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N-substituted heterocyclic amines as modulators of chemokine receptor activity

  • US 6,919,356 B2
  • Filed: 09/25/2003
  • Issued: 07/19/2005
  • Est. Priority Date: 09/26/2002
  • Status: Expired due to Term
First Claim
Patent Images

1. A compound of formula (I):

  • embedded imageor stereoisomers or pharmaceutically acceptable salts thereof, wherein;

    Z is selected from O, S, N(Rd), C(CN)2, CH(NO2), and CH(CN);

    X is C(R8)(R9);

    R1 and R2 are independently selected from H, C1-8 alkyl, C2-8 alkenyl, and C2-8 alkynyl;

    Rd is selected from H, C1-C6 alkyl, C3-C6 cycloalkyl, CON(Rf)Rf, ORe, CN, NO2, and (CH2)r-phenyl substituted with 0-3 R18;

    Re, at each occurrence, is independently selected from H, C1-6 alkyl, C3-6 cycloalkyl, and phenyl substituted with 0-3 R18;

    Rf, at each occurrence, is independently selected from H, C1-6 alkyl, C3-6 cycloaklyl, and phenyl substituted with 0-3 R18, or optionally, two Rf may be taken together with the nitrogen to which both are attached to form a pyrrolidine, piperidine, piperazine or morpholine ring;

    R3 is selected from a (CR3

    R3

    )r

    C3-6 carbocyclic residue substituted with 0-5 R15;

    R3

    , at each occurrence, is independently selected from H, C1-6 alkyl, (CH2)rC3-6 cycloalkyl, and phenyl;

    R4 is absent, taken with the nitrogen to which it is attached to form an N-oxide, or selected from C1-8 alkyl, C2-8 alkenyl, C2-8 alkynyl, (CH2)rC3-6 cycloalkyl, (CH2)qC(O)R4b, (CH2)qC(O)NR4aR4a, (CH2)qC(O)OR4b, and a (CH2)r

    C3-6 carbocyclic residue substituted with 0-3 R4c;

    R4a, at each occurrence, is independently selected from H, C1-6 alkyl, (CH2)rC3-6 cycloalkyl, and phenyl;

    R4b, at each occurrence, is independently selected from C1-6 alkyl, C2-8 alkenyl, (CH2)rC3-6 cycloalkyl, C2-8 alkynyl, and phenyl;

    R4c, at each occurrence, is independently selected from C1-6 alkyl, C2-8 alkenyl, C2-8 alkynyl, C3-6 cycloalkyl, Cl, F, Br, I, CN, NO2, (CF2)rCF3, (CH2)rOC1-5 alkyl, (CH2)rOH, (CH2)rSC1-5 alkyl, (CH2)rNR4aR4a, and (CH2)rphenyl;

    R5 is selected from embedded imageY is selected from O, N(R25), S, S(O) and S(O)2;

    ring B is a 5-7 membered cycloalkyl ring optionally containing a C═

    O, and being substituted with 0-2 R11a, wherein the cycloalkyl is fused with a benzo group substituted with 0-3 R16 or is fused with a 5-6 membered aromatic heterocyclic ring having 0-3 N, 0-1 O, or 0-1 S, the heterocyclic ring being substituted with 0-3 R16;

    alternatively, ring B is a fused 5-7 membered saturated heterocyclic ring containing 0-1 O, N(R16), S, S(O), and S(O)2, substituted with 0-2 R11a, the heterocyclic ring being fused with a benzo group substituted with 0-3 R16 or is fused with a 5-6 membered heterocyclic ring having 0-3 N, 0-1 O, or 0-1 S, the heterocyclic ring being substituted with 0-3 R16;

    provided that if ring B is a heterocyclic ring, then the number of carbon atoms separating the heteroatom of ring B and the nitrogen atom of structure (I) bonded to R5 is at least 2;

    R5a is selected from a C3-10 carbocyclic residue substituted with 0-5 R16, and a 5-10 membered heterocyclic residue containing 1-4 heteroatoms selected from N, O, and S, substituted with 0-3 R16;

    R6, at each occurrence, is independently selected from C1-6 alkyl, C2-8 alkenyl, C2-8 alkynyl, (CH2)rC3-6 cycloalkyl, (CF2)rCF3, CN, (CH2)rNR6aR6a, (CH2)qOH, (CH2)qOR6b, (CH2)qSH, (CH2)qSR6b, (CH2)rC(O)OH, (CH2)rC(O)R6b, (CH2)rC(O)NR6aR6a, (CH2)qNR6dC(O)R6a, (CH2)rC(O)OR6b, (CH2)qOC(O)R6b, (CH2)rS(O)pR6b, (CH2)rS(O)2NR6aR6a, (CH2)rNR6dS(O)2R6b, and (CH2)tphenyl substituted with 0-3 R6c;

    R6a, at each occurrence, is independently selected from H, C1-6 alkyl, C3-6 cycloalkyl, and phenyl substituted with 0-3 R6c;

    R6b, at each occurrence, is independently selected from C1-6 alkyl, C3-6 cycloalkyl, and phenyl substituted with 0-3 R6c;

    R6c, at each occurrence, is independently selected from C1-6 alkyl, C3-6 cycloalkyl, Cl, F, Br, I, CN, NO2, (CF2)rCF3, (CH2)rOC1-5 alkyl, (CH2)rOH, (CH2)rSC1-5 alkyl, and (CH2)rNR6dR6d;

    R6d, at each occurrence, is independently selected from H, C16 alkyl, and C3-6 cycloalkyl;

    R7, at each occurrence, is independently selected from H, C1-6 alkyl, C2-8 alkenyl, C2-8 alkynyl, (CH2)qOH, (CH2)qSH, (CH2)qOR7d, (CH2)qSR7d, (CH2)qNR7aR7a, (CH2)rC(O)OH, (CH2)rC(O)R7b, (CH2)rC(O)NR7aR7a, (CH2)qNR7aC(O)R7a, (CH2)qNR7aC(O)H, (CH2)rC(O)OR7b, (CH2)qOC(O)R7b, (CH2)qS(O)pR7b, (CH2)qS(O)2NR7aR7a, (CH2)qNR7aS(O)2R7b, C1-6 haloalkyl, a (CH2)r

    C3-6 carbocyclic residue substituted with 0-3 R7c, and a (CH2)r-5-10 membered heterocyclic system containing 1-4 heteroatoms selected from N, O, and S, substituted with 0-2 R7c;

    R7a, at each occurrence, is independently selected from H, C1-6 alkyl, C2-8 alkenyl, C2-8 alkynyl, a (CH2)r

    C3-6 carbocyclic residue substituted with 0-5 R7e, and a (CH2)r-5-10 membered heterocyclic system containing 1-4 heteroatoms selected from N, O, and S, substituted with 0-3 R7e;

    R7b, at each occurrence, is independently selected from C1-6 alkyl, C2-8 alkenyl, C2-8 alkynyl, a (CH2)r

    C3-6 carbocyclic residue substituted with 0-2 R7e, and a (CH2)r-5-6 membered heterocyclic system containing 1-4 heteroatoms selected from N, O, and S, substituted with 0-3 R7e;

    R7c, at each occurrence, is independently selected from C1-6 alkyl, C2-8 alkenyl, C2-8 alkynyl, (CH2)rC3-6 cycloalkyl, Cl, Br, I, F, (CF2)rCF3, NO2, CN, (CH2)rNR7fR7f, (CH2)rOH, (CH2)rOC1-4 alkyl, (CH2)rSC1-4 alkyl, (CH2)rC(O)OH, (CH2)rC(O)R7b, (CH2)rC(O)NR7fR7f, (CH2)rNR7fC(O)R7a, (CH2)rC(O)OC1-4 alkyl, (CH2)rOC(O)R7b, (CH2)rC(═

    NR7f)NR7fR7f, (CH2)rS(O)pR7b, (CH2)rNHC(═

    NR7f)NR7fR7f, (CH2)rS(O)2NR7fR7f, (CH2)rNR7fS(O)2R7b, and (CH2)rphenyl substituted with 0-3 R7e;

    R7d, at each occurrence, is independently selected from C1-6 alkyl substituted with 0-3 R7e, alkenyl, alkynyl, and a C3-6 carbocyclic residue substituted with 0-3 R7c;

    R7e, at each occurrence, is independently selected from C1-6 alkyl, C2-8 alkenyl, C2-8 alkynyl, C3-6 cycloalkyl, Cl, F, Br, I, CN, NO2, (CF2)rCF3, (CH2)rOC1-5 alkyl, OH, SH, (CH2)rSC1-5 alkyl, (CH2)rNR7fR7f, and (CH2)rphenyl;

    R7f, at each occurrence, is independently selected from H, C1-6 alkyl, and C3-6 cycloalkyl;

    R8 is selected from H, C1-6 alkyl, C2-8 alkenyl, C2-8 alkynyl, (CH2)rC3-6 cycloalkyl, (CF2)rCF3, (CH2)rN(R18a)R18b), (CH2)rOH, (CH2)rOR19, (CH2)rSH, (CH2)rSR19, (CH2)rC(O)OH, (CH2)rC(O)R19, (CH2)rC(O)N(R18a)R18b, (CH2)rN(R18c)C(O)R19, (CH2)rC(O)OR19, (CH2)rOC(O)R19, (CH2)rS(O)R19, (CH2)rS(O)2R19, (CH2)rS(O)2N(R18a)R18b, (CH2)rN(R18c)S(O)2R19, a (C(R8a)(R8b))r

    C3-10 carbocyclic residue substituted with 0-5 R17, and a (C(R8a)(R8b))r-5-10 membered heterocyclic system containing 1-4 heteroatoms selected from N, O, and S, substituted with 0-3 R17;

    R8a and R8b, at each occurrence, are independently selected from H, C1-6 alkyl, (CH2)rC3-6 cycloalkyl, and (CH2)rphenyl substituted with 0-3 R18;

    R9 is selected from H, C1-6 alkyl, C2-8 alkenyl, C2-8 alkynyl, (CH2)rC3-6 cycloalkyl, (CF2)rCF3, (CH2)qN(R18a)R18b), (CH2)qOH, (CH2)qOR19, (CH2)qSH, (CH2)qSR19, (CH2)qC(O)OH, (CH2)qC(O)R19, (CH2)qC(O)N(R18a)R18b, (CH2)qN(R18c)C(O)R19, (CH2)qC(O)OR19, (CH2)qOC(O)R19, (CH2)qS(O)R19, (CH2)qS(O)2R19, (CH2)qs(O)2N(R18a)R18b, (CH2)qN(R18c)S(O)2R19, a (C(R8a)(R8b))r

    C3-10 carbocyclic residue substituted with 0-5 R17, and a (C(R8a)(R8b))r-5-10 membered heterocyclic system containing 1-4 heteroatoms selected from N, O, and S, substituted with 0-3 R17;

    alternatively, R8 and R9 taken together are selected from ═

    O, ═

    S, ═

    NR9a;

    R9a is selected from H, C1-6 alkyl, C2-8 alkenyl, C2-8 alkynyl, (CH2)rC3-6 cycloalkyl, (CH2)rOH, (CH2)rOC1-6 alkyl, (CH2)rC(O)R19, (CH2)rC(O)N(R18a)R18b, (CH2)rC(O)OR19, (CH2)rS(O)2R19, (CH2)rS(O)2N(R18a)R18b, and (CH2)rphenyl substituted with 0-3 R17;

    R9b, at each occurrence are independently selected from H, C1-6 alkyl, C2-8 alkenyl, C2-8 alkynyl, (CH2)rC3-6 cycloalkyl, (CF2)rCF3, (CH2)rN(R18a)R18b, (CH2)rOH, (CH2)rOR19, (CH2)rSH, (CH2)rSR19, (CH2)rC(O)OH, (CH2)rC(O)R19, (CH2)rC(O)N(R18a)R18b, (CH2)rN(R18c)C(O)R19, (CH2)rC(O)OR19, (CH2)rOC(O)R19, (CH2)rS(O)R19, (CH2)rS(O)2R19, (CH2)rS(O)2N(R18a)R18b, (CH2)rN(R18c)S(O)2R19, and (CH2)rphenyl substituted with 0-3 R17;

    R10, at each occurrence, is independently selected from H, C1-6 alkyl, C2-8 alkenyl, C2-8 alkynyl, (CH2)rC3-6 cycloalkyl, (CF2)rCF3, CN, (CH2)rNR10aR10a, (CH2)rOH, (CH2)rOR10b, (CH2)rSH, (CH2)rSR10b, (CH2)rC(O)OH, (CH2)rC(O)R10b, (CH2)rC(O)NR10aR10a, (CH2)rNR10dC(O)R10a, (CH2)rC(O)OR10b, (CH2)rOC(O)R10b, (CH2)rS(O)pR10b, (CH2)rS(O)2NR10aR10a, (CH2)rNR10dS(O)2R10b, and (CH2)tphenyl substituted with 0-3 R10c;

    R10a, at each occurrence, is independently selected from H, C1-6 alkyl, C3-6 cycloalkyl, and phenyl substituted with 0-3 R10c;

    R10b, at each occurrence, is independently selected from C1-6 alkyl, C3-6 cycloalkyl, and phenyl substituted with 0-3 R10c;

    R10c, at each occurrence, is independently selected from C1-6 alkyl, C3-6 cycloalkyl, Cl, F, Br, I, CN, NO2, (CF2)rCF3, (CH2)rOC1-5 alkyl, (CH2)rOH, (CH2)rSC1-5 alkyl, and (CH2)rNR10dR10d;

    R10d, at each occurrence, is independently selected from H, C1-6 alkyl, and C3-10 cycloalkyl;

    R11a and R12a, at each occurrence are independently selected from H, C1-6 alkyl, C2-8 alkenyl, C2-8 alkynyl, (CH2)rC3-6 cycloalkyl, (CF2)rCF3, (CH2)rN(R18a)R18b, (CH2)rOH, (CH2)rOR19, (CH2)rSH, (CH2)rSR19, (CH2)rC(O)OH, (CH2)rC(O)R19, (CH2)rC(O)N(R18a)R18b, (CH2)rN(R18c)C(O)R19, (CH2)rC(O)OR19, (CH2)rOC(O)R19, (CH2)rS(O)R19, (CH2)rS(O)2R19, (CH2)rS(O)2N(R18a)R18b, (CH2)rN(R18c)S(O)2R19, and (CH2)rphenyl substituted with 0-3 R18;

    R11b, R12b, R14a and R14b at each occurrence are independently selected from H, C1-6 alkyl, C2-8 alkenyl, C2-8 alkynyl, (CH2)rC3-6 cycloalkyl, (CF2)rCF3, (CH2)qN(R18a)R18b, (CH2)qOH, (CH2)qOR19, (CH2)qSH, (CH2)qSR19, (CH2)rC(O)OH, (CH2)rC(O)R19, (CH2)rC(O)N(R18a)R18b, (CH2)qN(R18c)C(O)R19, (CH2)rC(O)OR19, (CH2)qOC(O)R19, (CH2)qS(O)R19, (CH2)qS(O)2R19, (CH2)qS(O)2N(R18a)R18b, (CH2)qN(R18c)S(O)2R19, and (CH2)rphenyl substituted with 0-3 R18;

    alternatively, R11a and R11b taken together are selected from ═

    O, or ═

    NOH, or alternatively, R12a and R12b taken together are selected from ═

    O, or ═

    NOH;

    R15, at each occurrence, is independently selected from C1-8 alkyl, (CH2)rC3-6 cycloalkyl, Cl, Br, I, F, NO2, CN, (CHR′

    )rNR15aR15a, (CHR′

    )rOH, (CHR′

    )rO(CHR′

    )rR15d, (CHR′

    )rSH, (CHR′

    )rC(O)H, (CHR′

    )rS(CHR′

    )rR15d, (CHR′

    )rC(O)OH, (CHR′

    )rC(O)(CHR′

    )rR15b, (CHR′

    )rC(O)NR15aR15a, (CHR′

    )rNR15fC(O)(CHR )rR15b, (CHR′

    )rNR15fC(O)NR15fR15f, (CHR′

    )rC(O)O(CHR′

    )rR15d, (CHR′

    )rOC(O)(CHR′

    )rR15b, (CHR′

    )rC(═

    NR15f)NR15aR15a, (CHR′

    )rNHC(═

    NR15f)NR15fR15f, (CHR′

    )rS(O)p(CHR′

    )rR15b, (CHR′

    )rS(O)2NR15aR15a, (CHR′

    )rNR15fS(O)2(CHR′

    )rR15b, C1-6 haloalkyl, C2-8 alkenyl substituted with 0-3 R′

    , C2-8 alkynyl substituted with 0-3 R′

    , (CHR′

    )rphenyl substituted with 0-3 R15e, and a (CH2)r-5-10 membered heterocyclic system containing 1-4 heteroatoms selected from N, O, and S, substituted with 0-2 R15e;

    R′

    , at each occurrence, is independently selected from H, C1-6 alkyl, C2-8 alkenyl, C2-8 alkynyl, (CH2)rC3-6 cycloalkyl, and (CH2)rphenyl substituted with R15e;

    R15a, at each occurrence, are selected from H, C1-6 alkyl, C2-8 alkenyl, C2-8 alkynyl, a (CH2)r

    C3-6 carbocyclic residue substituted with 0-5 R15e, and a (CH2)r-5-10 membered heterocyclic system containing 1-4 heteroatoms selected from N, O, and S, substituted with 0-2 R15 e;

    R15b, at each occurrence, is independently selected from C1-6 alkyl, C2-8 alkenyl, C2-8 alkynyl, a (CH2)r

    C3-6 carbocyclic residue substituted with 0-3 R15e, and (CH2)r-5-6 membered heterocyclic system containing 1-4 heteroatoms selected from N, O, and S, substituted with 0-2 R15e;

    R15d, at each occurrence, is independently selected from C2-8 alkenyl, C2-8 alkynyl, C1-6 alkyl substituted with 0-3 R15e, a (CH2)r

    C3-6 carbocyclic residue substituted with 0-3 R15e, and a (CH2)r5-6 membered heterocyclic system containing 1-4 heteroatoms selected from N, O, and S, substituted with 0-3 R15e;

    R15e, at each occurrence, is independently selected from C1-6 alkyl, C2-8 alkenyl, C2-8 alkynyl, (CH2)rC3-6 cycloalkyl, Cl, F, Br, I, CN, NO2, (CF2)rCF3, (CH2)rOC1-5 alkyl, OH, SH, (CH2)rSC1-5 alkyl, (CH2)rNR15fR15f, and (CH2)rphenyl;

    R15f, at each occurrence, is independently selected from H, C1-6 alkyl, C3-6 cycloalkyl, and phenyl;

    R16, at each occurrence, is independently selected from C1-8 alkyl, C2-8 alkenyl, C2-8 alkynyl, (CH2)rC3-6 cycloalkyl, Cl, Br, I, F, NO2, CN, (CHR′

    )rNR16aR16a, (CHR′

    )rOH, (CHR′

    )rO(CHR′

    )rR16d, (CHR′

    )rSH, (CHR′

    )rC(O)H, (CHR′

    )rS(CHR′

    )rR16d, (CHR′

    )rC(O)OH, (CHR′

    )rC(O)(CHR′

    )rR16b, (CHR′

    )rC(O)NR16aR16a, (CHR′

    )rNR16fC(O)(CHR′

    )rR16b, (CHR′

    )rC(O)O(CHR′

    )rR16d, (CHR′

    )rOC(O)(CHR′

    )rR16b, (CHR′

    )rC(═

    NR16f)NR16aR16a, (CHR′

    )rNHC(═

    NR16f)NR16fR16f, (CHR′

    )rS(O)p(CHR′

    )rR16b, (CHR′

    )rS(O)2NR16aR16a, (CHR′

    )rNR16fS(O)2(CHR′

    )rR16b, C1-6 haloalkyl, C2-8 alkenyl substituted with 0-3 R′

    , C2-8 alkynyl substituted with 0-3 R′

    , and (CHR′

    )rphenyl substituted with 0-3 R16e;

    R16a, at each occurrence, is independently selected from H, C1-6 alkyl, C2-8 alkenyl, C2-8 alkynyl, a (CH2)r

    C3-6 carbocyclic residue substituted with 0-5 R16e, and a (CH2)r-5-10 membered heterocyclic system containing 1-4 heteroatoms selected from N, O, and S, substituted with 0-2 R16e;

    R16b, at each occurrence, is independently selected from C1-6 alkyl, C2-8 alkenyl, C2-8 alkynyl, a (CH2)rC3-6 carbocyclic residue substituted with 0-3 R16e, and a (CH2)r-5-6 membered heterocyclic system containing 1-4 heteroatoms selected from N, O, and S, substituted with 0-2 R16e;

    R16d, at each ocurrence, is independently selected from C2-8 alkenyl, C2-8 alkynyl, C1-6 alkyl substituted with 0-3 R16e, a (CH2)r

    C3-6 carbocyclic residue substituted with 0-3 R16e, and a (CH2)r-5-6 membered heterocyclic system containing 1-4 heteroatoms selected from N, O, and S, substituted with 0-3 R16e;

    R16e, at each occurrence, is independently selected from C1-6 alkyl, C2-8 alkenyl, C2-8 alkynyl, (CH2)rC3-6 cycloalkyl, Cl, F, Br, I, CN, NO2, (CF2)rCF3, (CH2)rOC1-5 alkyl, OH, SH, (CH2)rSC1-5 alkyl, (CH2)rNR16fR16f, and (CH2)rphenyl;

    R16f, at each occurrence, is independently selected from H, C1-5 alkyl, and C3-6 cycloalkyl, and phenyl;

    R17 at each occurrence is independently selected from ═

    O, C1-6 alkyl, (CH2)rC3-6 cycloalkyl, Cl, F, Br, I, CN, NO2, (CH2)rOR19, (CH2)rOH, (CH2)rSR19, (CH2)rS(O)R19, (CH2)rS(O)2R19, (CH2)rS(O)2N(R18a)R18b, (CH2)rN(R18c)C(O)R19(CH2)rN(R18c)S(O)2R19, (CH2)rC(O)OH, (CH2)rC(O)OR19, (CH2)rC(O)N(R18a)R18b, (CH2)rN(R18c)C(O)N(R18a)R18b, (CH2)rN(R18c)C(O)OR19, (CH2)rOC(O)N(R18a)R18b, (CH2)rN(R18a)R18b, C1-6 haloalkyl, C2-8 alkenyl substituted with 0-3 R17a, C2-8 alkynyl substituted with 0-3 R17a, (CH(R17a))rphenyl substituted with 1-3 R18, and (CH(R17a))r-5-10 membered heterocyclic system containing 1-4 heteroatoms selected from N, O, and S, substituted with 0-2 R18;

    R17a at each occurrence is independently selected from H, C1-6 alkyl, C2-8 alkenyl, C2-8 alkynyl, (CH2)rC3-6 cycloalkyl, and (CH2)rphenyl substituted with 0-3 R18;

    R18 at each occurrence is independently selected from C1-6 alkyl, C3-6 cycloalkyl, Cl, F, Br, I, CN, NO2, (CF2)rCF3, (CH2)rOC1-5 alkyl, (CH2)rOH, (CH2)rSC1-5 alkyl, (CH2)rS(O)C1-5 alkyl, (CH2)rS(O)2C1-5 alkyl, (CH2)rS(O)2N(R18a)R18b, (CH2)rN(R18c)C(O)C1-5 alkyl, (CH2)rN(R18c)S(O)2C1-5 alkyl, (CH2)rC(O)N(R18a)R18b, (CH2)rC(O)OC1-5 alkyl, (CH2)rC(O)C1-5 alkyl, and (CH2)rN(R18a)R18b;

    R18a, R18b, and R18c at each occurrence are independently selected from H, C1-6 alkyl, and C3-6 cycloalkyl;

    R19 at each occurrence is independently selected from C1-6 alkyl, C3-6 cycloalkyl, and phenyl substituted with 0-3 R18;

    alternatively, R18a and R18b along with the nitrogen to which both are attached form a pyrrolidine, piperidine, piperazine or morpholine ring;

    R25 at each occurrence is independently selected from H, C1-6 alkyl, C2-8 alkenyl, C2-8 alkynyl, (CH2)rC3-6 cycloalkyl, (CH2)rC(O)R19, (CH2)rC(O)N(R18a)R18b, (CH2)rC(O)OR19, (CH2)rS(O)2R19, (CH2)rS(O)2N(R18a)R18b, and (CH2)rphenyl substituted with 0-3 R17;

    i is selected from 0, 1, and 2;

    m is selected from 0, 1, and 2;

    s is selected from 0 and 1;

    with the proviso;

    m+s is selected from 0, 1, and 2;

    v is selected from 0, 1, 2, and 3;

    with the proviso;

    that the total number of atoms between the nitrogen of which R′

    is attached and the fused ring B is less than or equal to 4;

    r is selected from 0, 1, 2, 3, 4, and 5;

    t is selected from 0, 1, 2, 3, 4, and 5;

    q is selected from 1, 2, 3, 4, and 5;

    p is selected from 1, 2, and 3;

    u is selected from 0, 1 and, 2.

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