice_5_5_7 <= 1 Continuous
Choice_5_5_8 <= 1 Continuous
Choice_5_5_9 <= 1 Continuous
Choice_5_6_1 <= 1 Continuous
Choice_5_6_2 <= 1 Continuous
Choice_5_6_3 <= 1 Continuous
Choice_5_6_4 <= 1 Continuous
Choice_5_6_5 <= 1 Continuous
Choice_5_6_6 <= 1 Continuous
Choice_5_6_7 <= 1 Continuous
Choice_5_6_8 <= 1 Continuous
Choice_5_6_9 <= 1 Continuous
Choice_5_7_1 <= 1 Continuous
Choice_5_7_2 <= 1 Continuous
Choice_5_7_3 <= 1 Continuous
Choice_5_7_4 <= 1 Continuous
Choice_5_7_5 <= 1 Continuous
Choice_5_7_6 <= 1 Continuous
Choice_5_7_7 <= 1 Continuous
Choice_5_7_8 <= 1 Continuous
Choice_5_7_9 <= 1 Continuous
Choice_5_8_1 <= 1 Continuous
Choice_5_8_2 <= 1 Continuous
Choice_5_8_3 <= 1 Continuous
Choice_5_8_4 <= 1 Continuous
Choice_5_8_5 <= 1 Continuous
Choice_5_8_6 <= 1 Continuous
Choice_5_8_7 <= 1 Continuous
Choice_5_8_8 <= 1 Continuous
Choice_5_8_9 <= 1 Continuous
Choice_5_9_1 <= 1 Continuous
Choice_5_9_2 <= 1 Continuous
Choice_5_9_3 <= 1 Continuous
Choice_5_9_4 <= 1 Continuous
Choice_5_9_5 <= 1 Continuous
Choice_5_9_6 <= 1 Continuous
Choice_5_9_7 <= 1 Continuous
Choice_5_9_8 <= 1 Continuous
Choice_5_9_9 <= 1 Continuous
Choice_6_1_1 <= 1 Continuous
Choice_6_1_2 <= 1 Continuous
Choice_6_1_3 <= 1 Continuous
Choice_6_1_4 <= 1 Continuous
Choice_6_1_5 <= 1 Continuous
Choice_6_1_6 <= 1 Continuous
Choice_6_1_7 <= 1 Continuous
Choice_6_1_8 <= 1 Continuous
Choice_6_1_9 <= 1 Continuous
Choice_6_2_1 <= 1 Continuous
Choice_6_2_2 <= 1 Continuous
Choice_6_2_3 <= 1 Continuous
Choice_6_2_4 <= 1 Continuous
Choice_6_2_5 <= 1 Continuous
Choice_6_2_6 <= 1 Continuous
Choice_6_2_7 <= 1 Continuous
Choice_6_2_8 <= 1 Continuous
Choice_6_2_9 <= 1 Continuous
Choice_6_3_1 <= 1 Continuous
Choice_6_3_2 <= 1 Continuous
Choice_6_3_3 <= 1 Continuous
Choice_6_3_4 <= 1 Continuous
Choice_6_3_5 <= 1 Continuous
Choice_6_3_6 <= 1 Continuous
Choice_6_3_7 <= 1 Continuous
Choice_6_3_8 <= 1 Continuous
Choice_6_3_9 <= 1 Continuous
Choice_6_4_1 <= 1 Continuous
Choice_6_4_2 <= 1 Continuous
Choice_6_4_3 <= 1 Continuous
Choice_6_4_4 <= 1 Continuous
Choice_6_4_5 <= 1 Continuous
Choice_6_4_6 <= 1 Continuous
Choice_6_4_7 <= 1 Continuous
Choice_6_4_8 <= 1 Continuous
Choice_6_4_9 <= 1 Continuous
Choice_6_5_1 <= 1 Continuous
Choice_6_5_2 <= 1 Continuous
Choice_6_5_3 <= 1 Continuous
Choice_6_5_4 <= 1 Continuous
Choice_6_5_5 <= 1 Continuous
Choice_6_5_6 <= 1 Continuous
Choice_6_5_7 <= 1 Continuous
Choice_6_5_8 <= 1 Continuous
Choice_6_5_9 <= 1 Continuous
Choice_6_6_1 <= 1 Continuous
Choice_6_6_2 <= 1 Continuous
Choice_6_6_3 <= 1 Continuous
Choice_6_6_4 <= 1 Continuous
Choice_6_6_5 <= 1 Continuous
Choice_6_6_6 <= 1 Continuous
Choice_6_6_7 <= 1 Continuous
Choice_6_6_8 <= 1 Continuous
Choice_6_6_9 <= 1 Continuous
Choice_6_7_1 <= 1 Continuous
Choice_6_7_2 <= 1 Continuous
Choice_6_7_3 <= 1 Continuous
Choice_6_7_4 <= 1 Continuous
Choice_6_7_5 <= 1 Continuous
Choice_6_7_6 <= 1 Continuous
Choice_6_7_7 <= 1 Continuous
Choice_6_7_8 <= 1 Continuous
Choice_6_7_9 <= 1 Continuous
Choice_6_8_1 <= 1 Continuous
Choice_6_8_2 <= 1 Continuous
Choice_6_8_3 <= 1 Continuous
Choice_6_8_4 <= 1 Continuous
Choice_6_8_5 <= 1 Continuous
Choice_6_8_6 <= 1 Continuous
Choice_6_8_7 <= 1 Continuous
Choice_6_8_8 <= 1 Continuous
Choice_6_8_9 <= 1 Continuous
Choice_6_9_1 <= 1 Continuous
Choice_6_9_2 <= 1 Continuous
Choice_6_9_3 <= 1 Continuous
Choice_6_9_4 <= 1 Continuous
Choice_6_9_5 <= 1 Continuous
Choice_6_9_6 <= 1 Continuous
Choice_6_9_7 <= 1 Continuous
Choice_6_9_8 <= 1 Continuous
Choice_6_9_9 <= 1 Continuous
Choice_7_1_1 <= 1 Continuous
Choice_7_1_2 <= 1 Continuous
Choice_7_1_3 <= 1 Continuous
Choice_7_1_4 <= 1 Continuous
Choice_7_1_5 <= 1 Continuous
Choice_7_1_6 <= 1 Continuous
Choice_7_1_7 <= 1 Continuous
Choice_7_1_8 <= 1 Continuous
Choice_7_1_9 <= 1 Continuous
Choice_7_2_1 <= 1 Continuous
Choice_7_2_2 <= 1 Continuous
Choice_7_2_3 <= 1 Continuous
Choice_7_2_4 <= 1 Continuous
Choice_7_2_5 <= 1 Continuous
Choice_7_2_6 <= 1 Continuous
Choice_7_2_7 <= 1 Continuous
Choice_7_2_8 <= 1 Continuous
Choice_7_2_9 <= 1 Continuous
Choice_7_3_1 <= 1 Continuous
Choice_7_3_2 <= 1 Continuous
Choice_7_3_3 <= 1 Continuous
Choice_7_3_4 <= 1 Continuous
Choice_7_3_5 <= 1 Continuous
Choice_7_3_6 <= 1 Continuous
Choice_7_3_7 <= 1 Continuous
Choice_7_3_8 <= 1 Continuous
Choice_7_3_9 <= 1 Continuous
Choice_7_4_1 <= 1 Continuous
Choice_7_4_2 <= 1 Continuous
Choice_7_4_3 <= 1 Continuous
Choice_7_4_4 <= 1 Continuous
Choice_7_4_5 <= 1 Continuous
Choice_7_4_6 <= 1 Continuous
Choice_7_4_7 <= 1 Continuous
Choice_7_4_8 <= 1 Continuous
Choice_7_4_9 <= 1 Continuous
Choice_7_5_1 <= 1 Continuous
Choice_7_5_2 <= 1 Continuous
Choice_7_5_3 <= 1 Continuous
Choice_7_5_4 <= 1 Continuous
Choice_7_5_5 <= 1 Continuous
Choice_7_5_6 <= 1 Continuous
Choice_7_5_7 <= 1 Continuous
Choice_7_5_8 <= 1 Continuous
Choice_7_5_9 <= 1 Continuous
Choice_7_6_1 <= 1 Continuous
Choice_7_6_2 <= 1 Continuous
Choice_7_6_3 <= 1 Continuous
Choice_7_6_4 <= 1 Continuous
Choice_7_6_5 <= 1 Continuous
Choice_7_6_6 <= 1 Continuous
Choice_7_6_7 <= 1 Continuous
Choice_7_6_8 <= 1 Continuous
Choice_7_6_9 <= 1 Continuous
Choice_7_7_1 <= 1 Continuous
Choice_7_7_2 <= 1 Continuous
Choice_7_7_3 <= 1 Continuous
Choice_7_7_4 <= 1 Continuous
Choice_7_7_5 <= 1 Continuous
Choice_7_7_6 <= 1 Continuous
Choice_7_7_7 <= 1 Continuous
Choice_7_7_8 <= 1 Continuous
Choice_7_7_9 <= 1 Continuous
Choice_7_8_1 <= 1 Continuous
Choice_7_8_2 <= 1 Continuous
Choice_7_8_3 <= 1 Continuous
Choice_7_8_4 <= 1 Continuous
Choice_7_8_5 <= 1 Continuous
Choice_7_8_6 <= 1 Continuous
Choice_7_8_7 <= 1 Continuous
Choice_7_8_8 <= 1 Continuous
Choice_7_8_9 <= 1 Continuous
Choice_7_9_1 <= 1 Continuous
Choice_7_9_2 <= 1 Continuous
Choice_7_9_3 <= 1 Continuous
Choice_7_9_4 <= 1 Continuous
Choice_7_9_5 <= 1 Continuous
Choice_7_9_6 <= 1 Continuous
Choice_7_9_7 <= 1 Continuous
Choice_7_9_8 <= 1 Continuous
Choice_7_9_9 <= 1 Continuous
Choice_8_1_1 <= 1 Continuous
Choice_8_1_2 <= 1 Continuous
Choice_8_1_3 <= 1 Continuous
Choice_8_1_4 <= 1 Continuous
Choice_8_1_5 <= 1 Continuous
Choice_8_1_6 <= 1 Continuous
Choice_8_1_7 <= 1 Continuous
Choice_8_1_8 <= 1 Continuous
Choice_8_1_9 <= 1 Continuous
Choice_8_2_1 <= 1 Continuous
Choice_8_2_2 <= 1 Continuous
Choice_8_2_3 <= 1 Continuous
Choice_8_2_4 <= 1 Continuous
Choice_8_2_5 <= 1 Continuous
Choice_8_2_6 <= 1 Continuous
Choice_8_2_7 <= 1 Continuous
Choice_8_2_8 <= 1 Continuous
Choice_8_2_9 <= 1 Continuous
Choice_8_3_1 <= 1 Continuous
Choice_8_3_2 <= 1 Continuous
Choice_8_3_3 <= 1 Continuous
Choice_8_3_4 <= 1 Continuous
Choice_8_3_5 <= 1 Continuous
Choice_8_3_6 <= 1 Continuous
Choice_8_3_7 <= 1 Continuous
Choice_8_3_8 <= 1 Continuous
Choice_8_3_9 <= 1 Continuous
Choice_8_4_1 <= 1 Continuous
Choice_8_4_2 <= 1 Continuous
Choice_8_4_3 <= 1 Continuous
Choice_8_4_4 <= 1 Continuous
Choice_8_4_5 <= 1 Continuous
Choice_8_4_6 <= 1 Continuous
Choice_8_4_7 <= 1 Continuous
Choice_8_4_8 <= 1 Continuous
Choice_8_4_9 <= 1 Continuous
Choice_8_5_1 <= 1 Continuous
Choice_8_5_2 <= 1 Continuous
Choice_8_5_3 <= 1 Continuous
Choice_8_5_4 <= 1 Continuous
Choice_8_5_5 <= 1 Continuous
Choice_8_5_6 <= 1 Continuous
Choice_8_5_7 <= 1 Continuous
Choice_8_5_8 <= 1 Continuous
Choice_8_5_9 <= 1 Continuous
Choice_8_6_1 <= 1 Continuous
Choice_8_6_2 <= 1 Continuous
Choice_8_6_3 <= 1 Continuous
Choice_8_6_4 <= 1 Continuous
Choice_8_6_5 <= 1 Continuous
Choice_8_6_6 <= 1 Continuous
Choice_8_6_7 <= 1 Continuous
Choice_8_6_8 <= 1 Continuous
Choice_8_6_9 <= 1 Continuous
Choice_8_7_1 <= 1 Continuous
Choice_8_7_2 <= 1 Continuous
Choice_8_7_3 <= 1 Continuous
Choice_8_7_4 <= 1 Continuous
Choice_8_7_5 <= 1 Continuous
Choice_8_7_6 <= 1 Continuous
Choice_8_7_7 <= 1 Continuous
Choice_8_7_8 <= 1 Continuous
Choice_8_7_9 <= 1 Continuous
Choice_8_8_1 <= 1 Continuous
Choice_8_8_2 <= 1 Continuous
Choice_8_8_3 <= 1 Continuous
Choice_8_8_4 <= 1 Continuous
Choice_8_8_5 <= 1 Continuous
Choice_8_8_6 <= 1 Continuous
Choice_8_8_7 <= 1 Continuous
Choice_8_8_8 <= 1 Continuous
Choice_8_8_9 <= 1 Continuous
Choice_8_9_1 <= 1 Continuous
Choice_8_9_2 <= 1 Continuous
Choice_8_9_3 <= 1 Continuous
Choice_8_9_4 <= 1 Continuous
Choice_8_9_5 <= 1 Continuous
Choice_8_9_6 <= 1 Continuous
Choice_8_9_7 <= 1 Continuous
Choice_8_9_8 <= 1 Continuous
Choice_8_9_9 <= 1 Continuous
Choice_9_1_1 <= 1 Continuous
Choice_9_1_2 <= 1 Continuous
Choice_9_1_3 <= 1 Continuous
Choice_9_1_4 <= 1 Continuous
Choice_9_1_5 <= 1 Continuous
Choice_9_1_6 <= 1 Continuous
Choice_9_1_7 <= 1 Continuous
Choice_9_1_8 <= 1 Continuous
Choice_9_1_9 <= 1 Continuous
Choice_9_2_1 <= 1 Continuous
Choice_9_2_2 <= 1 Continuous
Choice_9_2_3 <= 1 Continuous
Choice_9_2_4 <= 1 Continuous
Choice_9_2_5 <= 1 Continuous
Choice_9_2_6 <= 1 Continuous
Choice_9_2_7 <= 1 Continuous
Choice_9_2_8 <= 1 Continuous
Choice_9_2_9 <= 1 Continuous
Choice_9_3_1 <= 1 Continuous
Choice_9_3_2 <= 1 Continuous
Choice_9_3_3 <= 1 Continuous
Choice_9_3_4 <= 1 Continuous
Choice_9_3_5 <= 1 Continuous
Choice_9_3_6 <= 1 Continuous
Choice_9_3_7 <= 1 Continuous
Choice_9_3_8 <= 1 Continuous
Choice_9_3_9 <= 1 Continuous
Choice_9_4_1 <= 1 Continuous
Choice_9_4_2 <= 1 Continuous
Choice_9_4_3 <= 1 Continuous
Choice_9_4_4 <= 1 Continuous
Choice_9_4_5 <= 1 Continuous
Choice_9_4_6 <= 1 Continuous
Choice_9_4_7 <= 1 Continuous
Choice_9_4_8 <= 1 Continuous
Choice_9_4_9 <= 1 Continuous
Choice_9_5_1 <= 1 Continuous
Choice_9_5_2 <= 1 Continuous
Choice_9_5_3 <= 1 Continuous
Choice_9_5_4 <= 1 Continuous
Choice_9_5_5 <= 1 Continuous
Choice_9_5_6 <= 1 Continuous
Choice_9_5_7 <= 1 Continuous
Choice_9_5_8 <= 1 Continuous
Choice_9_5_9 <= 1 Continuous
Choice_9_6_1 <= 1 Continuous
Choice_9_6_2 <= 1 Continuous
Choice_9_6_3 <= 1 Continuous
Choice_9_6_4 <= 1 Continuous
Choice_9_6_5 <= 1 Continuous
Choice_9_6_6 <= 1 Continuous
Choice_9_6_7 <= 1 Continuous
Choice_9_6_8 <= 1 Continuous
Choice_9_6_9 <= 1 Continuous
Choice_9_7_1 <= 1 Continuous
Choice_9_7_2 <= 1 Continuous
Choice_9_7_3 <= 1 Continuous
Choice_9_7_4 <= 1 Continuous
Choice_9_7_5 <= 1 Continuous
Choice_9_7_6 <= 1 Continuous
Choice_9_7_7 <= 1 Continuous
Choice_9_7_8 <= 1 Continuous
Choice_9_7_9 <= 1 Continuous
Choice_9_8_1 <= 1 Continuous
Choice_9_8_2 <= 1 Continuous
Choice_9_8_3 <= 1 Continuous
Choice_9_8_4 <= 1 Continuous
Choice_9_8_5 <= 1 Continuous
Choice_9_8_6 <= 1 Continuous
Choice_9_8_7 <= 1 Continuous
Choice_9_8_8 <= 1 Continuous
Choice_9_8_9 <= 1 Continuous
Choice_9_9_1 <= 1 Continuous
Choice_9_9_2 <= 1 Continuous
Choice_9_9_3 <= 1 Continuous
Choice_9_9_4 <= 1 Continuous
Choice_9_9_5 <= 1 Continuous
Choice_9_9_6 <= 1 Continuous
Choice_9_9_7 <= 1 Continuous
Choice_9_9_8 <= 1 Continuous
Choice_9_9_9 <= 1 Continuous
__dummy = 0 Continuous
In [19]:
print open("sudokuout2.txt").read()
+-------+-------+-------+
9 5 7 |
| 7 8 9 4 5 |
5 8 +-------+-------+-------+
3 2 | 5 | 6 | 5 8 1 3 |
+-------+-------+-------+
1 | 7 5 | 9 6 +-------+-------+-------+
In [ ]: