gap('LoadPackage("QPA");')

import tempfile as _tf, os as _os
_gap_code = r"""
DeclareOperation("ARQuiver", [IsList]);

InstallMethod(ARQuiver, "for an algebra and bound", [IsList], 0, function(LIST)
    local A, L, N, PI, bound, dim, f, h, inj, injA, j;
    A := LIST[1];
    bound := LIST[2];
    injA := IndecInjectiveModules(A);
    L := [];
    for inj in injA do
        dim := Dimension(inj);
        for j in [0..dim-1] do
            if j = 0 then
                f := IdentityMapping(inj);
            else
                f := RadicalOfModuleInclusion(inj);
                N := Source(f);
                h := 1;
                while h < j do
                    f := RadicalOfModuleInclusion(N);
                    N := Source(f);
                    h := h + 1;
                od;
            fi;
            Add(L, Source(f));
        od;
    od;
    PI := Filtered(L, x -> IsProjectiveModule(x) and IsInjectiveModule(x));
    return [PI, L];
end);

DeclareOperation("TiltingModulesProjDim1",[IsList]);

InstallMethod(TiltingModulesProjDim1, "for a representation of a quiver", [IsList],0,function(LIST)
    local A, L, LL, LL2, W, r, subsets1, subsets2, u;
    u := LIST[1];
    A := NakayamaAlgebra(GF(3),u);
    L := ARQuiver([A,1000])[2];
    LL := Filtered(L,x->(IsProjectiveModule(x)=false or IsInjectiveModule(x)=false));
    LL2 := Filtered(LL,x->ProjDimensionOfModule(x,100)<=1);
    r := Size(SimpleModules(A))-(Size(L)-Size(LL));
    subsets1 := Combinations([1..Length(LL2)],r);
    subsets2 := List(subsets1,x->LL2{x});
    W := Filtered(subsets2,x->N_RigidModule(DirectSumOfQPAModules(x),1)=true);

    return([u,Size(W)]);
end);
"""
with _tf.NamedTemporaryFile(mode="w", suffix=".g", delete=False, dir="/tmp") as _f:
    _f.write('LoadPackage("QPA");;\n')
    _f.write(_gap_code)
    _tmp = _f.name
gap.eval('Read("' + _tmp + '");')
_os.unlink(_tmp)

def kupisch(D):
    DR = D.reverse()
    H = DR.heights()
    return [1 + H[i] for i, s in enumerate(DR) if s == 0] + [1]

def statistic(D):
    K = kupisch(D)
    result = gap.TiltingModulesProjDim1([K])
    return ZZ(result[2])  # GAP returns [kupisch, count], extract count