! Linear Programming Model To Solve SUDOKU (Model generated for LINGO);

! (c) Dr. Claudio Soto, 27 April 2010, Uruguay, e-mail: srvet@adinet.com.uy ;


! COMMENTS: Example provided by Rathinagiri (N 5) ;

! ************** Draw SUDOKU *************************************;

!     C1  C2  C3  C4  C5  C6  C7  C8  C9 ;

! R1   4       8           6       9   7 ;
! R2       9       7       1             ;
! R3       3       2   9       8       1 ;
! R4           3                   4   2 ;
! R5   9       1               5       8 ;
! R6   8   2                   7         ;
! R7   2       9       4   5       7     ;
! R8               6       8       2     ;
! R9   1   6       3           4         ;


! ************** MODEL: Objective Function ************************;

MIN = R1C1_n1;

! ************** MODEL: Restrictions *****************************;


! ************** Numbers/Cells Restrictions ************************;

R1C1_n1 + R1C1_n2 + R1C1_n3 + R1C1_n4 + R1C1_n5 + R1C1_n6 + R1C1_n7 + R1C1_n8 + R1C1_n9 = 1;
R1C2_n1 + R1C2_n2 + R1C2_n3 + R1C2_n4 + R1C2_n5 + R1C2_n6 + R1C2_n7 + R1C2_n8 + R1C2_n9 = 1;
R1C3_n1 + R1C3_n2 + R1C3_n3 + R1C3_n4 + R1C3_n5 + R1C3_n6 + R1C3_n7 + R1C3_n8 + R1C3_n9 = 1;
R1C4_n1 + R1C4_n2 + R1C4_n3 + R1C4_n4 + R1C4_n5 + R1C4_n6 + R1C4_n7 + R1C4_n8 + R1C4_n9 = 1;
R1C5_n1 + R1C5_n2 + R1C5_n3 + R1C5_n4 + R1C5_n5 + R1C5_n6 + R1C5_n7 + R1C5_n8 + R1C5_n9 = 1;
R1C6_n1 + R1C6_n2 + R1C6_n3 + R1C6_n4 + R1C6_n5 + R1C6_n6 + R1C6_n7 + R1C6_n8 + R1C6_n9 = 1;
R1C7_n1 + R1C7_n2 + R1C7_n3 + R1C7_n4 + R1C7_n5 + R1C7_n6 + R1C7_n7 + R1C7_n8 + R1C7_n9 = 1;
R1C8_n1 + R1C8_n2 + R1C8_n3 + R1C8_n4 + R1C8_n5 + R1C8_n6 + R1C8_n7 + R1C8_n8 + R1C8_n9 = 1;
R1C9_n1 + R1C9_n2 + R1C9_n3 + R1C9_n4 + R1C9_n5 + R1C9_n6 + R1C9_n7 + R1C9_n8 + R1C9_n9 = 1;

R2C1_n1 + R2C1_n2 + R2C1_n3 + R2C1_n4 + R2C1_n5 + R2C1_n6 + R2C1_n7 + R2C1_n8 + R2C1_n9 = 1;
R2C2_n1 + R2C2_n2 + R2C2_n3 + R2C2_n4 + R2C2_n5 + R2C2_n6 + R2C2_n7 + R2C2_n8 + R2C2_n9 = 1;
R2C3_n1 + R2C3_n2 + R2C3_n3 + R2C3_n4 + R2C3_n5 + R2C3_n6 + R2C3_n7 + R2C3_n8 + R2C3_n9 = 1;
R2C4_n1 + R2C4_n2 + R2C4_n3 + R2C4_n4 + R2C4_n5 + R2C4_n6 + R2C4_n7 + R2C4_n8 + R2C4_n9 = 1;
R2C5_n1 + R2C5_n2 + R2C5_n3 + R2C5_n4 + R2C5_n5 + R2C5_n6 + R2C5_n7 + R2C5_n8 + R2C5_n9 = 1;
R2C6_n1 + R2C6_n2 + R2C6_n3 + R2C6_n4 + R2C6_n5 + R2C6_n6 + R2C6_n7 + R2C6_n8 + R2C6_n9 = 1;
R2C7_n1 + R2C7_n2 + R2C7_n3 + R2C7_n4 + R2C7_n5 + R2C7_n6 + R2C7_n7 + R2C7_n8 + R2C7_n9 = 1;
R2C8_n1 + R2C8_n2 + R2C8_n3 + R2C8_n4 + R2C8_n5 + R2C8_n6 + R2C8_n7 + R2C8_n8 + R2C8_n9 = 1;
R2C9_n1 + R2C9_n2 + R2C9_n3 + R2C9_n4 + R2C9_n5 + R2C9_n6 + R2C9_n7 + R2C9_n8 + R2C9_n9 = 1;

R3C1_n1 + R3C1_n2 + R3C1_n3 + R3C1_n4 + R3C1_n5 + R3C1_n6 + R3C1_n7 + R3C1_n8 + R3C1_n9 = 1;
R3C2_n1 + R3C2_n2 + R3C2_n3 + R3C2_n4 + R3C2_n5 + R3C2_n6 + R3C2_n7 + R3C2_n8 + R3C2_n9 = 1;
R3C3_n1 + R3C3_n2 + R3C3_n3 + R3C3_n4 + R3C3_n5 + R3C3_n6 + R3C3_n7 + R3C3_n8 + R3C3_n9 = 1;
R3C4_n1 + R3C4_n2 + R3C4_n3 + R3C4_n4 + R3C4_n5 + R3C4_n6 + R3C4_n7 + R3C4_n8 + R3C4_n9 = 1;
R3C5_n1 + R3C5_n2 + R3C5_n3 + R3C5_n4 + R3C5_n5 + R3C5_n6 + R3C5_n7 + R3C5_n8 + R3C5_n9 = 1;
R3C6_n1 + R3C6_n2 + R3C6_n3 + R3C6_n4 + R3C6_n5 + R3C6_n6 + R3C6_n7 + R3C6_n8 + R3C6_n9 = 1;
R3C7_n1 + R3C7_n2 + R3C7_n3 + R3C7_n4 + R3C7_n5 + R3C7_n6 + R3C7_n7 + R3C7_n8 + R3C7_n9 = 1;
R3C8_n1 + R3C8_n2 + R3C8_n3 + R3C8_n4 + R3C8_n5 + R3C8_n6 + R3C8_n7 + R3C8_n8 + R3C8_n9 = 1;
R3C9_n1 + R3C9_n2 + R3C9_n3 + R3C9_n4 + R3C9_n5 + R3C9_n6 + R3C9_n7 + R3C9_n8 + R3C9_n9 = 1;

R4C1_n1 + R4C1_n2 + R4C1_n3 + R4C1_n4 + R4C1_n5 + R4C1_n6 + R4C1_n7 + R4C1_n8 + R4C1_n9 = 1;
R4C2_n1 + R4C2_n2 + R4C2_n3 + R4C2_n4 + R4C2_n5 + R4C2_n6 + R4C2_n7 + R4C2_n8 + R4C2_n9 = 1;
R4C3_n1 + R4C3_n2 + R4C3_n3 + R4C3_n4 + R4C3_n5 + R4C3_n6 + R4C3_n7 + R4C3_n8 + R4C3_n9 = 1;
R4C4_n1 + R4C4_n2 + R4C4_n3 + R4C4_n4 + R4C4_n5 + R4C4_n6 + R4C4_n7 + R4C4_n8 + R4C4_n9 = 1;
R4C5_n1 + R4C5_n2 + R4C5_n3 + R4C5_n4 + R4C5_n5 + R4C5_n6 + R4C5_n7 + R4C5_n8 + R4C5_n9 = 1;
R4C6_n1 + R4C6_n2 + R4C6_n3 + R4C6_n4 + R4C6_n5 + R4C6_n6 + R4C6_n7 + R4C6_n8 + R4C6_n9 = 1;
R4C7_n1 + R4C7_n2 + R4C7_n3 + R4C7_n4 + R4C7_n5 + R4C7_n6 + R4C7_n7 + R4C7_n8 + R4C7_n9 = 1;
R4C8_n1 + R4C8_n2 + R4C8_n3 + R4C8_n4 + R4C8_n5 + R4C8_n6 + R4C8_n7 + R4C8_n8 + R4C8_n9 = 1;
R4C9_n1 + R4C9_n2 + R4C9_n3 + R4C9_n4 + R4C9_n5 + R4C9_n6 + R4C9_n7 + R4C9_n8 + R4C9_n9 = 1;

R5C1_n1 + R5C1_n2 + R5C1_n3 + R5C1_n4 + R5C1_n5 + R5C1_n6 + R5C1_n7 + R5C1_n8 + R5C1_n9 = 1;
R5C2_n1 + R5C2_n2 + R5C2_n3 + R5C2_n4 + R5C2_n5 + R5C2_n6 + R5C2_n7 + R5C2_n8 + R5C2_n9 = 1;
R5C3_n1 + R5C3_n2 + R5C3_n3 + R5C3_n4 + R5C3_n5 + R5C3_n6 + R5C3_n7 + R5C3_n8 + R5C3_n9 = 1;
R5C4_n1 + R5C4_n2 + R5C4_n3 + R5C4_n4 + R5C4_n5 + R5C4_n6 + R5C4_n7 + R5C4_n8 + R5C4_n9 = 1;
R5C5_n1 + R5C5_n2 + R5C5_n3 + R5C5_n4 + R5C5_n5 + R5C5_n6 + R5C5_n7 + R5C5_n8 + R5C5_n9 = 1;
R5C6_n1 + R5C6_n2 + R5C6_n3 + R5C6_n4 + R5C6_n5 + R5C6_n6 + R5C6_n7 + R5C6_n8 + R5C6_n9 = 1;
R5C7_n1 + R5C7_n2 + R5C7_n3 + R5C7_n4 + R5C7_n5 + R5C7_n6 + R5C7_n7 + R5C7_n8 + R5C7_n9 = 1;
R5C8_n1 + R5C8_n2 + R5C8_n3 + R5C8_n4 + R5C8_n5 + R5C8_n6 + R5C8_n7 + R5C8_n8 + R5C8_n9 = 1;
R5C9_n1 + R5C9_n2 + R5C9_n3 + R5C9_n4 + R5C9_n5 + R5C9_n6 + R5C9_n7 + R5C9_n8 + R5C9_n9 = 1;

R6C1_n1 + R6C1_n2 + R6C1_n3 + R6C1_n4 + R6C1_n5 + R6C1_n6 + R6C1_n7 + R6C1_n8 + R6C1_n9 = 1;
R6C2_n1 + R6C2_n2 + R6C2_n3 + R6C2_n4 + R6C2_n5 + R6C2_n6 + R6C2_n7 + R6C2_n8 + R6C2_n9 = 1;
R6C3_n1 + R6C3_n2 + R6C3_n3 + R6C3_n4 + R6C3_n5 + R6C3_n6 + R6C3_n7 + R6C3_n8 + R6C3_n9 = 1;
R6C4_n1 + R6C4_n2 + R6C4_n3 + R6C4_n4 + R6C4_n5 + R6C4_n6 + R6C4_n7 + R6C4_n8 + R6C4_n9 = 1;
R6C5_n1 + R6C5_n2 + R6C5_n3 + R6C5_n4 + R6C5_n5 + R6C5_n6 + R6C5_n7 + R6C5_n8 + R6C5_n9 = 1;
R6C6_n1 + R6C6_n2 + R6C6_n3 + R6C6_n4 + R6C6_n5 + R6C6_n6 + R6C6_n7 + R6C6_n8 + R6C6_n9 = 1;
R6C7_n1 + R6C7_n2 + R6C7_n3 + R6C7_n4 + R6C7_n5 + R6C7_n6 + R6C7_n7 + R6C7_n8 + R6C7_n9 = 1;
R6C8_n1 + R6C8_n2 + R6C8_n3 + R6C8_n4 + R6C8_n5 + R6C8_n6 + R6C8_n7 + R6C8_n8 + R6C8_n9 = 1;
R6C9_n1 + R6C9_n2 + R6C9_n3 + R6C9_n4 + R6C9_n5 + R6C9_n6 + R6C9_n7 + R6C9_n8 + R6C9_n9 = 1;

R7C1_n1 + R7C1_n2 + R7C1_n3 + R7C1_n4 + R7C1_n5 + R7C1_n6 + R7C1_n7 + R7C1_n8 + R7C1_n9 = 1;
R7C2_n1 + R7C2_n2 + R7C2_n3 + R7C2_n4 + R7C2_n5 + R7C2_n6 + R7C2_n7 + R7C2_n8 + R7C2_n9 = 1;
R7C3_n1 + R7C3_n2 + R7C3_n3 + R7C3_n4 + R7C3_n5 + R7C3_n6 + R7C3_n7 + R7C3_n8 + R7C3_n9 = 1;
R7C4_n1 + R7C4_n2 + R7C4_n3 + R7C4_n4 + R7C4_n5 + R7C4_n6 + R7C4_n7 + R7C4_n8 + R7C4_n9 = 1;
R7C5_n1 + R7C5_n2 + R7C5_n3 + R7C5_n4 + R7C5_n5 + R7C5_n6 + R7C5_n7 + R7C5_n8 + R7C5_n9 = 1;
R7C6_n1 + R7C6_n2 + R7C6_n3 + R7C6_n4 + R7C6_n5 + R7C6_n6 + R7C6_n7 + R7C6_n8 + R7C6_n9 = 1;
R7C7_n1 + R7C7_n2 + R7C7_n3 + R7C7_n4 + R7C7_n5 + R7C7_n6 + R7C7_n7 + R7C7_n8 + R7C7_n9 = 1;
R7C8_n1 + R7C8_n2 + R7C8_n3 + R7C8_n4 + R7C8_n5 + R7C8_n6 + R7C8_n7 + R7C8_n8 + R7C8_n9 = 1;
R7C9_n1 + R7C9_n2 + R7C9_n3 + R7C9_n4 + R7C9_n5 + R7C9_n6 + R7C9_n7 + R7C9_n8 + R7C9_n9 = 1;

R8C1_n1 + R8C1_n2 + R8C1_n3 + R8C1_n4 + R8C1_n5 + R8C1_n6 + R8C1_n7 + R8C1_n8 + R8C1_n9 = 1;
R8C2_n1 + R8C2_n2 + R8C2_n3 + R8C2_n4 + R8C2_n5 + R8C2_n6 + R8C2_n7 + R8C2_n8 + R8C2_n9 = 1;
R8C3_n1 + R8C3_n2 + R8C3_n3 + R8C3_n4 + R8C3_n5 + R8C3_n6 + R8C3_n7 + R8C3_n8 + R8C3_n9 = 1;
R8C4_n1 + R8C4_n2 + R8C4_n3 + R8C4_n4 + R8C4_n5 + R8C4_n6 + R8C4_n7 + R8C4_n8 + R8C4_n9 = 1;
R8C5_n1 + R8C5_n2 + R8C5_n3 + R8C5_n4 + R8C5_n5 + R8C5_n6 + R8C5_n7 + R8C5_n8 + R8C5_n9 = 1;
R8C6_n1 + R8C6_n2 + R8C6_n3 + R8C6_n4 + R8C6_n5 + R8C6_n6 + R8C6_n7 + R8C6_n8 + R8C6_n9 = 1;
R8C7_n1 + R8C7_n2 + R8C7_n3 + R8C7_n4 + R8C7_n5 + R8C7_n6 + R8C7_n7 + R8C7_n8 + R8C7_n9 = 1;
R8C8_n1 + R8C8_n2 + R8C8_n3 + R8C8_n4 + R8C8_n5 + R8C8_n6 + R8C8_n7 + R8C8_n8 + R8C8_n9 = 1;
R8C9_n1 + R8C9_n2 + R8C9_n3 + R8C9_n4 + R8C9_n5 + R8C9_n6 + R8C9_n7 + R8C9_n8 + R8C9_n9 = 1;

R9C1_n1 + R9C1_n2 + R9C1_n3 + R9C1_n4 + R9C1_n5 + R9C1_n6 + R9C1_n7 + R9C1_n8 + R9C1_n9 = 1;
R9C2_n1 + R9C2_n2 + R9C2_n3 + R9C2_n4 + R9C2_n5 + R9C2_n6 + R9C2_n7 + R9C2_n8 + R9C2_n9 = 1;
R9C3_n1 + R9C3_n2 + R9C3_n3 + R9C3_n4 + R9C3_n5 + R9C3_n6 + R9C3_n7 + R9C3_n8 + R9C3_n9 = 1;
R9C4_n1 + R9C4_n2 + R9C4_n3 + R9C4_n4 + R9C4_n5 + R9C4_n6 + R9C4_n7 + R9C4_n8 + R9C4_n9 = 1;
R9C5_n1 + R9C5_n2 + R9C5_n3 + R9C5_n4 + R9C5_n5 + R9C5_n6 + R9C5_n7 + R9C5_n8 + R9C5_n9 = 1;
R9C6_n1 + R9C6_n2 + R9C6_n3 + R9C6_n4 + R9C6_n5 + R9C6_n6 + R9C6_n7 + R9C6_n8 + R9C6_n9 = 1;
R9C7_n1 + R9C7_n2 + R9C7_n3 + R9C7_n4 + R9C7_n5 + R9C7_n6 + R9C7_n7 + R9C7_n8 + R9C7_n9 = 1;
R9C8_n1 + R9C8_n2 + R9C8_n3 + R9C8_n4 + R9C8_n5 + R9C8_n6 + R9C8_n7 + R9C8_n8 + R9C8_n9 = 1;
R9C9_n1 + R9C9_n2 + R9C9_n3 + R9C9_n4 + R9C9_n5 + R9C9_n6 + R9C9_n7 + R9C9_n8 + R9C9_n9 = 1;

! ************** Restrictions REGION A ************************;

R1C1_n1 + R1C2_n1 + R1C3_n1 + R2C1_n1 + R2C2_n1 + R2C3_n1 + R3C1_n1 + R3C2_n1 + R3C3_n1 = 1;
R1C1_n2 + R1C2_n2 + R1C3_n2 + R2C1_n2 + R2C2_n2 + R2C3_n2 + R3C1_n2 + R3C2_n2 + R3C3_n2 = 1;
R1C1_n3 + R1C2_n3 + R1C3_n3 + R2C1_n3 + R2C2_n3 + R2C3_n3 + R3C1_n3 + R3C2_n3 + R3C3_n3 = 1;
R1C1_n4 + R1C2_n4 + R1C3_n4 + R2C1_n4 + R2C2_n4 + R2C3_n4 + R3C1_n4 + R3C2_n4 + R3C3_n4 = 1;
R1C1_n5 + R1C2_n5 + R1C3_n5 + R2C1_n5 + R2C2_n5 + R2C3_n5 + R3C1_n5 + R3C2_n5 + R3C3_n5 = 1;
R1C1_n6 + R1C2_n6 + R1C3_n6 + R2C1_n6 + R2C2_n6 + R2C3_n6 + R3C1_n6 + R3C2_n6 + R3C3_n6 = 1;
R1C1_n7 + R1C2_n7 + R1C3_n7 + R2C1_n7 + R2C2_n7 + R2C3_n7 + R3C1_n7 + R3C2_n7 + R3C3_n7 = 1;
R1C1_n8 + R1C2_n8 + R1C3_n8 + R2C1_n8 + R2C2_n8 + R2C3_n8 + R3C1_n8 + R3C2_n8 + R3C3_n8 = 1;
R1C1_n9 + R1C2_n9 + R1C3_n9 + R2C1_n9 + R2C2_n9 + R2C3_n9 + R3C1_n9 + R3C2_n9 + R3C3_n9 = 1;

! ************** Restrictions REGION B ************************;

R1C4_n1 + R1C5_n1 + R1C6_n1 + R2C4_n1 + R2C5_n1 + R2C6_n1 + R3C4_n1 + R3C5_n1 + R3C6_n1 = 1;
R1C4_n2 + R1C5_n2 + R1C6_n2 + R2C4_n2 + R2C5_n2 + R2C6_n2 + R3C4_n2 + R3C5_n2 + R3C6_n2 = 1;
R1C4_n3 + R1C5_n3 + R1C6_n3 + R2C4_n3 + R2C5_n3 + R2C6_n3 + R3C4_n3 + R3C5_n3 + R3C6_n3 = 1;
R1C4_n4 + R1C5_n4 + R1C6_n4 + R2C4_n4 + R2C5_n4 + R2C6_n4 + R3C4_n4 + R3C5_n4 + R3C6_n4 = 1;
R1C4_n5 + R1C5_n5 + R1C6_n5 + R2C4_n5 + R2C5_n5 + R2C6_n5 + R3C4_n5 + R3C5_n5 + R3C6_n5 = 1;
R1C4_n6 + R1C5_n6 + R1C6_n6 + R2C4_n6 + R2C5_n6 + R2C6_n6 + R3C4_n6 + R3C5_n6 + R3C6_n6 = 1;
R1C4_n7 + R1C5_n7 + R1C6_n7 + R2C4_n7 + R2C5_n7 + R2C6_n7 + R3C4_n7 + R3C5_n7 + R3C6_n7 = 1;
R1C4_n8 + R1C5_n8 + R1C6_n8 + R2C4_n8 + R2C5_n8 + R2C6_n8 + R3C4_n8 + R3C5_n8 + R3C6_n8 = 1;
R1C4_n9 + R1C5_n9 + R1C6_n9 + R2C4_n9 + R2C5_n9 + R2C6_n9 + R3C4_n9 + R3C5_n9 + R3C6_n9 = 1;

! ************** Restrictions REGION C ************************;

R1C7_n1 + R1C8_n1 + R1C9_n1 + R2C7_n1 + R2C8_n1 + R2C9_n1 + R3C7_n1 + R3C8_n1 + R3C9_n1 = 1;
R1C7_n2 + R1C8_n2 + R1C9_n2 + R2C7_n2 + R2C8_n2 + R2C9_n2 + R3C7_n2 + R3C8_n2 + R3C9_n2 = 1;
R1C7_n3 + R1C8_n3 + R1C9_n3 + R2C7_n3 + R2C8_n3 + R2C9_n3 + R3C7_n3 + R3C8_n3 + R3C9_n3 = 1;
R1C7_n4 + R1C8_n4 + R1C9_n4 + R2C7_n4 + R2C8_n4 + R2C9_n4 + R3C7_n4 + R3C8_n4 + R3C9_n4 = 1;
R1C7_n5 + R1C8_n5 + R1C9_n5 + R2C7_n5 + R2C8_n5 + R2C9_n5 + R3C7_n5 + R3C8_n5 + R3C9_n5 = 1;
R1C7_n6 + R1C8_n6 + R1C9_n6 + R2C7_n6 + R2C8_n6 + R2C9_n6 + R3C7_n6 + R3C8_n6 + R3C9_n6 = 1;
R1C7_n7 + R1C8_n7 + R1C9_n7 + R2C7_n7 + R2C8_n7 + R2C9_n7 + R3C7_n7 + R3C8_n7 + R3C9_n7 = 1;
R1C7_n8 + R1C8_n8 + R1C9_n8 + R2C7_n8 + R2C8_n8 + R2C9_n8 + R3C7_n8 + R3C8_n8 + R3C9_n8 = 1;
R1C7_n9 + R1C8_n9 + R1C9_n9 + R2C7_n9 + R2C8_n9 + R2C9_n9 + R3C7_n9 + R3C8_n9 + R3C9_n9 = 1;

! ************** Restrictions REGION D ************************;

R4C1_n1 + R4C2_n1 + R4C3_n1 + R5C1_n1 + R5C2_n1 + R5C3_n1 + R6C1_n1 + R6C2_n1 + R6C3_n1 = 1;
R4C1_n2 + R4C2_n2 + R4C3_n2 + R5C1_n2 + R5C2_n2 + R5C3_n2 + R6C1_n2 + R6C2_n2 + R6C3_n2 = 1;
R4C1_n3 + R4C2_n3 + R4C3_n3 + R5C1_n3 + R5C2_n3 + R5C3_n3 + R6C1_n3 + R6C2_n3 + R6C3_n3 = 1;
R4C1_n4 + R4C2_n4 + R4C3_n4 + R5C1_n4 + R5C2_n4 + R5C3_n4 + R6C1_n4 + R6C2_n4 + R6C3_n4 = 1;
R4C1_n5 + R4C2_n5 + R4C3_n5 + R5C1_n5 + R5C2_n5 + R5C3_n5 + R6C1_n5 + R6C2_n5 + R6C3_n5 = 1;
R4C1_n6 + R4C2_n6 + R4C3_n6 + R5C1_n6 + R5C2_n6 + R5C3_n6 + R6C1_n6 + R6C2_n6 + R6C3_n6 = 1;
R4C1_n7 + R4C2_n7 + R4C3_n7 + R5C1_n7 + R5C2_n7 + R5C3_n7 + R6C1_n7 + R6C2_n7 + R6C3_n7 = 1;
R4C1_n8 + R4C2_n8 + R4C3_n8 + R5C1_n8 + R5C2_n8 + R5C3_n8 + R6C1_n8 + R6C2_n8 + R6C3_n8 = 1;
R4C1_n9 + R4C2_n9 + R4C3_n9 + R5C1_n9 + R5C2_n9 + R5C3_n9 + R6C1_n9 + R6C2_n9 + R6C3_n9 = 1;

! ************** Restrictions REGION E ************************;

R4C4_n1 + R4C5_n1 + R4C6_n1 + R5C4_n1 + R5C5_n1 + R5C6_n1 + R6C4_n1 + R6C5_n1 + R6C6_n1 = 1;
R4C4_n2 + R4C5_n2 + R4C6_n2 + R5C4_n2 + R5C5_n2 + R5C6_n2 + R6C4_n2 + R6C5_n2 + R6C6_n2 = 1;
R4C4_n3 + R4C5_n3 + R4C6_n3 + R5C4_n3 + R5C5_n3 + R5C6_n3 + R6C4_n3 + R6C5_n3 + R6C6_n3 = 1;
R4C4_n4 + R4C5_n4 + R4C6_n4 + R5C4_n4 + R5C5_n4 + R5C6_n4 + R6C4_n4 + R6C5_n4 + R6C6_n4 = 1;
R4C4_n5 + R4C5_n5 + R4C6_n5 + R5C4_n5 + R5C5_n5 + R5C6_n5 + R6C4_n5 + R6C5_n5 + R6C6_n5 = 1;
R4C4_n6 + R4C5_n6 + R4C6_n6 + R5C4_n6 + R5C5_n6 + R5C6_n6 + R6C4_n6 + R6C5_n6 + R6C6_n6 = 1;
R4C4_n7 + R4C5_n7 + R4C6_n7 + R5C4_n7 + R5C5_n7 + R5C6_n7 + R6C4_n7 + R6C5_n7 + R6C6_n7 = 1;
R4C4_n8 + R4C5_n8 + R4C6_n8 + R5C4_n8 + R5C5_n8 + R5C6_n8 + R6C4_n8 + R6C5_n8 + R6C6_n8 = 1;
R4C4_n9 + R4C5_n9 + R4C6_n9 + R5C4_n9 + R5C5_n9 + R5C6_n9 + R6C4_n9 + R6C5_n9 + R6C6_n9 = 1;

! ************** Restrictions REGION F ************************;

R4C7_n1 + R4C8_n1 + R4C9_n1 + R5C7_n1 + R5C8_n1 + R5C9_n1 + R6C7_n1 + R6C8_n1 + R6C9_n1 = 1;
R4C7_n2 + R4C8_n2 + R4C9_n2 + R5C7_n2 + R5C8_n2 + R5C9_n2 + R6C7_n2 + R6C8_n2 + R6C9_n2 = 1;
R4C7_n3 + R4C8_n3 + R4C9_n3 + R5C7_n3 + R5C8_n3 + R5C9_n3 + R6C7_n3 + R6C8_n3 + R6C9_n3 = 1;
R4C7_n4 + R4C8_n4 + R4C9_n4 + R5C7_n4 + R5C8_n4 + R5C9_n4 + R6C7_n4 + R6C8_n4 + R6C9_n4 = 1;
R4C7_n5 + R4C8_n5 + R4C9_n5 + R5C7_n5 + R5C8_n5 + R5C9_n5 + R6C7_n5 + R6C8_n5 + R6C9_n5 = 1;
R4C7_n6 + R4C8_n6 + R4C9_n6 + R5C7_n6 + R5C8_n6 + R5C9_n6 + R6C7_n6 + R6C8_n6 + R6C9_n6 = 1;
R4C7_n7 + R4C8_n7 + R4C9_n7 + R5C7_n7 + R5C8_n7 + R5C9_n7 + R6C7_n7 + R6C8_n7 + R6C9_n7 = 1;
R4C7_n8 + R4C8_n8 + R4C9_n8 + R5C7_n8 + R5C8_n8 + R5C9_n8 + R6C7_n8 + R6C8_n8 + R6C9_n8 = 1;
R4C7_n9 + R4C8_n9 + R4C9_n9 + R5C7_n9 + R5C8_n9 + R5C9_n9 + R6C7_n9 + R6C8_n9 + R6C9_n9 = 1;

! ************** Restrictions REGION G ************************;

R7C1_n1 + R7C2_n1 + R7C3_n1 + R8C1_n1 + R8C2_n1 + R8C3_n1 + R9C1_n1 + R9C2_n1 + R9C3_n1 = 1;
R7C1_n2 + R7C2_n2 + R7C3_n2 + R8C1_n2 + R8C2_n2 + R8C3_n2 + R9C1_n2 + R9C2_n2 + R9C3_n2 = 1;
R7C1_n3 + R7C2_n3 + R7C3_n3 + R8C1_n3 + R8C2_n3 + R8C3_n3 + R9C1_n3 + R9C2_n3 + R9C3_n3 = 1;
R7C1_n4 + R7C2_n4 + R7C3_n4 + R8C1_n4 + R8C2_n4 + R8C3_n4 + R9C1_n4 + R9C2_n4 + R9C3_n4 = 1;
R7C1_n5 + R7C2_n5 + R7C3_n5 + R8C1_n5 + R8C2_n5 + R8C3_n5 + R9C1_n5 + R9C2_n5 + R9C3_n5 = 1;
R7C1_n6 + R7C2_n6 + R7C3_n6 + R8C1_n6 + R8C2_n6 + R8C3_n6 + R9C1_n6 + R9C2_n6 + R9C3_n6 = 1;
R7C1_n7 + R7C2_n7 + R7C3_n7 + R8C1_n7 + R8C2_n7 + R8C3_n7 + R9C1_n7 + R9C2_n7 + R9C3_n7 = 1;
R7C1_n8 + R7C2_n8 + R7C3_n8 + R8C1_n8 + R8C2_n8 + R8C3_n8 + R9C1_n8 + R9C2_n8 + R9C3_n8 = 1;
R7C1_n9 + R7C2_n9 + R7C3_n9 + R8C1_n9 + R8C2_n9 + R8C3_n9 + R9C1_n9 + R9C2_n9 + R9C3_n9 = 1;

! ************** Restrictions REGION H ************************;

R7C4_n1 + R7C5_n1 + R7C6_n1 + R8C4_n1 + R8C5_n1 + R8C6_n1 + R9C4_n1 + R9C5_n1 + R9C6_n1 = 1;
R7C4_n2 + R7C5_n2 + R7C6_n2 + R8C4_n2 + R8C5_n2 + R8C6_n2 + R9C4_n2 + R9C5_n2 + R9C6_n2 = 1;
R7C4_n3 + R7C5_n3 + R7C6_n3 + R8C4_n3 + R8C5_n3 + R8C6_n3 + R9C4_n3 + R9C5_n3 + R9C6_n3 = 1;
R7C4_n4 + R7C5_n4 + R7C6_n4 + R8C4_n4 + R8C5_n4 + R8C6_n4 + R9C4_n4 + R9C5_n4 + R9C6_n4 = 1;
R7C4_n5 + R7C5_n5 + R7C6_n5 + R8C4_n5 + R8C5_n5 + R8C6_n5 + R9C4_n5 + R9C5_n5 + R9C6_n5 = 1;
R7C4_n6 + R7C5_n6 + R7C6_n6 + R8C4_n6 + R8C5_n6 + R8C6_n6 + R9C4_n6 + R9C5_n6 + R9C6_n6 = 1;
R7C4_n7 + R7C5_n7 + R7C6_n7 + R8C4_n7 + R8C5_n7 + R8C6_n7 + R9C4_n7 + R9C5_n7 + R9C6_n7 = 1;
R7C4_n8 + R7C5_n8 + R7C6_n8 + R8C4_n8 + R8C5_n8 + R8C6_n8 + R9C4_n8 + R9C5_n8 + R9C6_n8 = 1;
R7C4_n9 + R7C5_n9 + R7C6_n9 + R8C4_n9 + R8C5_n9 + R8C6_n9 + R9C4_n9 + R9C5_n9 + R9C6_n9 = 1;

! ************** Restrictions REGION I ************************;

R7C7_n1 + R7C8_n1 + R7C9_n1 + R8C7_n1 + R8C8_n1 + R8C9_n1 + R9C7_n1 + R9C8_n1 + R9C9_n1 = 1;
R7C7_n2 + R7C8_n2 + R7C9_n2 + R8C7_n2 + R8C8_n2 + R8C9_n2 + R9C7_n2 + R9C8_n2 + R9C9_n2 = 1;
R7C7_n3 + R7C8_n3 + R7C9_n3 + R8C7_n3 + R8C8_n3 + R8C9_n3 + R9C7_n3 + R9C8_n3 + R9C9_n3 = 1;
R7C7_n4 + R7C8_n4 + R7C9_n4 + R8C7_n4 + R8C8_n4 + R8C9_n4 + R9C7_n4 + R9C8_n4 + R9C9_n4 = 1;
R7C7_n5 + R7C8_n5 + R7C9_n5 + R8C7_n5 + R8C8_n5 + R8C9_n5 + R9C7_n5 + R9C8_n5 + R9C9_n5 = 1;
R7C7_n6 + R7C8_n6 + R7C9_n6 + R8C7_n6 + R8C8_n6 + R8C9_n6 + R9C7_n6 + R9C8_n6 + R9C9_n6 = 1;
R7C7_n7 + R7C8_n7 + R7C9_n7 + R8C7_n7 + R8C8_n7 + R8C9_n7 + R9C7_n7 + R9C8_n7 + R9C9_n7 = 1;
R7C7_n8 + R7C8_n8 + R7C9_n8 + R8C7_n8 + R8C8_n8 + R8C9_n8 + R9C7_n8 + R9C8_n8 + R9C9_n8 = 1;
R7C7_n9 + R7C8_n9 + R7C9_n9 + R8C7_n9 + R8C8_n9 + R8C9_n9 + R9C7_n9 + R9C8_n9 + R9C9_n9 = 1;

! ************** Horizontal Restrictions ************************;

R1C1_n1 + R1C2_n1 + R1C3_n1 + R1C4_n1 + R1C5_n1 + R1C6_n1 + R1C7_n1 + R1C8_n1 + R1C9_n1 = 1;
R1C1_n2 + R1C2_n2 + R1C3_n2 + R1C4_n2 + R1C5_n2 + R1C6_n2 + R1C7_n2 + R1C8_n2 + R1C9_n2 = 1;
R1C1_n3 + R1C2_n3 + R1C3_n3 + R1C4_n3 + R1C5_n3 + R1C6_n3 + R1C7_n3 + R1C8_n3 + R1C9_n3 = 1;
R1C1_n4 + R1C2_n4 + R1C3_n4 + R1C4_n4 + R1C5_n4 + R1C6_n4 + R1C7_n4 + R1C8_n4 + R1C9_n4 = 1;
R1C1_n5 + R1C2_n5 + R1C3_n5 + R1C4_n5 + R1C5_n5 + R1C6_n5 + R1C7_n5 + R1C8_n5 + R1C9_n5 = 1;
R1C1_n6 + R1C2_n6 + R1C3_n6 + R1C4_n6 + R1C5_n6 + R1C6_n6 + R1C7_n6 + R1C8_n6 + R1C9_n6 = 1;
R1C1_n7 + R1C2_n7 + R1C3_n7 + R1C4_n7 + R1C5_n7 + R1C6_n7 + R1C7_n7 + R1C8_n7 + R1C9_n7 = 1;
R1C1_n8 + R1C2_n8 + R1C3_n8 + R1C4_n8 + R1C5_n8 + R1C6_n8 + R1C7_n8 + R1C8_n8 + R1C9_n8 = 1;
R1C1_n9 + R1C2_n9 + R1C3_n9 + R1C4_n9 + R1C5_n9 + R1C6_n9 + R1C7_n9 + R1C8_n9 + R1C9_n9 = 1;

R2C1_n1 + R2C2_n1 + R2C3_n1 + R2C4_n1 + R2C5_n1 + R2C6_n1 + R2C7_n1 + R2C8_n1 + R2C9_n1 = 1;
R2C1_n2 + R2C2_n2 + R2C3_n2 + R2C4_n2 + R2C5_n2 + R2C6_n2 + R2C7_n2 + R2C8_n2 + R2C9_n2 = 1;
R2C1_n3 + R2C2_n3 + R2C3_n3 + R2C4_n3 + R2C5_n3 + R2C6_n3 + R2C7_n3 + R2C8_n3 + R2C9_n3 = 1;
R2C1_n4 + R2C2_n4 + R2C3_n4 + R2C4_n4 + R2C5_n4 + R2C6_n4 + R2C7_n4 + R2C8_n4 + R2C9_n4 = 1;
R2C1_n5 + R2C2_n5 + R2C3_n5 + R2C4_n5 + R2C5_n5 + R2C6_n5 + R2C7_n5 + R2C8_n5 + R2C9_n5 = 1;
R2C1_n6 + R2C2_n6 + R2C3_n6 + R2C4_n6 + R2C5_n6 + R2C6_n6 + R2C7_n6 + R2C8_n6 + R2C9_n6 = 1;
R2C1_n7 + R2C2_n7 + R2C3_n7 + R2C4_n7 + R2C5_n7 + R2C6_n7 + R2C7_n7 + R2C8_n7 + R2C9_n7 = 1;
R2C1_n8 + R2C2_n8 + R2C3_n8 + R2C4_n8 + R2C5_n8 + R2C6_n8 + R2C7_n8 + R2C8_n8 + R2C9_n8 = 1;
R2C1_n9 + R2C2_n9 + R2C3_n9 + R2C4_n9 + R2C5_n9 + R2C6_n9 + R2C7_n9 + R2C8_n9 + R2C9_n9 = 1;

R3C1_n1 + R3C2_n1 + R3C3_n1 + R3C4_n1 + R3C5_n1 + R3C6_n1 + R3C7_n1 + R3C8_n1 + R3C9_n1 = 1;
R3C1_n2 + R3C2_n2 + R3C3_n2 + R3C4_n2 + R3C5_n2 + R3C6_n2 + R3C7_n2 + R3C8_n2 + R3C9_n2 = 1;
R3C1_n3 + R3C2_n3 + R3C3_n3 + R3C4_n3 + R3C5_n3 + R3C6_n3 + R3C7_n3 + R3C8_n3 + R3C9_n3 = 1;
R3C1_n4 + R3C2_n4 + R3C3_n4 + R3C4_n4 + R3C5_n4 + R3C6_n4 + R3C7_n4 + R3C8_n4 + R3C9_n4 = 1;
R3C1_n5 + R3C2_n5 + R3C3_n5 + R3C4_n5 + R3C5_n5 + R3C6_n5 + R3C7_n5 + R3C8_n5 + R3C9_n5 = 1;
R3C1_n6 + R3C2_n6 + R3C3_n6 + R3C4_n6 + R3C5_n6 + R3C6_n6 + R3C7_n6 + R3C8_n6 + R3C9_n6 = 1;
R3C1_n7 + R3C2_n7 + R3C3_n7 + R3C4_n7 + R3C5_n7 + R3C6_n7 + R3C7_n7 + R3C8_n7 + R3C9_n7 = 1;
R3C1_n8 + R3C2_n8 + R3C3_n8 + R3C4_n8 + R3C5_n8 + R3C6_n8 + R3C7_n8 + R3C8_n8 + R3C9_n8 = 1;
R3C1_n9 + R3C2_n9 + R3C3_n9 + R3C4_n9 + R3C5_n9 + R3C6_n9 + R3C7_n9 + R3C8_n9 + R3C9_n9 = 1;

R4C1_n1 + R4C2_n1 + R4C3_n1 + R4C4_n1 + R4C5_n1 + R4C6_n1 + R4C7_n1 + R4C8_n1 + R4C9_n1 = 1;
R4C1_n2 + R4C2_n2 + R4C3_n2 + R4C4_n2 + R4C5_n2 + R4C6_n2 + R4C7_n2 + R4C8_n2 + R4C9_n2 = 1;
R4C1_n3 + R4C2_n3 + R4C3_n3 + R4C4_n3 + R4C5_n3 + R4C6_n3 + R4C7_n3 + R4C8_n3 + R4C9_n3 = 1;
R4C1_n4 + R4C2_n4 + R4C3_n4 + R4C4_n4 + R4C5_n4 + R4C6_n4 + R4C7_n4 + R4C8_n4 + R4C9_n4 = 1;
R4C1_n5 + R4C2_n5 + R4C3_n5 + R4C4_n5 + R4C5_n5 + R4C6_n5 + R4C7_n5 + R4C8_n5 + R4C9_n5 = 1;
R4C1_n6 + R4C2_n6 + R4C3_n6 + R4C4_n6 + R4C5_n6 + R4C6_n6 + R4C7_n6 + R4C8_n6 + R4C9_n6 = 1;
R4C1_n7 + R4C2_n7 + R4C3_n7 + R4C4_n7 + R4C5_n7 + R4C6_n7 + R4C7_n7 + R4C8_n7 + R4C9_n7 = 1;
R4C1_n8 + R4C2_n8 + R4C3_n8 + R4C4_n8 + R4C5_n8 + R4C6_n8 + R4C7_n8 + R4C8_n8 + R4C9_n8 = 1;
R4C1_n9 + R4C2_n9 + R4C3_n9 + R4C4_n9 + R4C5_n9 + R4C6_n9 + R4C7_n9 + R4C8_n9 + R4C9_n9 = 1;

R5C1_n1 + R5C2_n1 + R5C3_n1 + R5C4_n1 + R5C5_n1 + R5C6_n1 + R5C7_n1 + R5C8_n1 + R5C9_n1 = 1;
R5C1_n2 + R5C2_n2 + R5C3_n2 + R5C4_n2 + R5C5_n2 + R5C6_n2 + R5C7_n2 + R5C8_n2 + R5C9_n2 = 1;
R5C1_n3 + R5C2_n3 + R5C3_n3 + R5C4_n3 + R5C5_n3 + R5C6_n3 + R5C7_n3 + R5C8_n3 + R5C9_n3 = 1;
R5C1_n4 + R5C2_n4 + R5C3_n4 + R5C4_n4 + R5C5_n4 + R5C6_n4 + R5C7_n4 + R5C8_n4 + R5C9_n4 = 1;
R5C1_n5 + R5C2_n5 + R5C3_n5 + R5C4_n5 + R5C5_n5 + R5C6_n5 + R5C7_n5 + R5C8_n5 + R5C9_n5 = 1;
R5C1_n6 + R5C2_n6 + R5C3_n6 + R5C4_n6 + R5C5_n6 + R5C6_n6 + R5C7_n6 + R5C8_n6 + R5C9_n6 = 1;
R5C1_n7 + R5C2_n7 + R5C3_n7 + R5C4_n7 + R5C5_n7 + R5C6_n7 + R5C7_n7 + R5C8_n7 + R5C9_n7 = 1;
R5C1_n8 + R5C2_n8 + R5C3_n8 + R5C4_n8 + R5C5_n8 + R5C6_n8 + R5C7_n8 + R5C8_n8 + R5C9_n8 = 1;
R5C1_n9 + R5C2_n9 + R5C3_n9 + R5C4_n9 + R5C5_n9 + R5C6_n9 + R5C7_n9 + R5C8_n9 + R5C9_n9 = 1;

R6C1_n1 + R6C2_n1 + R6C3_n1 + R6C4_n1 + R6C5_n1 + R6C6_n1 + R6C7_n1 + R6C8_n1 + R6C9_n1 = 1;
R6C1_n2 + R6C2_n2 + R6C3_n2 + R6C4_n2 + R6C5_n2 + R6C6_n2 + R6C7_n2 + R6C8_n2 + R6C9_n2 = 1;
R6C1_n3 + R6C2_n3 + R6C3_n3 + R6C4_n3 + R6C5_n3 + R6C6_n3 + R6C7_n3 + R6C8_n3 + R6C9_n3 = 1;
R6C1_n4 + R6C2_n4 + R6C3_n4 + R6C4_n4 + R6C5_n4 + R6C6_n4 + R6C7_n4 + R6C8_n4 + R6C9_n4 = 1;
R6C1_n5 + R6C2_n5 + R6C3_n5 + R6C4_n5 + R6C5_n5 + R6C6_n5 + R6C7_n5 + R6C8_n5 + R6C9_n5 = 1;
R6C1_n6 + R6C2_n6 + R6C3_n6 + R6C4_n6 + R6C5_n6 + R6C6_n6 + R6C7_n6 + R6C8_n6 + R6C9_n6 = 1;
R6C1_n7 + R6C2_n7 + R6C3_n7 + R6C4_n7 + R6C5_n7 + R6C6_n7 + R6C7_n7 + R6C8_n7 + R6C9_n7 = 1;
R6C1_n8 + R6C2_n8 + R6C3_n8 + R6C4_n8 + R6C5_n8 + R6C6_n8 + R6C7_n8 + R6C8_n8 + R6C9_n8 = 1;
R6C1_n9 + R6C2_n9 + R6C3_n9 + R6C4_n9 + R6C5_n9 + R6C6_n9 + R6C7_n9 + R6C8_n9 + R6C9_n9 = 1;

R7C1_n1 + R7C2_n1 + R7C3_n1 + R7C4_n1 + R7C5_n1 + R7C6_n1 + R7C7_n1 + R7C8_n1 + R7C9_n1 = 1;
R7C1_n2 + R7C2_n2 + R7C3_n2 + R7C4_n2 + R7C5_n2 + R7C6_n2 + R7C7_n2 + R7C8_n2 + R7C9_n2 = 1;
R7C1_n3 + R7C2_n3 + R7C3_n3 + R7C4_n3 + R7C5_n3 + R7C6_n3 + R7C7_n3 + R7C8_n3 + R7C9_n3 = 1;
R7C1_n4 + R7C2_n4 + R7C3_n4 + R7C4_n4 + R7C5_n4 + R7C6_n4 + R7C7_n4 + R7C8_n4 + R7C9_n4 = 1;
R7C1_n5 + R7C2_n5 + R7C3_n5 + R7C4_n5 + R7C5_n5 + R7C6_n5 + R7C7_n5 + R7C8_n5 + R7C9_n5 = 1;
R7C1_n6 + R7C2_n6 + R7C3_n6 + R7C4_n6 + R7C5_n6 + R7C6_n6 + R7C7_n6 + R7C8_n6 + R7C9_n6 = 1;
R7C1_n7 + R7C2_n7 + R7C3_n7 + R7C4_n7 + R7C5_n7 + R7C6_n7 + R7C7_n7 + R7C8_n7 + R7C9_n7 = 1;
R7C1_n8 + R7C2_n8 + R7C3_n8 + R7C4_n8 + R7C5_n8 + R7C6_n8 + R7C7_n8 + R7C8_n8 + R7C9_n8 = 1;
R7C1_n9 + R7C2_n9 + R7C3_n9 + R7C4_n9 + R7C5_n9 + R7C6_n9 + R7C7_n9 + R7C8_n9 + R7C9_n9 = 1;

R8C1_n1 + R8C2_n1 + R8C3_n1 + R8C4_n1 + R8C5_n1 + R8C6_n1 + R8C7_n1 + R8C8_n1 + R8C9_n1 = 1;
R8C1_n2 + R8C2_n2 + R8C3_n2 + R8C4_n2 + R8C5_n2 + R8C6_n2 + R8C7_n2 + R8C8_n2 + R8C9_n2 = 1;
R8C1_n3 + R8C2_n3 + R8C3_n3 + R8C4_n3 + R8C5_n3 + R8C6_n3 + R8C7_n3 + R8C8_n3 + R8C9_n3 = 1;
R8C1_n4 + R8C2_n4 + R8C3_n4 + R8C4_n4 + R8C5_n4 + R8C6_n4 + R8C7_n4 + R8C8_n4 + R8C9_n4 = 1;
R8C1_n5 + R8C2_n5 + R8C3_n5 + R8C4_n5 + R8C5_n5 + R8C6_n5 + R8C7_n5 + R8C8_n5 + R8C9_n5 = 1;
R8C1_n6 + R8C2_n6 + R8C3_n6 + R8C4_n6 + R8C5_n6 + R8C6_n6 + R8C7_n6 + R8C8_n6 + R8C9_n6 = 1;
R8C1_n7 + R8C2_n7 + R8C3_n7 + R8C4_n7 + R8C5_n7 + R8C6_n7 + R8C7_n7 + R8C8_n7 + R8C9_n7 = 1;
R8C1_n8 + R8C2_n8 + R8C3_n8 + R8C4_n8 + R8C5_n8 + R8C6_n8 + R8C7_n8 + R8C8_n8 + R8C9_n8 = 1;
R8C1_n9 + R8C2_n9 + R8C3_n9 + R8C4_n9 + R8C5_n9 + R8C6_n9 + R8C7_n9 + R8C8_n9 + R8C9_n9 = 1;

R9C1_n1 + R9C2_n1 + R9C3_n1 + R9C4_n1 + R9C5_n1 + R9C6_n1 + R9C7_n1 + R9C8_n1 + R9C9_n1 = 1;
R9C1_n2 + R9C2_n2 + R9C3_n2 + R9C4_n2 + R9C5_n2 + R9C6_n2 + R9C7_n2 + R9C8_n2 + R9C9_n2 = 1;
R9C1_n3 + R9C2_n3 + R9C3_n3 + R9C4_n3 + R9C5_n3 + R9C6_n3 + R9C7_n3 + R9C8_n3 + R9C9_n3 = 1;
R9C1_n4 + R9C2_n4 + R9C3_n4 + R9C4_n4 + R9C5_n4 + R9C6_n4 + R9C7_n4 + R9C8_n4 + R9C9_n4 = 1;
R9C1_n5 + R9C2_n5 + R9C3_n5 + R9C4_n5 + R9C5_n5 + R9C6_n5 + R9C7_n5 + R9C8_n5 + R9C9_n5 = 1;
R9C1_n6 + R9C2_n6 + R9C3_n6 + R9C4_n6 + R9C5_n6 + R9C6_n6 + R9C7_n6 + R9C8_n6 + R9C9_n6 = 1;
R9C1_n7 + R9C2_n7 + R9C3_n7 + R9C4_n7 + R9C5_n7 + R9C6_n7 + R9C7_n7 + R9C8_n7 + R9C9_n7 = 1;
R9C1_n8 + R9C2_n8 + R9C3_n8 + R9C4_n8 + R9C5_n8 + R9C6_n8 + R9C7_n8 + R9C8_n8 + R9C9_n8 = 1;
R9C1_n9 + R9C2_n9 + R9C3_n9 + R9C4_n9 + R9C5_n9 + R9C6_n9 + R9C7_n9 + R9C8_n9 + R9C9_n9 = 1;

! ************** Vertical Restrictions ************************;

R1C1_n1 + R2C1_n1 + R3C1_n1 + R4C1_n1 + R5C1_n1 + R6C1_n1 + R7C1_n1 + R8C1_n1 + R9C1_n1 = 1;
R1C1_n2 + R2C1_n2 + R3C1_n2 + R4C1_n2 + R5C1_n2 + R6C1_n2 + R7C1_n2 + R8C1_n2 + R9C1_n2 = 1;
R1C1_n3 + R2C1_n3 + R3C1_n3 + R4C1_n3 + R5C1_n3 + R6C1_n3 + R7C1_n3 + R8C1_n3 + R9C1_n3 = 1;
R1C1_n4 + R2C1_n4 + R3C1_n4 + R4C1_n4 + R5C1_n4 + R6C1_n4 + R7C1_n4 + R8C1_n4 + R9C1_n4 = 1;
R1C1_n5 + R2C1_n5 + R3C1_n5 + R4C1_n5 + R5C1_n5 + R6C1_n5 + R7C1_n5 + R8C1_n5 + R9C1_n5 = 1;
R1C1_n6 + R2C1_n6 + R3C1_n6 + R4C1_n6 + R5C1_n6 + R6C1_n6 + R7C1_n6 + R8C1_n6 + R9C1_n6 = 1;
R1C1_n7 + R2C1_n7 + R3C1_n7 + R4C1_n7 + R5C1_n7 + R6C1_n7 + R7C1_n7 + R8C1_n7 + R9C1_n7 = 1;
R1C1_n8 + R2C1_n8 + R3C1_n8 + R4C1_n8 + R5C1_n8 + R6C1_n8 + R7C1_n8 + R8C1_n8 + R9C1_n8 = 1;
R1C1_n9 + R2C1_n9 + R3C1_n9 + R4C1_n9 + R5C1_n9 + R6C1_n9 + R7C1_n9 + R8C1_n9 + R9C1_n9 = 1;

R1C2_n1 + R2C2_n1 + R3C2_n1 + R4C2_n1 + R5C2_n1 + R6C2_n1 + R7C2_n1 + R8C2_n1 + R9C2_n1 = 1;
R1C2_n2 + R2C2_n2 + R3C2_n2 + R4C2_n2 + R5C2_n2 + R6C2_n2 + R7C2_n2 + R8C2_n2 + R9C2_n2 = 1;
R1C2_n3 + R2C2_n3 + R3C2_n3 + R4C2_n3 + R5C2_n3 + R6C2_n3 + R7C2_n3 + R8C2_n3 + R9C2_n3 = 1;
R1C2_n4 + R2C2_n4 + R3C2_n4 + R4C2_n4 + R5C2_n4 + R6C2_n4 + R7C2_n4 + R8C2_n4 + R9C2_n4 = 1;
R1C2_n5 + R2C2_n5 + R3C2_n5 + R4C2_n5 + R5C2_n5 + R6C2_n5 + R7C2_n5 + R8C2_n5 + R9C2_n5 = 1;
R1C2_n6 + R2C2_n6 + R3C2_n6 + R4C2_n6 + R5C2_n6 + R6C2_n6 + R7C2_n6 + R8C2_n6 + R9C2_n6 = 1;
R1C2_n7 + R2C2_n7 + R3C2_n7 + R4C2_n7 + R5C2_n7 + R6C2_n7 + R7C2_n7 + R8C2_n7 + R9C2_n7 = 1;
R1C2_n8 + R2C2_n8 + R3C2_n8 + R4C2_n8 + R5C2_n8 + R6C2_n8 + R7C2_n8 + R8C2_n8 + R9C2_n8 = 1;
R1C2_n9 + R2C2_n9 + R3C2_n9 + R4C2_n9 + R5C2_n9 + R6C2_n9 + R7C2_n9 + R8C2_n9 + R9C2_n9 = 1;

R1C3_n1 + R2C3_n1 + R3C3_n1 + R4C3_n1 + R5C3_n1 + R6C3_n1 + R7C3_n1 + R8C3_n1 + R9C3_n1 = 1;
R1C3_n2 + R2C3_n2 + R3C3_n2 + R4C3_n2 + R5C3_n2 + R6C3_n2 + R7C3_n2 + R8C3_n2 + R9C3_n2 = 1;
R1C3_n3 + R2C3_n3 + R3C3_n3 + R4C3_n3 + R5C3_n3 + R6C3_n3 + R7C3_n3 + R8C3_n3 + R9C3_n3 = 1;
R1C3_n4 + R2C3_n4 + R3C3_n4 + R4C3_n4 + R5C3_n4 + R6C3_n4 + R7C3_n4 + R8C3_n4 + R9C3_n4 = 1;
R1C3_n5 + R2C3_n5 + R3C3_n5 + R4C3_n5 + R5C3_n5 + R6C3_n5 + R7C3_n5 + R8C3_n5 + R9C3_n5 = 1;
R1C3_n6 + R2C3_n6 + R3C3_n6 + R4C3_n6 + R5C3_n6 + R6C3_n6 + R7C3_n6 + R8C3_n6 + R9C3_n6 = 1;
R1C3_n7 + R2C3_n7 + R3C3_n7 + R4C3_n7 + R5C3_n7 + R6C3_n7 + R7C3_n7 + R8C3_n7 + R9C3_n7 = 1;
R1C3_n8 + R2C3_n8 + R3C3_n8 + R4C3_n8 + R5C3_n8 + R6C3_n8 + R7C3_n8 + R8C3_n8 + R9C3_n8 = 1;
R1C3_n9 + R2C3_n9 + R3C3_n9 + R4C3_n9 + R5C3_n9 + R6C3_n9 + R7C3_n9 + R8C3_n9 + R9C3_n9 = 1;

R1C4_n1 + R2C4_n1 + R3C4_n1 + R4C4_n1 + R5C4_n1 + R6C4_n1 + R7C4_n1 + R8C4_n1 + R9C4_n1 = 1;
R1C4_n2 + R2C4_n2 + R3C4_n2 + R4C4_n2 + R5C4_n2 + R6C4_n2 + R7C4_n2 + R8C4_n2 + R9C4_n2 = 1;
R1C4_n3 + R2C4_n3 + R3C4_n3 + R4C4_n3 + R5C4_n3 + R6C4_n3 + R7C4_n3 + R8C4_n3 + R9C4_n3 = 1;
R1C4_n4 + R2C4_n4 + R3C4_n4 + R4C4_n4 + R5C4_n4 + R6C4_n4 + R7C4_n4 + R8C4_n4 + R9C4_n4 = 1;
R1C4_n5 + R2C4_n5 + R3C4_n5 + R4C4_n5 + R5C4_n5 + R6C4_n5 + R7C4_n5 + R8C4_n5 + R9C4_n5 = 1;
R1C4_n6 + R2C4_n6 + R3C4_n6 + R4C4_n6 + R5C4_n6 + R6C4_n6 + R7C4_n6 + R8C4_n6 + R9C4_n6 = 1;
R1C4_n7 + R2C4_n7 + R3C4_n7 + R4C4_n7 + R5C4_n7 + R6C4_n7 + R7C4_n7 + R8C4_n7 + R9C4_n7 = 1;
R1C4_n8 + R2C4_n8 + R3C4_n8 + R4C4_n8 + R5C4_n8 + R6C4_n8 + R7C4_n8 + R8C4_n8 + R9C4_n8 = 1;
R1C4_n9 + R2C4_n9 + R3C4_n9 + R4C4_n9 + R5C4_n9 + R6C4_n9 + R7C4_n9 + R8C4_n9 + R9C4_n9 = 1;

R1C5_n1 + R2C5_n1 + R3C5_n1 + R4C5_n1 + R5C5_n1 + R6C5_n1 + R7C5_n1 + R8C5_n1 + R9C5_n1 = 1;
R1C5_n2 + R2C5_n2 + R3C5_n2 + R4C5_n2 + R5C5_n2 + R6C5_n2 + R7C5_n2 + R8C5_n2 + R9C5_n2 = 1;
R1C5_n3 + R2C5_n3 + R3C5_n3 + R4C5_n3 + R5C5_n3 + R6C5_n3 + R7C5_n3 + R8C5_n3 + R9C5_n3 = 1;
R1C5_n4 + R2C5_n4 + R3C5_n4 + R4C5_n4 + R5C5_n4 + R6C5_n4 + R7C5_n4 + R8C5_n4 + R9C5_n4 = 1;
R1C5_n5 + R2C5_n5 + R3C5_n5 + R4C5_n5 + R5C5_n5 + R6C5_n5 + R7C5_n5 + R8C5_n5 + R9C5_n5 = 1;
R1C5_n6 + R2C5_n6 + R3C5_n6 + R4C5_n6 + R5C5_n6 + R6C5_n6 + R7C5_n6 + R8C5_n6 + R9C5_n6 = 1;
R1C5_n7 + R2C5_n7 + R3C5_n7 + R4C5_n7 + R5C5_n7 + R6C5_n7 + R7C5_n7 + R8C5_n7 + R9C5_n7 = 1;
R1C5_n8 + R2C5_n8 + R3C5_n8 + R4C5_n8 + R5C5_n8 + R6C5_n8 + R7C5_n8 + R8C5_n8 + R9C5_n8 = 1;
R1C5_n9 + R2C5_n9 + R3C5_n9 + R4C5_n9 + R5C5_n9 + R6C5_n9 + R7C5_n9 + R8C5_n9 + R9C5_n9 = 1;

R1C6_n1 + R2C6_n1 + R3C6_n1 + R4C6_n1 + R5C6_n1 + R6C6_n1 + R7C6_n1 + R8C6_n1 + R9C6_n1 = 1;
R1C6_n2 + R2C6_n2 + R3C6_n2 + R4C6_n2 + R5C6_n2 + R6C6_n2 + R7C6_n2 + R8C6_n2 + R9C6_n2 = 1;
R1C6_n3 + R2C6_n3 + R3C6_n3 + R4C6_n3 + R5C6_n3 + R6C6_n3 + R7C6_n3 + R8C6_n3 + R9C6_n3 = 1;
R1C6_n4 + R2C6_n4 + R3C6_n4 + R4C6_n4 + R5C6_n4 + R6C6_n4 + R7C6_n4 + R8C6_n4 + R9C6_n4 = 1;
R1C6_n5 + R2C6_n5 + R3C6_n5 + R4C6_n5 + R5C6_n5 + R6C6_n5 + R7C6_n5 + R8C6_n5 + R9C6_n5 = 1;
R1C6_n6 + R2C6_n6 + R3C6_n6 + R4C6_n6 + R5C6_n6 + R6C6_n6 + R7C6_n6 + R8C6_n6 + R9C6_n6 = 1;
R1C6_n7 + R2C6_n7 + R3C6_n7 + R4C6_n7 + R5C6_n7 + R6C6_n7 + R7C6_n7 + R8C6_n7 + R9C6_n7 = 1;
R1C6_n8 + R2C6_n8 + R3C6_n8 + R4C6_n8 + R5C6_n8 + R6C6_n8 + R7C6_n8 + R8C6_n8 + R9C6_n8 = 1;
R1C6_n9 + R2C6_n9 + R3C6_n9 + R4C6_n9 + R5C6_n9 + R6C6_n9 + R7C6_n9 + R8C6_n9 + R9C6_n9 = 1;

R1C7_n1 + R2C7_n1 + R3C7_n1 + R4C7_n1 + R5C7_n1 + R6C7_n1 + R7C7_n1 + R8C7_n1 + R9C7_n1 = 1;
R1C7_n2 + R2C7_n2 + R3C7_n2 + R4C7_n2 + R5C7_n2 + R6C7_n2 + R7C7_n2 + R8C7_n2 + R9C7_n2 = 1;
R1C7_n3 + R2C7_n3 + R3C7_n3 + R4C7_n3 + R5C7_n3 + R6C7_n3 + R7C7_n3 + R8C7_n3 + R9C7_n3 = 1;
R1C7_n4 + R2C7_n4 + R3C7_n4 + R4C7_n4 + R5C7_n4 + R6C7_n4 + R7C7_n4 + R8C7_n4 + R9C7_n4 = 1;
R1C7_n5 + R2C7_n5 + R3C7_n5 + R4C7_n5 + R5C7_n5 + R6C7_n5 + R7C7_n5 + R8C7_n5 + R9C7_n5 = 1;
R1C7_n6 + R2C7_n6 + R3C7_n6 + R4C7_n6 + R5C7_n6 + R6C7_n6 + R7C7_n6 + R8C7_n6 + R9C7_n6 = 1;
R1C7_n7 + R2C7_n7 + R3C7_n7 + R4C7_n7 + R5C7_n7 + R6C7_n7 + R7C7_n7 + R8C7_n7 + R9C7_n7 = 1;
R1C7_n8 + R2C7_n8 + R3C7_n8 + R4C7_n8 + R5C7_n8 + R6C7_n8 + R7C7_n8 + R8C7_n8 + R9C7_n8 = 1;
R1C7_n9 + R2C7_n9 + R3C7_n9 + R4C7_n9 + R5C7_n9 + R6C7_n9 + R7C7_n9 + R8C7_n9 + R9C7_n9 = 1;

R1C8_n1 + R2C8_n1 + R3C8_n1 + R4C8_n1 + R5C8_n1 + R6C8_n1 + R7C8_n1 + R8C8_n1 + R9C8_n1 = 1;
R1C8_n2 + R2C8_n2 + R3C8_n2 + R4C8_n2 + R5C8_n2 + R6C8_n2 + R7C8_n2 + R8C8_n2 + R9C8_n2 = 1;
R1C8_n3 + R2C8_n3 + R3C8_n3 + R4C8_n3 + R5C8_n3 + R6C8_n3 + R7C8_n3 + R8C8_n3 + R9C8_n3 = 1;
R1C8_n4 + R2C8_n4 + R3C8_n4 + R4C8_n4 + R5C8_n4 + R6C8_n4 + R7C8_n4 + R8C8_n4 + R9C8_n4 = 1;
R1C8_n5 + R2C8_n5 + R3C8_n5 + R4C8_n5 + R5C8_n5 + R6C8_n5 + R7C8_n5 + R8C8_n5 + R9C8_n5 = 1;
R1C8_n6 + R2C8_n6 + R3C8_n6 + R4C8_n6 + R5C8_n6 + R6C8_n6 + R7C8_n6 + R8C8_n6 + R9C8_n6 = 1;
R1C8_n7 + R2C8_n7 + R3C8_n7 + R4C8_n7 + R5C8_n7 + R6C8_n7 + R7C8_n7 + R8C8_n7 + R9C8_n7 = 1;
R1C8_n8 + R2C8_n8 + R3C8_n8 + R4C8_n8 + R5C8_n8 + R6C8_n8 + R7C8_n8 + R8C8_n8 + R9C8_n8 = 1;
R1C8_n9 + R2C8_n9 + R3C8_n9 + R4C8_n9 + R5C8_n9 + R6C8_n9 + R7C8_n9 + R8C8_n9 + R9C8_n9 = 1;

R1C9_n1 + R2C9_n1 + R3C9_n1 + R4C9_n1 + R5C9_n1 + R6C9_n1 + R7C9_n1 + R8C9_n1 + R9C9_n1 = 1;
R1C9_n2 + R2C9_n2 + R3C9_n2 + R4C9_n2 + R5C9_n2 + R6C9_n2 + R7C9_n2 + R8C9_n2 + R9C9_n2 = 1;
R1C9_n3 + R2C9_n3 + R3C9_n3 + R4C9_n3 + R5C9_n3 + R6C9_n3 + R7C9_n3 + R8C9_n3 + R9C9_n3 = 1;
R1C9_n4 + R2C9_n4 + R3C9_n4 + R4C9_n4 + R5C9_n4 + R6C9_n4 + R7C9_n4 + R8C9_n4 + R9C9_n4 = 1;
R1C9_n5 + R2C9_n5 + R3C9_n5 + R4C9_n5 + R5C9_n5 + R6C9_n5 + R7C9_n5 + R8C9_n5 + R9C9_n5 = 1;
R1C9_n6 + R2C9_n6 + R3C9_n6 + R4C9_n6 + R5C9_n6 + R6C9_n6 + R7C9_n6 + R8C9_n6 + R9C9_n6 = 1;
R1C9_n7 + R2C9_n7 + R3C9_n7 + R4C9_n7 + R5C9_n7 + R6C9_n7 + R7C9_n7 + R8C9_n7 + R9C9_n7 = 1;
R1C9_n8 + R2C9_n8 + R3C9_n8 + R4C9_n8 + R5C9_n8 + R6C9_n8 + R7C9_n8 + R8C9_n8 + R9C9_n8 = 1;
R1C9_n9 + R2C9_n9 + R3C9_n9 + R4C9_n9 + R5C9_n9 + R6C9_n9 + R7C9_n9 + R8C9_n9 + R9C9_n9 = 1;

! ************** Transfer Restrictions ************************;

1* R1C1_n1 + 2* R1C1_n2 + 3* R1C1_n3 + 4* R1C1_n4 + 5* R1C1_n5 + 6* R1C1_n6 + 7* R1C1_n7 + 8* R1C1_n8 + 9* R1C1_n9 - R1C1 = 0;
1* R1C2_n1 + 2* R1C2_n2 + 3* R1C2_n3 + 4* R1C2_n4 + 5* R1C2_n5 + 6* R1C2_n6 + 7* R1C2_n7 + 8* R1C2_n8 + 9* R1C2_n9 - R1C2 = 0;
1* R1C3_n1 + 2* R1C3_n2 + 3* R1C3_n3 + 4* R1C3_n4 + 5* R1C3_n5 + 6* R1C3_n6 + 7* R1C3_n7 + 8* R1C3_n8 + 9* R1C3_n9 - R1C3 = 0;
1* R1C4_n1 + 2* R1C4_n2 + 3* R1C4_n3 + 4* R1C4_n4 + 5* R1C4_n5 + 6* R1C4_n6 + 7* R1C4_n7 + 8* R1C4_n8 + 9* R1C4_n9 - R1C4 = 0;
1* R1C5_n1 + 2* R1C5_n2 + 3* R1C5_n3 + 4* R1C5_n4 + 5* R1C5_n5 + 6* R1C5_n6 + 7* R1C5_n7 + 8* R1C5_n8 + 9* R1C5_n9 - R1C5 = 0;
1* R1C6_n1 + 2* R1C6_n2 + 3* R1C6_n3 + 4* R1C6_n4 + 5* R1C6_n5 + 6* R1C6_n6 + 7* R1C6_n7 + 8* R1C6_n8 + 9* R1C6_n9 - R1C6 = 0;
1* R1C7_n1 + 2* R1C7_n2 + 3* R1C7_n3 + 4* R1C7_n4 + 5* R1C7_n5 + 6* R1C7_n6 + 7* R1C7_n7 + 8* R1C7_n8 + 9* R1C7_n9 - R1C7 = 0;
1* R1C8_n1 + 2* R1C8_n2 + 3* R1C8_n3 + 4* R1C8_n4 + 5* R1C8_n5 + 6* R1C8_n6 + 7* R1C8_n7 + 8* R1C8_n8 + 9* R1C8_n9 - R1C8 = 0;
1* R1C9_n1 + 2* R1C9_n2 + 3* R1C9_n3 + 4* R1C9_n4 + 5* R1C9_n5 + 6* R1C9_n6 + 7* R1C9_n7 + 8* R1C9_n8 + 9* R1C9_n9 - R1C9 = 0;

1* R2C1_n1 + 2* R2C1_n2 + 3* R2C1_n3 + 4* R2C1_n4 + 5* R2C1_n5 + 6* R2C1_n6 + 7* R2C1_n7 + 8* R2C1_n8 + 9* R2C1_n9 - R2C1 = 0;
1* R2C2_n1 + 2* R2C2_n2 + 3* R2C2_n3 + 4* R2C2_n4 + 5* R2C2_n5 + 6* R2C2_n6 + 7* R2C2_n7 + 8* R2C2_n8 + 9* R2C2_n9 - R2C2 = 0;
1* R2C3_n1 + 2* R2C3_n2 + 3* R2C3_n3 + 4* R2C3_n4 + 5* R2C3_n5 + 6* R2C3_n6 + 7* R2C3_n7 + 8* R2C3_n8 + 9* R2C3_n9 - R2C3 = 0;
1* R2C4_n1 + 2* R2C4_n2 + 3* R2C4_n3 + 4* R2C4_n4 + 5* R2C4_n5 + 6* R2C4_n6 + 7* R2C4_n7 + 8* R2C4_n8 + 9* R2C4_n9 - R2C4 = 0;
1* R2C5_n1 + 2* R2C5_n2 + 3* R2C5_n3 + 4* R2C5_n4 + 5* R2C5_n5 + 6* R2C5_n6 + 7* R2C5_n7 + 8* R2C5_n8 + 9* R2C5_n9 - R2C5 = 0;
1* R2C6_n1 + 2* R2C6_n2 + 3* R2C6_n3 + 4* R2C6_n4 + 5* R2C6_n5 + 6* R2C6_n6 + 7* R2C6_n7 + 8* R2C6_n8 + 9* R2C6_n9 - R2C6 = 0;
1* R2C7_n1 + 2* R2C7_n2 + 3* R2C7_n3 + 4* R2C7_n4 + 5* R2C7_n5 + 6* R2C7_n6 + 7* R2C7_n7 + 8* R2C7_n8 + 9* R2C7_n9 - R2C7 = 0;
1* R2C8_n1 + 2* R2C8_n2 + 3* R2C8_n3 + 4* R2C8_n4 + 5* R2C8_n5 + 6* R2C8_n6 + 7* R2C8_n7 + 8* R2C8_n8 + 9* R2C8_n9 - R2C8 = 0;
1* R2C9_n1 + 2* R2C9_n2 + 3* R2C9_n3 + 4* R2C9_n4 + 5* R2C9_n5 + 6* R2C9_n6 + 7* R2C9_n7 + 8* R2C9_n8 + 9* R2C9_n9 - R2C9 = 0;

1* R3C1_n1 + 2* R3C1_n2 + 3* R3C1_n3 + 4* R3C1_n4 + 5* R3C1_n5 + 6* R3C1_n6 + 7* R3C1_n7 + 8* R3C1_n8 + 9* R3C1_n9 - R3C1 = 0;
1* R3C2_n1 + 2* R3C2_n2 + 3* R3C2_n3 + 4* R3C2_n4 + 5* R3C2_n5 + 6* R3C2_n6 + 7* R3C2_n7 + 8* R3C2_n8 + 9* R3C2_n9 - R3C2 = 0;
1* R3C3_n1 + 2* R3C3_n2 + 3* R3C3_n3 + 4* R3C3_n4 + 5* R3C3_n5 + 6* R3C3_n6 + 7* R3C3_n7 + 8* R3C3_n8 + 9* R3C3_n9 - R3C3 = 0;
1* R3C4_n1 + 2* R3C4_n2 + 3* R3C4_n3 + 4* R3C4_n4 + 5* R3C4_n5 + 6* R3C4_n6 + 7* R3C4_n7 + 8* R3C4_n8 + 9* R3C4_n9 - R3C4 = 0;
1* R3C5_n1 + 2* R3C5_n2 + 3* R3C5_n3 + 4* R3C5_n4 + 5* R3C5_n5 + 6* R3C5_n6 + 7* R3C5_n7 + 8* R3C5_n8 + 9* R3C5_n9 - R3C5 = 0;
1* R3C6_n1 + 2* R3C6_n2 + 3* R3C6_n3 + 4* R3C6_n4 + 5* R3C6_n5 + 6* R3C6_n6 + 7* R3C6_n7 + 8* R3C6_n8 + 9* R3C6_n9 - R3C6 = 0;
1* R3C7_n1 + 2* R3C7_n2 + 3* R3C7_n3 + 4* R3C7_n4 + 5* R3C7_n5 + 6* R3C7_n6 + 7* R3C7_n7 + 8* R3C7_n8 + 9* R3C7_n9 - R3C7 = 0;
1* R3C8_n1 + 2* R3C8_n2 + 3* R3C8_n3 + 4* R3C8_n4 + 5* R3C8_n5 + 6* R3C8_n6 + 7* R3C8_n7 + 8* R3C8_n8 + 9* R3C8_n9 - R3C8 = 0;
1* R3C9_n1 + 2* R3C9_n2 + 3* R3C9_n3 + 4* R3C9_n4 + 5* R3C9_n5 + 6* R3C9_n6 + 7* R3C9_n7 + 8* R3C9_n8 + 9* R3C9_n9 - R3C9 = 0;

1* R4C1_n1 + 2* R4C1_n2 + 3* R4C1_n3 + 4* R4C1_n4 + 5* R4C1_n5 + 6* R4C1_n6 + 7* R4C1_n7 + 8* R4C1_n8 + 9* R4C1_n9 - R4C1 = 0;
1* R4C2_n1 + 2* R4C2_n2 + 3* R4C2_n3 + 4* R4C2_n4 + 5* R4C2_n5 + 6* R4C2_n6 + 7* R4C2_n7 + 8* R4C2_n8 + 9* R4C2_n9 - R4C2 = 0;
1* R4C3_n1 + 2* R4C3_n2 + 3* R4C3_n3 + 4* R4C3_n4 + 5* R4C3_n5 + 6* R4C3_n6 + 7* R4C3_n7 + 8* R4C3_n8 + 9* R4C3_n9 - R4C3 = 0;
1* R4C4_n1 + 2* R4C4_n2 + 3* R4C4_n3 + 4* R4C4_n4 + 5* R4C4_n5 + 6* R4C4_n6 + 7* R4C4_n7 + 8* R4C4_n8 + 9* R4C4_n9 - R4C4 = 0;
1* R4C5_n1 + 2* R4C5_n2 + 3* R4C5_n3 + 4* R4C5_n4 + 5* R4C5_n5 + 6* R4C5_n6 + 7* R4C5_n7 + 8* R4C5_n8 + 9* R4C5_n9 - R4C5 = 0;
1* R4C6_n1 + 2* R4C6_n2 + 3* R4C6_n3 + 4* R4C6_n4 + 5* R4C6_n5 + 6* R4C6_n6 + 7* R4C6_n7 + 8* R4C6_n8 + 9* R4C6_n9 - R4C6 = 0;
1* R4C7_n1 + 2* R4C7_n2 + 3* R4C7_n3 + 4* R4C7_n4 + 5* R4C7_n5 + 6* R4C7_n6 + 7* R4C7_n7 + 8* R4C7_n8 + 9* R4C7_n9 - R4C7 = 0;
1* R4C8_n1 + 2* R4C8_n2 + 3* R4C8_n3 + 4* R4C8_n4 + 5* R4C8_n5 + 6* R4C8_n6 + 7* R4C8_n7 + 8* R4C8_n8 + 9* R4C8_n9 - R4C8 = 0;
1* R4C9_n1 + 2* R4C9_n2 + 3* R4C9_n3 + 4* R4C9_n4 + 5* R4C9_n5 + 6* R4C9_n6 + 7* R4C9_n7 + 8* R4C9_n8 + 9* R4C9_n9 - R4C9 = 0;

1* R5C1_n1 + 2* R5C1_n2 + 3* R5C1_n3 + 4* R5C1_n4 + 5* R5C1_n5 + 6* R5C1_n6 + 7* R5C1_n7 + 8* R5C1_n8 + 9* R5C1_n9 - R5C1 = 0;
1* R5C2_n1 + 2* R5C2_n2 + 3* R5C2_n3 + 4* R5C2_n4 + 5* R5C2_n5 + 6* R5C2_n6 + 7* R5C2_n7 + 8* R5C2_n8 + 9* R5C2_n9 - R5C2 = 0;
1* R5C3_n1 + 2* R5C3_n2 + 3* R5C3_n3 + 4* R5C3_n4 + 5* R5C3_n5 + 6* R5C3_n6 + 7* R5C3_n7 + 8* R5C3_n8 + 9* R5C3_n9 - R5C3 = 0;
1* R5C4_n1 + 2* R5C4_n2 + 3* R5C4_n3 + 4* R5C4_n4 + 5* R5C4_n5 + 6* R5C4_n6 + 7* R5C4_n7 + 8* R5C4_n8 + 9* R5C4_n9 - R5C4 = 0;
1* R5C5_n1 + 2* R5C5_n2 + 3* R5C5_n3 + 4* R5C5_n4 + 5* R5C5_n5 + 6* R5C5_n6 + 7* R5C5_n7 + 8* R5C5_n8 + 9* R5C5_n9 - R5C5 = 0;
1* R5C6_n1 + 2* R5C6_n2 + 3* R5C6_n3 + 4* R5C6_n4 + 5* R5C6_n5 + 6* R5C6_n6 + 7* R5C6_n7 + 8* R5C6_n8 + 9* R5C6_n9 - R5C6 = 0;
1* R5C7_n1 + 2* R5C7_n2 + 3* R5C7_n3 + 4* R5C7_n4 + 5* R5C7_n5 + 6* R5C7_n6 + 7* R5C7_n7 + 8* R5C7_n8 + 9* R5C7_n9 - R5C7 = 0;
1* R5C8_n1 + 2* R5C8_n2 + 3* R5C8_n3 + 4* R5C8_n4 + 5* R5C8_n5 + 6* R5C8_n6 + 7* R5C8_n7 + 8* R5C8_n8 + 9* R5C8_n9 - R5C8 = 0;
1* R5C9_n1 + 2* R5C9_n2 + 3* R5C9_n3 + 4* R5C9_n4 + 5* R5C9_n5 + 6* R5C9_n6 + 7* R5C9_n7 + 8* R5C9_n8 + 9* R5C9_n9 - R5C9 = 0;

1* R6C1_n1 + 2* R6C1_n2 + 3* R6C1_n3 + 4* R6C1_n4 + 5* R6C1_n5 + 6* R6C1_n6 + 7* R6C1_n7 + 8* R6C1_n8 + 9* R6C1_n9 - R6C1 = 0;
1* R6C2_n1 + 2* R6C2_n2 + 3* R6C2_n3 + 4* R6C2_n4 + 5* R6C2_n5 + 6* R6C2_n6 + 7* R6C2_n7 + 8* R6C2_n8 + 9* R6C2_n9 - R6C2 = 0;
1* R6C3_n1 + 2* R6C3_n2 + 3* R6C3_n3 + 4* R6C3_n4 + 5* R6C3_n5 + 6* R6C3_n6 + 7* R6C3_n7 + 8* R6C3_n8 + 9* R6C3_n9 - R6C3 = 0;
1* R6C4_n1 + 2* R6C4_n2 + 3* R6C4_n3 + 4* R6C4_n4 + 5* R6C4_n5 + 6* R6C4_n6 + 7* R6C4_n7 + 8* R6C4_n8 + 9* R6C4_n9 - R6C4 = 0;
1* R6C5_n1 + 2* R6C5_n2 + 3* R6C5_n3 + 4* R6C5_n4 + 5* R6C5_n5 + 6* R6C5_n6 + 7* R6C5_n7 + 8* R6C5_n8 + 9* R6C5_n9 - R6C5 = 0;
1* R6C6_n1 + 2* R6C6_n2 + 3* R6C6_n3 + 4* R6C6_n4 + 5* R6C6_n5 + 6* R6C6_n6 + 7* R6C6_n7 + 8* R6C6_n8 + 9* R6C6_n9 - R6C6 = 0;
1* R6C7_n1 + 2* R6C7_n2 + 3* R6C7_n3 + 4* R6C7_n4 + 5* R6C7_n5 + 6* R6C7_n6 + 7* R6C7_n7 + 8* R6C7_n8 + 9* R6C7_n9 - R6C7 = 0;
1* R6C8_n1 + 2* R6C8_n2 + 3* R6C8_n3 + 4* R6C8_n4 + 5* R6C8_n5 + 6* R6C8_n6 + 7* R6C8_n7 + 8* R6C8_n8 + 9* R6C8_n9 - R6C8 = 0;
1* R6C9_n1 + 2* R6C9_n2 + 3* R6C9_n3 + 4* R6C9_n4 + 5* R6C9_n5 + 6* R6C9_n6 + 7* R6C9_n7 + 8* R6C9_n8 + 9* R6C9_n9 - R6C9 = 0;

1* R7C1_n1 + 2* R7C1_n2 + 3* R7C1_n3 + 4* R7C1_n4 + 5* R7C1_n5 + 6* R7C1_n6 + 7* R7C1_n7 + 8* R7C1_n8 + 9* R7C1_n9 - R7C1 = 0;
1* R7C2_n1 + 2* R7C2_n2 + 3* R7C2_n3 + 4* R7C2_n4 + 5* R7C2_n5 + 6* R7C2_n6 + 7* R7C2_n7 + 8* R7C2_n8 + 9* R7C2_n9 - R7C2 = 0;
1* R7C3_n1 + 2* R7C3_n2 + 3* R7C3_n3 + 4* R7C3_n4 + 5* R7C3_n5 + 6* R7C3_n6 + 7* R7C3_n7 + 8* R7C3_n8 + 9* R7C3_n9 - R7C3 = 0;
1* R7C4_n1 + 2* R7C4_n2 + 3* R7C4_n3 + 4* R7C4_n4 + 5* R7C4_n5 + 6* R7C4_n6 + 7* R7C4_n7 + 8* R7C4_n8 + 9* R7C4_n9 - R7C4 = 0;
1* R7C5_n1 + 2* R7C5_n2 + 3* R7C5_n3 + 4* R7C5_n4 + 5* R7C5_n5 + 6* R7C5_n6 + 7* R7C5_n7 + 8* R7C5_n8 + 9* R7C5_n9 - R7C5 = 0;
1* R7C6_n1 + 2* R7C6_n2 + 3* R7C6_n3 + 4* R7C6_n4 + 5* R7C6_n5 + 6* R7C6_n6 + 7* R7C6_n7 + 8* R7C6_n8 + 9* R7C6_n9 - R7C6 = 0;
1* R7C7_n1 + 2* R7C7_n2 + 3* R7C7_n3 + 4* R7C7_n4 + 5* R7C7_n5 + 6* R7C7_n6 + 7* R7C7_n7 + 8* R7C7_n8 + 9* R7C7_n9 - R7C7 = 0;
1* R7C8_n1 + 2* R7C8_n2 + 3* R7C8_n3 + 4* R7C8_n4 + 5* R7C8_n5 + 6* R7C8_n6 + 7* R7C8_n7 + 8* R7C8_n8 + 9* R7C8_n9 - R7C8 = 0;
1* R7C9_n1 + 2* R7C9_n2 + 3* R7C9_n3 + 4* R7C9_n4 + 5* R7C9_n5 + 6* R7C9_n6 + 7* R7C9_n7 + 8* R7C9_n8 + 9* R7C9_n9 - R7C9 = 0;

1* R8C1_n1 + 2* R8C1_n2 + 3* R8C1_n3 + 4* R8C1_n4 + 5* R8C1_n5 + 6* R8C1_n6 + 7* R8C1_n7 + 8* R8C1_n8 + 9* R8C1_n9 - R8C1 = 0;
1* R8C2_n1 + 2* R8C2_n2 + 3* R8C2_n3 + 4* R8C2_n4 + 5* R8C2_n5 + 6* R8C2_n6 + 7* R8C2_n7 + 8* R8C2_n8 + 9* R8C2_n9 - R8C2 = 0;
1* R8C3_n1 + 2* R8C3_n2 + 3* R8C3_n3 + 4* R8C3_n4 + 5* R8C3_n5 + 6* R8C3_n6 + 7* R8C3_n7 + 8* R8C3_n8 + 9* R8C3_n9 - R8C3 = 0;
1* R8C4_n1 + 2* R8C4_n2 + 3* R8C4_n3 + 4* R8C4_n4 + 5* R8C4_n5 + 6* R8C4_n6 + 7* R8C4_n7 + 8* R8C4_n8 + 9* R8C4_n9 - R8C4 = 0;
1* R8C5_n1 + 2* R8C5_n2 + 3* R8C5_n3 + 4* R8C5_n4 + 5* R8C5_n5 + 6* R8C5_n6 + 7* R8C5_n7 + 8* R8C5_n8 + 9* R8C5_n9 - R8C5 = 0;
1* R8C6_n1 + 2* R8C6_n2 + 3* R8C6_n3 + 4* R8C6_n4 + 5* R8C6_n5 + 6* R8C6_n6 + 7* R8C6_n7 + 8* R8C6_n8 + 9* R8C6_n9 - R8C6 = 0;
1* R8C7_n1 + 2* R8C7_n2 + 3* R8C7_n3 + 4* R8C7_n4 + 5* R8C7_n5 + 6* R8C7_n6 + 7* R8C7_n7 + 8* R8C7_n8 + 9* R8C7_n9 - R8C7 = 0;
1* R8C8_n1 + 2* R8C8_n2 + 3* R8C8_n3 + 4* R8C8_n4 + 5* R8C8_n5 + 6* R8C8_n6 + 7* R8C8_n7 + 8* R8C8_n8 + 9* R8C8_n9 - R8C8 = 0;
1* R8C9_n1 + 2* R8C9_n2 + 3* R8C9_n3 + 4* R8C9_n4 + 5* R8C9_n5 + 6* R8C9_n6 + 7* R8C9_n7 + 8* R8C9_n8 + 9* R8C9_n9 - R8C9 = 0;

1* R9C1_n1 + 2* R9C1_n2 + 3* R9C1_n3 + 4* R9C1_n4 + 5* R9C1_n5 + 6* R9C1_n6 + 7* R9C1_n7 + 8* R9C1_n8 + 9* R9C1_n9 - R9C1 = 0;
1* R9C2_n1 + 2* R9C2_n2 + 3* R9C2_n3 + 4* R9C2_n4 + 5* R9C2_n5 + 6* R9C2_n6 + 7* R9C2_n7 + 8* R9C2_n8 + 9* R9C2_n9 - R9C2 = 0;
1* R9C3_n1 + 2* R9C3_n2 + 3* R9C3_n3 + 4* R9C3_n4 + 5* R9C3_n5 + 6* R9C3_n6 + 7* R9C3_n7 + 8* R9C3_n8 + 9* R9C3_n9 - R9C3 = 0;
1* R9C4_n1 + 2* R9C4_n2 + 3* R9C4_n3 + 4* R9C4_n4 + 5* R9C4_n5 + 6* R9C4_n6 + 7* R9C4_n7 + 8* R9C4_n8 + 9* R9C4_n9 - R9C4 = 0;
1* R9C5_n1 + 2* R9C5_n2 + 3* R9C5_n3 + 4* R9C5_n4 + 5* R9C5_n5 + 6* R9C5_n6 + 7* R9C5_n7 + 8* R9C5_n8 + 9* R9C5_n9 - R9C5 = 0;
1* R9C6_n1 + 2* R9C6_n2 + 3* R9C6_n3 + 4* R9C6_n4 + 5* R9C6_n5 + 6* R9C6_n6 + 7* R9C6_n7 + 8* R9C6_n8 + 9* R9C6_n9 - R9C6 = 0;
1* R9C7_n1 + 2* R9C7_n2 + 3* R9C7_n3 + 4* R9C7_n4 + 5* R9C7_n5 + 6* R9C7_n6 + 7* R9C7_n7 + 8* R9C7_n8 + 9* R9C7_n9 - R9C7 = 0;
1* R9C8_n1 + 2* R9C8_n2 + 3* R9C8_n3 + 4* R9C8_n4 + 5* R9C8_n5 + 6* R9C8_n6 + 7* R9C8_n7 + 8* R9C8_n8 + 9* R9C8_n9 - R9C8 = 0;
1* R9C9_n1 + 2* R9C9_n2 + 3* R9C9_n3 + 4* R9C9_n4 + 5* R9C9_n5 + 6* R9C9_n6 + 7* R9C9_n7 + 8* R9C9_n8 + 9* R9C9_n9 - R9C9 = 0;

! ************** Establish The Initials Numbers Of The Sudoku  **************;

R1C1_n4 = 1;
R1C3_n8 = 1;
R1C6_n6 = 1;
R1C8_n9 = 1;
R1C9_n7 = 1;
R2C2_n9 = 1;
R2C4_n7 = 1;
R2C6_n1 = 1;
R3C2_n3 = 1;
R3C4_n2 = 1;
R3C5_n9 = 1;
R3C7_n8 = 1;
R3C9_n1 = 1;
R4C3_n3 = 1;
R4C8_n4 = 1;
R4C9_n2 = 1;
R5C1_n9 = 1;
R5C3_n1 = 1;
R5C7_n5 = 1;
R5C9_n8 = 1;
R6C1_n8 = 1;
R6C2_n2 = 1;
R6C7_n7 = 1;
R7C1_n2 = 1;
R7C3_n9 = 1;
R7C5_n4 = 1;
R7C6_n5 = 1;
R7C8_n7 = 1;
R8C4_n6 = 1;
R8C6_n8 = 1;
R8C8_n2 = 1;
R9C1_n1 = 1;
R9C2_n6 = 1;
R9C4_n3 = 1;
R9C7_n4 = 1;

! ************** Declare BINARY (0/1) variables *****************************;

@BIN (R1C1_n1); @BIN (R1C1_n2); @BIN (R1C1_n3); @BIN (R1C1_n4); @BIN (R1C1_n5); @BIN (R1C1_n6); @BIN (R1C1_n7); @BIN (R1C1_n8); @BIN (R1C1_n9); 
@BIN (R1C2_n1); @BIN (R1C2_n2); @BIN (R1C2_n3); @BIN (R1C2_n4); @BIN (R1C2_n5); @BIN (R1C2_n6); @BIN (R1C2_n7); @BIN (R1C2_n8); @BIN (R1C2_n9); 
@BIN (R1C3_n1); @BIN (R1C3_n2); @BIN (R1C3_n3); @BIN (R1C3_n4); @BIN (R1C3_n5); @BIN (R1C3_n6); @BIN (R1C3_n7); @BIN (R1C3_n8); @BIN (R1C3_n9); 
@BIN (R1C4_n1); @BIN (R1C4_n2); @BIN (R1C4_n3); @BIN (R1C4_n4); @BIN (R1C4_n5); @BIN (R1C4_n6); @BIN (R1C4_n7); @BIN (R1C4_n8); @BIN (R1C4_n9); 
@BIN (R1C5_n1); @BIN (R1C5_n2); @BIN (R1C5_n3); @BIN (R1C5_n4); @BIN (R1C5_n5); @BIN (R1C5_n6); @BIN (R1C5_n7); @BIN (R1C5_n8); @BIN (R1C5_n9); 
@BIN (R1C6_n1); @BIN (R1C6_n2); @BIN (R1C6_n3); @BIN (R1C6_n4); @BIN (R1C6_n5); @BIN (R1C6_n6); @BIN (R1C6_n7); @BIN (R1C6_n8); @BIN (R1C6_n9); 
@BIN (R1C7_n1); @BIN (R1C7_n2); @BIN (R1C7_n3); @BIN (R1C7_n4); @BIN (R1C7_n5); @BIN (R1C7_n6); @BIN (R1C7_n7); @BIN (R1C7_n8); @BIN (R1C7_n9); 
@BIN (R1C8_n1); @BIN (R1C8_n2); @BIN (R1C8_n3); @BIN (R1C8_n4); @BIN (R1C8_n5); @BIN (R1C8_n6); @BIN (R1C8_n7); @BIN (R1C8_n8); @BIN (R1C8_n9); 
@BIN (R1C9_n1); @BIN (R1C9_n2); @BIN (R1C9_n3); @BIN (R1C9_n4); @BIN (R1C9_n5); @BIN (R1C9_n6); @BIN (R1C9_n7); @BIN (R1C9_n8); @BIN (R1C9_n9); 

@BIN (R2C1_n1); @BIN (R2C1_n2); @BIN (R2C1_n3); @BIN (R2C1_n4); @BIN (R2C1_n5); @BIN (R2C1_n6); @BIN (R2C1_n7); @BIN (R2C1_n8); @BIN (R2C1_n9); 
@BIN (R2C2_n1); @BIN (R2C2_n2); @BIN (R2C2_n3); @BIN (R2C2_n4); @BIN (R2C2_n5); @BIN (R2C2_n6); @BIN (R2C2_n7); @BIN (R2C2_n8); @BIN (R2C2_n9); 
@BIN (R2C3_n1); @BIN (R2C3_n2); @BIN (R2C3_n3); @BIN (R2C3_n4); @BIN (R2C3_n5); @BIN (R2C3_n6); @BIN (R2C3_n7); @BIN (R2C3_n8); @BIN (R2C3_n9); 
@BIN (R2C4_n1); @BIN (R2C4_n2); @BIN (R2C4_n3); @BIN (R2C4_n4); @BIN (R2C4_n5); @BIN (R2C4_n6); @BIN (R2C4_n7); @BIN (R2C4_n8); @BIN (R2C4_n9); 
@BIN (R2C5_n1); @BIN (R2C5_n2); @BIN (R2C5_n3); @BIN (R2C5_n4); @BIN (R2C5_n5); @BIN (R2C5_n6); @BIN (R2C5_n7); @BIN (R2C5_n8); @BIN (R2C5_n9); 
@BIN (R2C6_n1); @BIN (R2C6_n2); @BIN (R2C6_n3); @BIN (R2C6_n4); @BIN (R2C6_n5); @BIN (R2C6_n6); @BIN (R2C6_n7); @BIN (R2C6_n8); @BIN (R2C6_n9); 
@BIN (R2C7_n1); @BIN (R2C7_n2); @BIN (R2C7_n3); @BIN (R2C7_n4); @BIN (R2C7_n5); @BIN (R2C7_n6); @BIN (R2C7_n7); @BIN (R2C7_n8); @BIN (R2C7_n9); 
@BIN (R2C8_n1); @BIN (R2C8_n2); @BIN (R2C8_n3); @BIN (R2C8_n4); @BIN (R2C8_n5); @BIN (R2C8_n6); @BIN (R2C8_n7); @BIN (R2C8_n8); @BIN (R2C8_n9); 
@BIN (R2C9_n1); @BIN (R2C9_n2); @BIN (R2C9_n3); @BIN (R2C9_n4); @BIN (R2C9_n5); @BIN (R2C9_n6); @BIN (R2C9_n7); @BIN (R2C9_n8); @BIN (R2C9_n9); 

@BIN (R3C1_n1); @BIN (R3C1_n2); @BIN (R3C1_n3); @BIN (R3C1_n4); @BIN (R3C1_n5); @BIN (R3C1_n6); @BIN (R3C1_n7); @BIN (R3C1_n8); @BIN (R3C1_n9); 
@BIN (R3C2_n1); @BIN (R3C2_n2); @BIN (R3C2_n3); @BIN (R3C2_n4); @BIN (R3C2_n5); @BIN (R3C2_n6); @BIN (R3C2_n7); @BIN (R3C2_n8); @BIN (R3C2_n9); 
@BIN (R3C3_n1); @BIN (R3C3_n2); @BIN (R3C3_n3); @BIN (R3C3_n4); @BIN (R3C3_n5); @BIN (R3C3_n6); @BIN (R3C3_n7); @BIN (R3C3_n8); @BIN (R3C3_n9); 
@BIN (R3C4_n1); @BIN (R3C4_n2); @BIN (R3C4_n3); @BIN (R3C4_n4); @BIN (R3C4_n5); @BIN (R3C4_n6); @BIN (R3C4_n7); @BIN (R3C4_n8); @BIN (R3C4_n9); 
@BIN (R3C5_n1); @BIN (R3C5_n2); @BIN (R3C5_n3); @BIN (R3C5_n4); @BIN (R3C5_n5); @BIN (R3C5_n6); @BIN (R3C5_n7); @BIN (R3C5_n8); @BIN (R3C5_n9); 
@BIN (R3C6_n1); @BIN (R3C6_n2); @BIN (R3C6_n3); @BIN (R3C6_n4); @BIN (R3C6_n5); @BIN (R3C6_n6); @BIN (R3C6_n7); @BIN (R3C6_n8); @BIN (R3C6_n9); 
@BIN (R3C7_n1); @BIN (R3C7_n2); @BIN (R3C7_n3); @BIN (R3C7_n4); @BIN (R3C7_n5); @BIN (R3C7_n6); @BIN (R3C7_n7); @BIN (R3C7_n8); @BIN (R3C7_n9); 
@BIN (R3C8_n1); @BIN (R3C8_n2); @BIN (R3C8_n3); @BIN (R3C8_n4); @BIN (R3C8_n5); @BIN (R3C8_n6); @BIN (R3C8_n7); @BIN (R3C8_n8); @BIN (R3C8_n9); 
@BIN (R3C9_n1); @BIN (R3C9_n2); @BIN (R3C9_n3); @BIN (R3C9_n4); @BIN (R3C9_n5); @BIN (R3C9_n6); @BIN (R3C9_n7); @BIN (R3C9_n8); @BIN (R3C9_n9); 

@BIN (R4C1_n1); @BIN (R4C1_n2); @BIN (R4C1_n3); @BIN (R4C1_n4); @BIN (R4C1_n5); @BIN (R4C1_n6); @BIN (R4C1_n7); @BIN (R4C1_n8); @BIN (R4C1_n9); 
@BIN (R4C2_n1); @BIN (R4C2_n2); @BIN (R4C2_n3); @BIN (R4C2_n4); @BIN (R4C2_n5); @BIN (R4C2_n6); @BIN (R4C2_n7); @BIN (R4C2_n8); @BIN (R4C2_n9); 
@BIN (R4C3_n1); @BIN (R4C3_n2); @BIN (R4C3_n3); @BIN (R4C3_n4); @BIN (R4C3_n5); @BIN (R4C3_n6); @BIN (R4C3_n7); @BIN (R4C3_n8); @BIN (R4C3_n9); 
@BIN (R4C4_n1); @BIN (R4C4_n2); @BIN (R4C4_n3); @BIN (R4C4_n4); @BIN (R4C4_n5); @BIN (R4C4_n6); @BIN (R4C4_n7); @BIN (R4C4_n8); @BIN (R4C4_n9); 
@BIN (R4C5_n1); @BIN (R4C5_n2); @BIN (R4C5_n3); @BIN (R4C5_n4); @BIN (R4C5_n5); @BIN (R4C5_n6); @BIN (R4C5_n7); @BIN (R4C5_n8); @BIN (R4C5_n9); 
@BIN (R4C6_n1); @BIN (R4C6_n2); @BIN (R4C6_n3); @BIN (R4C6_n4); @BIN (R4C6_n5); @BIN (R4C6_n6); @BIN (R4C6_n7); @BIN (R4C6_n8); @BIN (R4C6_n9); 
@BIN (R4C7_n1); @BIN (R4C7_n2); @BIN (R4C7_n3); @BIN (R4C7_n4); @BIN (R4C7_n5); @BIN (R4C7_n6); @BIN (R4C7_n7); @BIN (R4C7_n8); @BIN (R4C7_n9); 
@BIN (R4C8_n1); @BIN (R4C8_n2); @BIN (R4C8_n3); @BIN (R4C8_n4); @BIN (R4C8_n5); @BIN (R4C8_n6); @BIN (R4C8_n7); @BIN (R4C8_n8); @BIN (R4C8_n9); 
@BIN (R4C9_n1); @BIN (R4C9_n2); @BIN (R4C9_n3); @BIN (R4C9_n4); @BIN (R4C9_n5); @BIN (R4C9_n6); @BIN (R4C9_n7); @BIN (R4C9_n8); @BIN (R4C9_n9); 

@BIN (R5C1_n1); @BIN (R5C1_n2); @BIN (R5C1_n3); @BIN (R5C1_n4); @BIN (R5C1_n5); @BIN (R5C1_n6); @BIN (R5C1_n7); @BIN (R5C1_n8); @BIN (R5C1_n9); 
@BIN (R5C2_n1); @BIN (R5C2_n2); @BIN (R5C2_n3); @BIN (R5C2_n4); @BIN (R5C2_n5); @BIN (R5C2_n6); @BIN (R5C2_n7); @BIN (R5C2_n8); @BIN (R5C2_n9); 
@BIN (R5C3_n1); @BIN (R5C3_n2); @BIN (R5C3_n3); @BIN (R5C3_n4); @BIN (R5C3_n5); @BIN (R5C3_n6); @BIN (R5C3_n7); @BIN (R5C3_n8); @BIN (R5C3_n9); 
@BIN (R5C4_n1); @BIN (R5C4_n2); @BIN (R5C4_n3); @BIN (R5C4_n4); @BIN (R5C4_n5); @BIN (R5C4_n6); @BIN (R5C4_n7); @BIN (R5C4_n8); @BIN (R5C4_n9); 
@BIN (R5C5_n1); @BIN (R5C5_n2); @BIN (R5C5_n3); @BIN (R5C5_n4); @BIN (R5C5_n5); @BIN (R5C5_n6); @BIN (R5C5_n7); @BIN (R5C5_n8); @BIN (R5C5_n9); 
@BIN (R5C6_n1); @BIN (R5C6_n2); @BIN (R5C6_n3); @BIN (R5C6_n4); @BIN (R5C6_n5); @BIN (R5C6_n6); @BIN (R5C6_n7); @BIN (R5C6_n8); @BIN (R5C6_n9); 
@BIN (R5C7_n1); @BIN (R5C7_n2); @BIN (R5C7_n3); @BIN (R5C7_n4); @BIN (R5C7_n5); @BIN (R5C7_n6); @BIN (R5C7_n7); @BIN (R5C7_n8); @BIN (R5C7_n9); 
@BIN (R5C8_n1); @BIN (R5C8_n2); @BIN (R5C8_n3); @BIN (R5C8_n4); @BIN (R5C8_n5); @BIN (R5C8_n6); @BIN (R5C8_n7); @BIN (R5C8_n8); @BIN (R5C8_n9); 
@BIN (R5C9_n1); @BIN (R5C9_n2); @BIN (R5C9_n3); @BIN (R5C9_n4); @BIN (R5C9_n5); @BIN (R5C9_n6); @BIN (R5C9_n7); @BIN (R5C9_n8); @BIN (R5C9_n9); 

@BIN (R6C1_n1); @BIN (R6C1_n2); @BIN (R6C1_n3); @BIN (R6C1_n4); @BIN (R6C1_n5); @BIN (R6C1_n6); @BIN (R6C1_n7); @BIN (R6C1_n8); @BIN (R6C1_n9); 
@BIN (R6C2_n1); @BIN (R6C2_n2); @BIN (R6C2_n3); @BIN (R6C2_n4); @BIN (R6C2_n5); @BIN (R6C2_n6); @BIN (R6C2_n7); @BIN (R6C2_n8); @BIN (R6C2_n9); 
@BIN (R6C3_n1); @BIN (R6C3_n2); @BIN (R6C3_n3); @BIN (R6C3_n4); @BIN (R6C3_n5); @BIN (R6C3_n6); @BIN (R6C3_n7); @BIN (R6C3_n8); @BIN (R6C3_n9); 
@BIN (R6C4_n1); @BIN (R6C4_n2); @BIN (R6C4_n3); @BIN (R6C4_n4); @BIN (R6C4_n5); @BIN (R6C4_n6); @BIN (R6C4_n7); @BIN (R6C4_n8); @BIN (R6C4_n9); 
@BIN (R6C5_n1); @BIN (R6C5_n2); @BIN (R6C5_n3); @BIN (R6C5_n4); @BIN (R6C5_n5); @BIN (R6C5_n6); @BIN (R6C5_n7); @BIN (R6C5_n8); @BIN (R6C5_n9); 
@BIN (R6C6_n1); @BIN (R6C6_n2); @BIN (R6C6_n3); @BIN (R6C6_n4); @BIN (R6C6_n5); @BIN (R6C6_n6); @BIN (R6C6_n7); @BIN (R6C6_n8); @BIN (R6C6_n9); 
@BIN (R6C7_n1); @BIN (R6C7_n2); @BIN (R6C7_n3); @BIN (R6C7_n4); @BIN (R6C7_n5); @BIN (R6C7_n6); @BIN (R6C7_n7); @BIN (R6C7_n8); @BIN (R6C7_n9); 
@BIN (R6C8_n1); @BIN (R6C8_n2); @BIN (R6C8_n3); @BIN (R6C8_n4); @BIN (R6C8_n5); @BIN (R6C8_n6); @BIN (R6C8_n7); @BIN (R6C8_n8); @BIN (R6C8_n9); 
@BIN (R6C9_n1); @BIN (R6C9_n2); @BIN (R6C9_n3); @BIN (R6C9_n4); @BIN (R6C9_n5); @BIN (R6C9_n6); @BIN (R6C9_n7); @BIN (R6C9_n8); @BIN (R6C9_n9); 

@BIN (R7C1_n1); @BIN (R7C1_n2); @BIN (R7C1_n3); @BIN (R7C1_n4); @BIN (R7C1_n5); @BIN (R7C1_n6); @BIN (R7C1_n7); @BIN (R7C1_n8); @BIN (R7C1_n9); 
@BIN (R7C2_n1); @BIN (R7C2_n2); @BIN (R7C2_n3); @BIN (R7C2_n4); @BIN (R7C2_n5); @BIN (R7C2_n6); @BIN (R7C2_n7); @BIN (R7C2_n8); @BIN (R7C2_n9); 
@BIN (R7C3_n1); @BIN (R7C3_n2); @BIN (R7C3_n3); @BIN (R7C3_n4); @BIN (R7C3_n5); @BIN (R7C3_n6); @BIN (R7C3_n7); @BIN (R7C3_n8); @BIN (R7C3_n9); 
@BIN (R7C4_n1); @BIN (R7C4_n2); @BIN (R7C4_n3); @BIN (R7C4_n4); @BIN (R7C4_n5); @BIN (R7C4_n6); @BIN (R7C4_n7); @BIN (R7C4_n8); @BIN (R7C4_n9); 
@BIN (R7C5_n1); @BIN (R7C5_n2); @BIN (R7C5_n3); @BIN (R7C5_n4); @BIN (R7C5_n5); @BIN (R7C5_n6); @BIN (R7C5_n7); @BIN (R7C5_n8); @BIN (R7C5_n9); 
@BIN (R7C6_n1); @BIN (R7C6_n2); @BIN (R7C6_n3); @BIN (R7C6_n4); @BIN (R7C6_n5); @BIN (R7C6_n6); @BIN (R7C6_n7); @BIN (R7C6_n8); @BIN (R7C6_n9); 
@BIN (R7C7_n1); @BIN (R7C7_n2); @BIN (R7C7_n3); @BIN (R7C7_n4); @BIN (R7C7_n5); @BIN (R7C7_n6); @BIN (R7C7_n7); @BIN (R7C7_n8); @BIN (R7C7_n9); 
@BIN (R7C8_n1); @BIN (R7C8_n2); @BIN (R7C8_n3); @BIN (R7C8_n4); @BIN (R7C8_n5); @BIN (R7C8_n6); @BIN (R7C8_n7); @BIN (R7C8_n8); @BIN (R7C8_n9); 
@BIN (R7C9_n1); @BIN (R7C9_n2); @BIN (R7C9_n3); @BIN (R7C9_n4); @BIN (R7C9_n5); @BIN (R7C9_n6); @BIN (R7C9_n7); @BIN (R7C9_n8); @BIN (R7C9_n9); 

@BIN (R8C1_n1); @BIN (R8C1_n2); @BIN (R8C1_n3); @BIN (R8C1_n4); @BIN (R8C1_n5); @BIN (R8C1_n6); @BIN (R8C1_n7); @BIN (R8C1_n8); @BIN (R8C1_n9); 
@BIN (R8C2_n1); @BIN (R8C2_n2); @BIN (R8C2_n3); @BIN (R8C2_n4); @BIN (R8C2_n5); @BIN (R8C2_n6); @BIN (R8C2_n7); @BIN (R8C2_n8); @BIN (R8C2_n9); 
@BIN (R8C3_n1); @BIN (R8C3_n2); @BIN (R8C3_n3); @BIN (R8C3_n4); @BIN (R8C3_n5); @BIN (R8C3_n6); @BIN (R8C3_n7); @BIN (R8C3_n8); @BIN (R8C3_n9); 
@BIN (R8C4_n1); @BIN (R8C4_n2); @BIN (R8C4_n3); @BIN (R8C4_n4); @BIN (R8C4_n5); @BIN (R8C4_n6); @BIN (R8C4_n7); @BIN (R8C4_n8); @BIN (R8C4_n9); 
@BIN (R8C5_n1); @BIN (R8C5_n2); @BIN (R8C5_n3); @BIN (R8C5_n4); @BIN (R8C5_n5); @BIN (R8C5_n6); @BIN (R8C5_n7); @BIN (R8C5_n8); @BIN (R8C5_n9); 
@BIN (R8C6_n1); @BIN (R8C6_n2); @BIN (R8C6_n3); @BIN (R8C6_n4); @BIN (R8C6_n5); @BIN (R8C6_n6); @BIN (R8C6_n7); @BIN (R8C6_n8); @BIN (R8C6_n9); 
@BIN (R8C7_n1); @BIN (R8C7_n2); @BIN (R8C7_n3); @BIN (R8C7_n4); @BIN (R8C7_n5); @BIN (R8C7_n6); @BIN (R8C7_n7); @BIN (R8C7_n8); @BIN (R8C7_n9); 
@BIN (R8C8_n1); @BIN (R8C8_n2); @BIN (R8C8_n3); @BIN (R8C8_n4); @BIN (R8C8_n5); @BIN (R8C8_n6); @BIN (R8C8_n7); @BIN (R8C8_n8); @BIN (R8C8_n9); 
@BIN (R8C9_n1); @BIN (R8C9_n2); @BIN (R8C9_n3); @BIN (R8C9_n4); @BIN (R8C9_n5); @BIN (R8C9_n6); @BIN (R8C9_n7); @BIN (R8C9_n8); @BIN (R8C9_n9); 

@BIN (R9C1_n1); @BIN (R9C1_n2); @BIN (R9C1_n3); @BIN (R9C1_n4); @BIN (R9C1_n5); @BIN (R9C1_n6); @BIN (R9C1_n7); @BIN (R9C1_n8); @BIN (R9C1_n9); 
@BIN (R9C2_n1); @BIN (R9C2_n2); @BIN (R9C2_n3); @BIN (R9C2_n4); @BIN (R9C2_n5); @BIN (R9C2_n6); @BIN (R9C2_n7); @BIN (R9C2_n8); @BIN (R9C2_n9); 
@BIN (R9C3_n1); @BIN (R9C3_n2); @BIN (R9C3_n3); @BIN (R9C3_n4); @BIN (R9C3_n5); @BIN (R9C3_n6); @BIN (R9C3_n7); @BIN (R9C3_n8); @BIN (R9C3_n9); 
@BIN (R9C4_n1); @BIN (R9C4_n2); @BIN (R9C4_n3); @BIN (R9C4_n4); @BIN (R9C4_n5); @BIN (R9C4_n6); @BIN (R9C4_n7); @BIN (R9C4_n8); @BIN (R9C4_n9); 
@BIN (R9C5_n1); @BIN (R9C5_n2); @BIN (R9C5_n3); @BIN (R9C5_n4); @BIN (R9C5_n5); @BIN (R9C5_n6); @BIN (R9C5_n7); @BIN (R9C5_n8); @BIN (R9C5_n9); 
@BIN (R9C6_n1); @BIN (R9C6_n2); @BIN (R9C6_n3); @BIN (R9C6_n4); @BIN (R9C6_n5); @BIN (R9C6_n6); @BIN (R9C6_n7); @BIN (R9C6_n8); @BIN (R9C6_n9); 
@BIN (R9C7_n1); @BIN (R9C7_n2); @BIN (R9C7_n3); @BIN (R9C7_n4); @BIN (R9C7_n5); @BIN (R9C7_n6); @BIN (R9C7_n7); @BIN (R9C7_n8); @BIN (R9C7_n9); 
@BIN (R9C8_n1); @BIN (R9C8_n2); @BIN (R9C8_n3); @BIN (R9C8_n4); @BIN (R9C8_n5); @BIN (R9C8_n6); @BIN (R9C8_n7); @BIN (R9C8_n8); @BIN (R9C8_n9); 
@BIN (R9C9_n1); @BIN (R9C9_n2); @BIN (R9C9_n3); @BIN (R9C9_n4); @BIN (R9C9_n5); @BIN (R9C9_n6); @BIN (R9C9_n7); @BIN (R9C9_n8); @BIN (R9C9_n9); 



