# these are the operators and group for megaminx
# the N suffix indicates an anti-clockwise turn
# remember to invert 2L type slice moves!!!!!

M_UN:=(13,38,24,27,15)(14,37,23,28,16)(73,89,102,85,76)(74,90,100,86,77)(75,88,101,87,78);
M_2UN:=(2,6,5,4,3)(7,11,10,9,8)(17,66,50,47,31)(18,65,49,48,32)(19,56,52,58,33)(20,55,51,57,34)(21,29,25,59,36)(22,30,26,60,35)(39,54,71,63,45)(40,53,72,64,46)(79,119,125,111,96)(80,120,126,109,94)(81,118,124,110,95)(82,93,117,113,97)(83,91,115,114,98)(84,92,116,112,99);
M_DN:=(41,43,62,68,70)(42,44,61,67,69)(103,122,128,131,108)(104,123,129,132,106)(105,121,127,130,107);
M_FN:=(15,22,31,19,29)(16,21,32,20,30)(76,86,99,94,82)(77,87,97,95,83)(78,85,98,96,84);
M_2FN:=(1,4,8,7,2)(5,9,12,11,6)(13,28,33,39,18)(14,27,34,40,17)(23,47,44,54,25)(24,48,43,53,26)(35,46,42,56,37)(36,45,41,55,38)(57,62,69,66,60)(58,61,70,65,59)(73,101,109,105,81)(74,102,110,103,79)(75,100,111,104,80)(88,112,123,107,93)(89,113,121,108,91)(90,114,122,106,92);
M_BFN:=(49,51,72,67,63)(50,52,71,68,64)(115,119,132,127,124)(116,120,130,128,125)(117,118,131,129,126);
M_LN:=(21,27,35,47,33)(22,28,36,48,34)(85,100,112,109,97)(86,101,113,110,98)(87,102,114,111,99);
M_2LN:=(1,5,9,8,3)(2,6,10,12,7)(13,59,63,43,20)(14,60,64,44,19)(15,23,58,45,32)(16,24,57,46,31)(17,26,51,68,42)(18,25,52,67,41)(29,37,50,61,39)(30,38,49,62,40)(73,117,127,103,83)(74,115,128,104,84)(75,116,129,105,82)(76,88,126,121,95)(77,89,124,122,96)(78,90,125,123,94);
M_EN:=(53,69,71,65,55)(54,70,72,66,56)(79,106,130,118,91)(80,107,131,119,92)(81,108,132,120,93);
M_BLN:=(23,59,49,57,35)(24,60,50,58,36)(88,117,124,114,100)(89,115,125,112,101)(90,116,126,113,102);
M_2BLN:=(1,6,10,9,4)(2,11,12,8,3)(13,65,68,46,22)(14,66,67,45,21)(15,25,71,62,34)(16,26,72,61,33)(27,37,52,63,48)(28,38,51,64,47)(29,56,69,43,32)(30,55,70,44,31)(73,118,128,111,86)(74,119,129,109,87)(75,120,127,110,85)(76,93,130,122,98)(77,91,131,123,99)(78,92,132,121,97);
M_CN:=(17,19,39,41,53)(18,20,40,42,54)(79,84,94,105,108)(80,82,95,103,106)(81,83,96,104,107);
M_BRN:=(25,65,51,60,37)(26,66,52,59,38)(73,91,119,116,88)(74,92,120,117,89)(75,93,118,115,90);
M_2BRN:=(1,2,11,10,5)(3,7,12,9,4)(13,55,72,50,23)(14,56,71,49,24)(15,18,70,64,35)(16,17,69,63,36)(19,42,62,48,21)(20,41,61,47,22)(27,29,54,68,57)(28,30,53,67,58)(76,81,131,125,100)(77,79,132,126,101)(78,80,130,124,102)(82,107,128,114,85)(83,108,129,112,86)(84,106,127,113,87);
M_AN:=(31,33,45,43,40)(32,34,46,44,39)(94,97,110,122,104)(95,98,111,123,105)(96,99,109,121,103);
M_RN:=(13,30,17,56,25)(14,29,18,55,26)(73,77,84,80,93)(74,78,82,81,91)(75,76,83,79,92);
M_2RN:=(1,3,7,11,6)(4,8,12,10,5)(15,20,53,66,37)(16,19,54,65,38)(21,39,70,51,24)(22,40,69,52,23)(27,32,41,72,60)(28,31,42,71,59)(33,44,68,49,36)(34,43,67,50,35)(85,95,108,119,90)(86,96,106,120,88)(87,94,107,118,89)(97,105,131,115,102)(98,103,132,116,100)(99,104,130,117,101);
M_IN:=(45,48,57,64,61)(46,47,58,63,62)(109,113,124,128,123)(110,114,125,129,121)(111,112,126,127,122);
M_U:=M_UN^-1;
M_2U:=(2,6,5,4,3)(7,11,10,9,8)(17,66,50,47,31)(18,65,49,48,32)(19,56,52,58,33)(20,55,51,57,34)(21,29,25,59,36)(22,30,26,60,35)(39,54,71,63,45)(40,53,72,64,46)(79,119,125,111,96)(80,120,126,109,94)(81,118,124,110,95)(82,93,117,113,97)(83,91,115,114,98)(84,92,116,112,99);
M_D:= M_DN^-1;
M_F:= M_FN^-1;
M_2F:=(1,4,8,7,2)(5,9,12,11,6)(13,28,33,39,18)(14,27,34,40,17)(23,47,44,54,25)(24,48,43,53,26)(35,46,42,56,37)(36,45,41,55,38)(57,62,69,66,60)(58,61,70,65,59)(73,101,109,105,81)(74,102,110,103,79)(75,100,111,104,80)(88,112,123,107,93)(89,113,121,108,91)(90,114,122,106,92);
M_BF:= M_BFN ^-1;
M_L:= M_LN^-1;
M_2L:=(1,5,9,8,3)(2,6,10,12,7)(13,59,63,43,20)(14,60,64,44,19)(15,23,58,45,32)(16,24,57,46,31)(17,26,51,68,42)(18,25,52,67,41)(29,37,50,61,39)(30,38,49,62,40)(73,117,127,103,83)(74,115,128,104,84)(75,116,129,105,82)(76,88,126,121,95)(77,89,124,122,96)(78,90,125,123,94);
M_E:= M_EN^-1;
M_BL:= M_BLN^-1;
M_2BL:=(1,6,10,9,4)(2,11,12,8,3)(13,65,68,46,22)(14,66,67,45,21)(15,25,71,62,34)(16,26,72,61,33)(27,37,52,63,48)(28,38,51,64,47)(29,56,69,43,32)(30,55,70,44,31)(73,118,128,111,86)(74,119,129,109,87)(75,120,127,110,85)(76,93,130,122,98)(77,91,131,123,99)(78,92,132,121,97);
M_C:= M_CN^-1;
M_BR:= M_BRN^-1;
M_2BR:=(1,2,11,10,5)(3,7,12,9,4)(13,55,72,50,23)(14,56,71,49,24)(15,18,70,64,35)(16,17,69,63,36)(19,42,62,48,21)(20,41,61,47,22)(27,29,54,68,57)(28,30,53,67,58)(76,81,131,125,100)(77,79,132,126,101)(78,80,130,124,102)(82,107,128,114,85)(83,108,129,112,86)(84,106,127,113,87);
M_A:= M_AN^-1;
M_R:= M_RN^-1;
M_2R:=(1,3,7,11,6)(4,8,12,10,5)(15,20,53,66,37)(16,19,54,65,38)(21,39,70,51,24)(22,40,69,52,23)(27,32,41,72,60)(28,31,42,71,59)(33,44,68,49,36)(34,43,67,50,35)(85,95,108,119,90)(86,96,106,120,88)(87,94,107,118,89)(97,105,131,115,102)(98,103,132,116,100)(99,104,130,117,101);
M_I:= M_IN^-1;

Gen:=[
M_U,M_2U,M_D,M_F,M_2F,M_BF,M_L,M_2L,M_E,M_BL,M_2BL,M_C,M_BR,M_2BR,M_A,M_R,M_2R,M_I
];

ip:=[[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12],[13],[15],[17],[19],[21],[23],[25],[27],[29],[31],[33],[35],[37],[39],[41],[43],[45],[47],[49],[51],[53],[55],[57],[59],[61],[63],[65],[67],[69],[71],[73],[76],[79],[82],[85],[88],[91],[94],[97],[100],[103],[106],[109],[112],[115],[118],[121],[124],[127],[130]];

M_SU := M_U * M_DN;
M_SL := M_L * M_EN;
M_SF := M_F * M_BFN;
M_SR := M_R * M_IN;
M_SBL:= M_BL * M_CN;
M_SBR:= M_BR * M_AN;

M_AU := M_U * M_D;
M_AL := M_L * M_E;
M_AF := M_F * M_BF;
M_AR := M_R * M_I;
M_ABL:= M_BL* M_C;
M_ABR:= M_BR* M_A;

M_2U := M_2UN^-1;
M_2L := M_2LN^-1;
M_2F := M_2FN^-1;
M_2R := M_2RN^-1;
M_2BR:= M_2BRN^-1;
M_2BL:= M_2BLN^-1;

Rot_U := M_U * M_D^-1 * M_2U;
Rot_L := M_L * M_E^-1 * M_2L;
Rot_F := M_F * M_BF^-1 * M_2F;
Rot_R := M_R * M_I^-1 * M_2R;
Rot_BL:= M_BL * M_C^-1 * M_2BL;
Rot_BR:= M_BR * M_A^-1 * M_2BR;

# Gen is the full megaminx generators
Gen:=[
M_U,M_D,M_F,M_BF,M_L,M_E,M_BL,M_C,M_BR,M_A,M_R,M_I
];

dod := Group(Gen);

# Gen10 is the generators for working on 10 spot
Gen10:=[
M_L,M_F,M_R,M_BR,M_BL,M_E,M_C,M_A,M_I,M_BF
];

Gen2:=[
M_U, M_R
];

Gen3:=[
M_U, M_L, M_F
];

Gen5:=[
M_BR, M_E, M_A, M_D, M_BF
];
# BR A R C
# BL A L U

Gen6:=[
M_BL, M_BF, M_C, M_E, M_BR 
];
#M_BL, M_BF, M_C, M_E, M_BR

Gen7:=[
M_F, M_C, M_A, M_BL, M_U
];

Gen8:=[
M_U, M_F, M_BL, M_R
];
# BL E D BF
#
Gen9:=[
M_E, M_BR, M_U, M_R, M_C
];

Gen11:=[
M_BF, M_I, M_D, M_E, M_BL 
];
#M_BF, M_I, M_D, M_E, M_BL
#
Gen12:=[
M_U, M_L, M_F, M_R, M_BR
]; 
# U, L, R, BF, D
# U,C,D,R,I,L
# M_U, M_R, M_D, M_C, M_L
# M_U, M_L, M_D, M_I, M_BL, M_E, M_R
#
#
Gen13:=[
M_L, M_F, M_R, M_BL, M_BR
];
#M_L, M_F, M_R, M_BL, M_BR
#
Gen14:=[
M_L, M_R, M_E, M_I
];

Gen15:=[
M_2L, Rot_U
];

Gen16:=[
M_2L, M_2U
];

Gen17:=[
M_2L, M_2U, M_2F, M_2R 
];

Gen18:=[
M_2U, M_2L, M_2F, M_2BL
];

Gen19:=[
M_2U, M_2L, M_2F, M_2R
];

Gen20:=[
M_2U, M_2L, M_2F
];

# L U R E D I
#

Gen21:=[
M_2L, Rot_U, Rot_F
];

Gen_slice :=[
M_SU, M_SL, M_SF, M_SR, M_SBL, M_SBR
];

Gen_slice1 :=[
M_2U, M_2L
#M_SU, M_SL, M_SF, M_SR
];

Gen_slicer :=[
M_2U, M_2L, M_2F, M_2R, M_2BL, M_2BR
];

Gen_antislice :=[
M_AU, M_AL, M_AF, M_AR, M_ABL, M_ABR
];

Gen_antislice1 :=[
M_AU, M_AL, M_AF
];

# C L BL U
#
#M_BR, M_E, M_BF, M_L, M_A, M_D, 

#fix is the minimal generators for fixing 10 spot
fix :=[
M_U, M_BR, M_E, M_D

#M_BL, M_R, M_C, M_I, M_A
# M_U, M_R, M_C, M_D   this one works
# M_U,M_R,M_E,M_D      also works

];
# M_R* , M_I* , M_A*, M_F*, M_BF*   all these are necessary
#

# BR U2' BR' U' BL U2 BL' L2 U2 L' U' F U2' F' U2 R U' R' U'

fix1 :=[
M_C, M_R, M_A, M_E, M_U
];


dod2 := Group(Gen2);
dod3 := Group(Gen3);
dod5 := Group(Gen5);
dod6 := Group(Gen6);
dod7 := Group(Gen7);
dod8 := Group(Gen8);
dod9 := Group(Gen9);

dod11 := Group(Gen11);
dod12 := Group(Gen12);
dod13 := Group(Gen13);
dod14 := Group(Gen14);
dod15 := Group(Gen15);
dod16 := Group(Gen16);
dod17 := Group(Gen17);
dod18 := Group(Gen18);
dod19 := Group(Gen19);
dod20 := Group(Gen20);
dod21 := Group(Gen21);

dod_slice := Group(Gen_slice);
dod_slice1:= Group(Gen_slice1);
dod_slicer:= Group(Gen_slicer);

dod_antislice := Group (Gen_antislice);
dod_antislice1 := Group (Gen_antislice1);

#          (L E' BL C' BR A' R I' F BF')7 L E'
spot10 := (M_L * M_EN * M_BL * M_CN * M_BR * M_AN * M_R * M_IN * M_F * M_BFN)^7 * M_L * M_EN;
spot10a :=(M_L * M_E^-1 * M_BL * M_C^-1 * M_BR * M_A^-1 * M_R * M_I^-1 * M_F * M_BF^-1)^7 * M_L * M_E^-1;

# 
# F2' L2 F L' F' L' F2 R U L U' R' L'
flip2 := M_FN^2  * M_L^2 * M_F * M_LN * M_FN * M_LN * M_F^2 * M_R * M_U * M_L * M_UN * M_RN * M_LN;

# R2' F U' F2' U F2' R L F2' U F2' U' F L' F R
dbl_edge_swap := M_RN^2  * M_F * M_UN * M_FN^2  * M_U * M_FN^2 * M_R * M_L * M_FN^2  * M_U * M_FN^2 *M_UN * M_F * M_LN *M_F * M_R;

int := M_U^2 * M_F^-2 * M_U^2 * M_F^2 * M_R^2 * M_U^-2 * M_F^-2 * M_R^-1 * M_U^-2 * M_R^-1 * M_U^2 * M_F^-1 * M_U^-1 * M_R^-1 * M_F * M_U * M_F^-2 * M_U^-1 * M_F^-1 * M_U^-2 * M_R^-2 * M_L^2 * M_U^2 * M_F^2 * M_U^-2 * M_L^-2 * M_BL * M_U^2 * M_F * M_U * M_F^-1 * M_U^-2 * M_BL^-1; 
#spotit := 
#M_L * M_L * M_EN * M_EN * M_R * M_R * M_IN * M_IN *  M_BL * M_BL * M_CN * M_CN F2 BF2' BR2 A2' 
#L2 E2' R2 I2' BL2 C2' F2 BF2' BR2 A2'
#L2 E2' R2 I2' BL2 C2' F2 BF2' BR2 A2'
#L2 E2' R2 I2' BL2 C2'
#L E' BL C' BR A' R I' **F BF'
#L E' BL C' BR A' R I' F BF'
#L E' BL C' BR A' R I' F BF'
#L E' BL C' BR A' R I' F BF'
#L E' BL C' BR A' R I' F BF'
#L E' BL C' BR A' R I' F BF'
#L E' BL C' BR A' R I' F BF'
#L E'
#
#10 spot new
#(L2 E2' R2 I2' BL2 C2' F2 BF2' BR2 A2')3 L2 E2' R2 I2' BL2 C2' (L E' BL C' BR A' R I' F BF')7 L E'

spot1 := (M_L^2 * M_E^-2 * M_R^2 * M_I^-2 * M_BL^2 * M_C^-2 * M_F^2 * M_BF^-2 * M_BR^2 * M_A^-2)^3;
spot2 := (M_L^2 * M_E^-2 * M_R^2 * M_I^-2 * M_BL^2 * M_C^-2);
spot3 := (M_L * M_E^-1 * M_BL * M_C^-1 * M_BR * M_A^-1 * M_R * M_I^-1 * M_F * M_BF^-1)^7 * M_L * M_E^-1;
spot_fix := spot1 * spot2 * spot3;

# BR U2' BR' U' BL U2 BL' L2 U2 L' U' F U2' F' U2 R U' R' U'

new1 :=M_BR * M_U^-2 * M_BR^-1 * M_U^-1 * M_BL * M_U^2 * M_BL^-1 * M_L^2 * M_U^2 * M_L^-1 * M_U^1 * M_F * M_U^-2 * M_F^-1 * M_U^2 * M_R * M_U^-1 * M_R^-1 *M_U^1;

# BL2' BR2 R2 BR2' BL BR2 R2' BR2 R' BR BL BR' R BR 
# C2 A2' I2' A2 C' A2' I2 A2' I A' C' A I' A'
#
3swap :=  M_L* M_U^2 * M_L^-1 * M_D^2 * M_I^2 * M_U^-2 * M_BL^-1 * M_I^-2 * M_U^2 * M_L * M_I^2 * M_U^-2 * M_BL *M_I^-2 * M_L^-1 * M_D^-2 * M_E * M_R * M_E * M_BR^-1 * M_R^-1 * M_E^-2 * M_R * M_E * M_BR * M_E * M_R * M_E^-1 * M_R^-1 * M_E^-1 * M_R^-1;
#  L U2 L' D2 I2 U2' BL' I2' U2 L I2 U2' BL I2' L' D2'
#  E R E BR' R' E2' R E BR E R E' R' E' R'

# U D I' L2 U L2 I2 D I2' L2 U' L2' I2' D' I2' D' L U'
#  L2 E2 D' I2' L I D2' E D2 I2' L' I2 D' E' D2 E2' I L2'
#
3swap1 := M_BL^2 * M_I^-2 *  M_L* M_U^2 * M_L^-1 * M_D^2 * M_I^2 * M_U^-2 * M_BL^-1 * M_I^-2 * M_U^2 * M_L * M_I^2 * M_U^-2 * M_BL *M_I^-2 * M_L^-1 * M_D^-2 * M_E * M_R * M_E * M_BR^-1 * M_R^-1 * M_E^-2 * M_R * M_E * M_BR * M_E * M_R * M_E^-1 * M_R^-1 * M_E^-1 * M_R^-1 * M_I^-1 * M_BL^-2 * M_A^-2 * M_C^-2 * M_I^2 * M_BL^-2;

bridge := M_C^2 * M_A^2 * M_BL^2 * M_I * M_D * M_L^-2 * M_E^-1 * M_I^-2 * M_D^-2 * M_E^-1 * M_D^2 * M_I^-2 * M_L * M_U * M_I^2 * M_D^2 * M_L * M_E * M_D^2 * M_I^-1 * M_D * M_L^2 * M_U * M_L^2 * M_E * M_I^2 * M_D * M_I^-2 * M_L^2 * M_U^-1 * M_L^-2 * M_U^-1 * M_I^-2 * M_D^-2 * M_L* M_I^-1 * M_BL^-2 * M_A^-2 * M_C^-2;

bridge1 := M_C^2 * M_A^2 * M_BF^-2 * M_I^-1 * M_D * M_L^-2 * M_E^-1 * M_I^-2 * M_D^-2 * M_E^-1 * M_D^2 * M_I^-2 * M_L * M_U * M_I^2 * M_D^2 * M_L * M_E * M_D^2 * M_I^-1 * M_D * M_L^2 * M_U * M_L^2 * M_E * M_I^2 * M_D * M_I^-2 * M_L^2 * M_U^-1 * M_L^-2 * M_U^-1 * M_I^-2 * M_D^-2 * M_L* M_I^1 * M_BF^2 * M_A^-2 * M_C^-2;

check1 := M_U^2 * M_BR^-1 * M_U^2 * M_BR * M_R^-1 * M_BR^-1 * M_U^-1 * M_R * M_U^-2 * M_R^-1 * M_BR * M_R * M_BR^-2 * M_U^-1 * M_BR * M_U^-1 * M_BL^-1 * M_L^-2 * M_U^-1 * M_BL * M_U * M_L * M_BR^-1 * M_BL^-1 * M_L * M_U * M_BL * M_U * M_BR^2 * M_U^-1; 

check_all := ((M_2L * Rot_U^-1)^18 * Rot_F)^9;
check_dbl := check_all * check_all;

check_rot := Rot_F;

bridge2 := M_A^2 * M_BF^-2 * M_I^-1 * M_D * M_L^-2 * M_E^-1 * M_I^-2 * M_D^-2 * M_E^-1 * M_D^2 * M_I^-2 * M_L * M_U * M_I^2 * M_D^2 * M_L * M_E * M_D^2 * M_I^-1 * M_D * M_L^2 * M_U * M_L^2 * M_E * M_I^2 * M_D * M_I^-2 * M_L^2 * M_U^-1 * M_L^-2 * M_U^-1 * M_I^-2 * M_D^-2 * M_L* M_I^1 * M_BF^2 * M_A^-2;

bridge_org :=  M_I * M_BF^2 * M_A^-2 * M_R * M_E^2 * M_R^-2 * M_E * M_R^-1 * M_U^-2 * M_E^-1 * M_C^2 * M_R * M_U^2 * M_C^-2 * M_E * M_R * M_U^-2 * M_E^-1 * M_C^2 * M_R^-1 * M_U^2 * M_C^-2 * M_R^2 * M_E^-2 * M_R^-1 * M_A^2 * M_BF^-2 * M_I^-1; 

bridge_org_alt :=  M_C^2 * M_I * M_BF^2 * M_A^-2 * M_R * M_E^2 * M_R^-2 * M_E * M_R^-1 * M_U^-2 * M_E^-1 * M_C^2 * M_R * M_U^2 * M_C^-2 * M_E * M_R * M_U^-2 * M_E^-1 * M_C^2 * M_R^-1 * M_U^2 * M_C^-2 * M_R^2 * M_E^-2 * M_R^-1 * M_A^2 * M_BF^-2 * M_I^-1 * M_C^-2; 

new2 :=M_BL^-2 * M_BR^2 * M_R^2 * M_BR^-2 * M_BL * M_BR^2 * M_R^-2 * M_BR^2 * M_R^-1 * M_BR * M_BL * M_BR^-1 * M_R * M_BR;
new2a:=M_C^2 * M_A^-2 * M_I^-2 * M_A^2 * M_C^-1 * M_A^-2 * M_I^2 * M_A^-2 * M_I * M_A^-1 * M_C^-1 * M_A * M_I^-1 *M_A^-1;
newt := new2 * new2a;

swap1 :=M_BR^2 * M_E * M_BF * M_L^-1 * M_F^-1 * M_A^2 * M_D * M_BR * M_E * M_BR * M_E * M_D^-1 * M_A^-1 * M_D^2 * M_E^-1 * M_BR^-1 * M_E^-1 * M_BR * M_E^2 * M_D^2 * M_A * M_D^2 * M_E^-2 * M_D^-1 * M_BR^-2 * M_A^-2 * M_F * M_L * M_BF^-1 * M_E^-1 * M_BR^-2;

swap2 :=M_BL^2 * M_BF * M_C * M_D * M_C * M_D * M_BF^-1 * M_BL^-1 * M_BF^2 * M_D^-1 * M_C^-1 * M_D^-1 * M_C * M_D^2 * M_BF^2 * M_BL * M_BF^2 * M_D^-2 * M_BF^-1 * M_C^2 * M_U * M_BR * M_BL * M_U * M_BR^-2 * M_U^-1 * M_BR * M_BL^-2* M_BR^2 * M_BL^2 * M_BR^-2 * M_BL * M_U^-1 * M_BL * M_A^-1 * M_F^-1 * M_C^-1 * M_A^-1 * M_F^2 * M_A * M_F^-1 * M_C^2 * M_F^-2 * M_C^-2 * M_F^2 * M_C^-1 * M_A * M_C^-2;

dbl_flip :=M_U * M_BR * M_BL * M_U * M_BR^-2 * M_U^-1 * M_BR * M_BL^-2* M_BR^2 * M_BL^2 * M_BR^-2 * M_BL * M_U^-1 * M_BL * M_A^-1 * M_F^-1 * M_C^-1 * M_A^-1 * M_F^2 * M_A * M_F^-1 * M_C^2 * M_F^-2 * M_C^-2 * M_F^2 * M_C^-1 * M_A * M_C^-2;

dbl_flip2 :=M_I^2 * M_A^-2 * M_L^2 * M_F^-2 * M_E^-1 * M_C^-2 * M_E^2 * M_C * M_E^2 * M_D^-1 * M_C^-1 * M_D * M_C * M_E^2 * M_C^-2 * M_E^-1 * M_C^-2 * M_D * M_E * M_D^-1 * M_F^2 * M_L^-2 * M_A^2 * M_I^-2;

c_move :=M_E^2 * M_C^-2 * M_E^2 * M_BR^2 * M_U * M_BR * M_U * M_R^-1 * M_BR^-1 * M_U^-1 * M_BL * M_BR * M_R * M_U^-1 * M_BR^-1 * M_BL^-1 * M_BR^-2 * M_E^-2 * M_C^2;

final := M_U^-1 * M_BF^2 * M_I^2 * M_D^-1 * M_I^2 * M_D^-1 * M_E^2 * M_D^2 * M_I^-1 * M_BF * M_I^2 * M_BF^2 * M_D^-2 * M_E * M_D^2 * M_E^2 * M_D^-2 * M_E^-1 * M_D^2 * M_E^2 * M_BF^-1 * M_D^-2 * M_BL^-2 * M_I^2 * M_BL^-1 * M_I^-1 * M_BL * M_I *M_BF^-1 * M_E * M_BF^-2 * M_I^-2 * M_BF^-1 * M_I * M_BF * M_E^-1 * M_BF^-2 * M_I^-1 * M_D^2 * M_BL^2 * M_BF * M_U;

bowties := M_R * M_F^-1 * M_L^-1 * M_F^-1 * M_L^-1 * M_F^-2 * M_R^2 * M_F * M_R^-1 * M_U^-1 * M_R * M_F * M_U * M_F^-2 * M_R^-2 * M_F^-2 * M_L^2 * M_F * M_R^-2 * M_BR * M_BL^2 * M_BR^-2 * M_R^-2 * M_BR^-2 * M_U * M_BR * M_R * M_U^-1 * M_R^-1 * M_BR * M_R^2 * M_BR^-2 * M_BL^-1 * M_BR^-1 * M_BL^-1 * M_BR^-1 * M_R;

interior := M_BR * M_R * M_F * M_U^2 * M_BR^-1 * M_U^2 * M_L * M_BL * M_L^-1 * M_U^-2 * M_L * M_U^-1 * M_BL^-1 * M_L^-1 * M_BL * M_U^2 * M_BL^-1 * M_U^-1 * M_BR * M_U^-2 * M_F^-1 * M_R^-1 * M_BR^-1;
# BR R F (U2 BR' U2 L BL L' U2' L U' BL' L' BL U2 BL' U' BR U2') F' R' BR'

testo :=  M_R * M_F * M_U^2 * M_BR^-1 * M_U^2 * M_L * M_BL * M_L^-1 * M_U^-2 * M_L * M_U^-1 * M_BL^-1 * M_L^-1 * M_BL * M_U^2 * M_BL^-1 * M_U^-1 * M_BR * M_U^-2 * M_F^-1 * M_R^-1; 

yyyy :=  M_2R^-2 * M_2U * M_2L^-1 * M_2R^-1 * M_2F^-2 * M_2R * M_2U^2 * M_2L^-1 * M_2U^-2 * M_2L * M_2F^2 * M_2L * M_2U^-1 * M_2R^2 * M_2F * M_2R^-2 * M_2U * M_2F^-2 * M_2L^-2 * M_2R^-1 * M_2L^-1 * M_2R^-2 * M_2L * M_2R * M_2L^2 * M_2F^-1 * M_2L * M_2F^-2 * M_2L^-1 * M_2F^-2 * M_2U^-1 * M_2R^2 * M_2F^-1;

starit := M_R^2 * M_E^-1 * M_BR^-2 * M_R^-2 * M_E^-1 * M_R^-2 * M_F^2 * M_R^2 * M_E * M_R^2 * M_BR^2 * M_E * M_R * M_F^-2 * M_R^2 * M_L^2 * M_A^-1 * M_F^-2 * M_L^-2 * M_A^-1 * M_L^-2 * M_BL^2 * M_L^2 * M_A * M_L^2 * M_F^2 * M_A * M_L * M_BL^-2 * M_L^2;      

# BR2 E BF L' F' A2 D BR E BR E D' A' D2 E' BR' E' BR E2 D2 A D2 E2' D' BR2' A2' F L BF' E' BR2'

ip:=[[1],[3],[5],[7],[9],[11],[13],[15],[17],[19],[21],[23],[25],[27],[29],[31],[33],[35],[37],[39],[41],[43],[45],[47],[49],[51],[53],[55],[57],[59],[61],[64],[67],[70],[73],[76],[79],[82],[85],[88],[91],[94],[97],[100],[103],[106],[109],[112],[115],[118]];