SetIgnorePrompt(true);

// ---------- Contribution  ----------
function Contribution(r, LL)
    QQ := Rationals();
    Poly<t> := PolynomialRing(QQ);
    L := [ Integers() | i : i in LL ];
    n := #LL;

    pi := &*[(1 - t^i) : i in L];
    A  := Poly!((1 - t^r) / (1 - t));
    G  := GCD(pi, A);  dG := Degree(G);
    B  := Poly!(A div G);  dB := Degree(B);

    // Avoid shadowing 'a' from outside; we only need 'be' anyway.
    uu, be, cc := XGCD(pi, B);  dbe := Degree(be);

    R<[v]> := PolynomialRing(QQ, dG + 2);
    va := R.(dG + 2);  // <-- fix from Name(R, dG+2)

    bnew := &+[ Coefficient(be, i)*va^i : i in [0..dbe] ];
    RR   := &+[ v[i]*va^(i-1)          : i in [1..dG+1] ];
    Bnew := &+[ Coefficient(B,  i)*va^i : i in [0..dB ] ];
    AA   := bnew - RR*Bnew;

    S := [Coefficient(AA, va, 0)] cat [Coefficient(AA, va, r - i) : i in [1..r-1]];
    empty := [];
    for a in L do
        dd := GCD(a, r);  tt := r div dd;
        relations := empty cat [ &+[ S[dd*l + i] : l in [0..tt-1] ] : i in [1..dd] ];
        empty := relations;
    end for;

    Mat := Matrix(QQ, [ [ Coefficient(empty[i], v[j], 1) : j in [1..dG+1] ] : i in [1..#empty] ]);
    zero := [ 0 : i in [1..dG+2] ];
    V := -Vector(QQ, [ Evaluate(empty[i], zero) : i in [1..#empty] ]);

    MF := Transpose(Mat);
    x, y, z := IsConsistent(MF, V);
    yy := &+[ y[i+1] * va^i : i in [0..dG] ];
    sigma := bnew - yy*Bnew;

    Sigma := [ QQ!Coefficient(sigma, va, 0) ] cat [ QQ!Coefficient(sigma, va, i) : i in [1..r-1] ];
    return Sigma;
end function;

// ---------- Helpers using Contribution ----------
function MakeCon(a, b, c)
    L1 := (a eq 1) select [0,0] else Contribution(a, [b,c]);
    L2 := (b eq 1) select [0,0] else Contribution(b, [a,c]);
    L3 := (c eq 1) select [0,0] else Contribution(c, [a,b]);
    return [
        ((a eq 1) select 0 else L1[(n mod a)+1] - L1[1]) +
        ((b eq 1) select 0 else L2[(n mod b)+1] - L2[1]) +
        ((c eq 1) select 0 else L3[(n mod c)+1] - L3[1])
        : n in [0..a*b*c-1]
    ];
end function;

function Con(n, a, b, c)
    if a eq 1 then L1 := [0,0]; else L1 := Contribution(a, [b,c]); end if;
    if b eq 1 then L2 := [0,0]; else L2 := Contribution(b, [a,c]); end if;
    if c eq 1 then L3 := [0,0]; else L3 := Contribution(c, [a,b]); end if;
    l1 := n mod a;  c1 := L1[l1+1] - L1[1];
    l2 := n mod b;  c2 := L2[l2+1] - L2[1];
    l3 := n mod c;  c3 := L3[l3+1] - L3[1];
    return c1 + c2 + c3;
end function;

// ---------- Simple utility ----------
function LargestElement(vec)
    maxElement := vec[1];
    for i in [2..#vec] do
        if vec[i] ge maxElement then
            maxElement := vec[i];
        end if;
    end for;
    return maxElement;
end function;

// ---------- Eff (unchanged logic; small guard already present) ----------

function Eff(a, b, c)
    Q := Rationals();
    P<x,y,z,t1,t2> := PolynomialRing(Q, 5);
    x := 1/(a*b*c); y := 0; z := -1;
    f := -(a+b+c);  g := 1;
    h1 := func<m,n | 1 + 1/2 * ((m^2 - m*f)*x + (2*m*n - (m*g + f*n))*y + (n^2 - n*g)*z)>;
    sum := a+b+c;
    pro := a*b*c;

    startk := 1;
    startn := 1;

    L := MakeCon(a,b,c);
    max := LargestElement(L);

    if Sqrt(pro) - sum le 0 then
        MaxN := 5000000;
    else
        MaxN := Floor((0 + max) * (2*pro / (Sqrt(pro) - sum)));
    end if;

    for m in [1..MaxN] do
        k := Floor(m/Sqrt(pro) + 1);
        if h1(m, -k) + L[m mod pro + 1] eq 1 and m^2/(a*b*c) - k^2 le 0 then
            startk := k;  startn := m;
            break m;
        end if;
    end for;

    return [startn, startk];
end function;

// -The following function help us to identify potential deficiency i degrees and multiplicities----
// The idea is to find the pairs [k, n] such that \Chi(\Oh(nH-kE))=1-i and (nH-kE)^2\leq 0.
// Output here is 1) the list of multiplicities and 2) the list of degrees.

function SEff(a, b, c, i)
    Q := Rationals();
    P<x,y,z,t1,t2> := PolynomialRing(Q, 5);
    x := 1/(a*b*c); y := 0; z := -1;
    f := -(a+b+c);  g := 1;
    h1 := func<n,k | 1 + 1/2 * ((n^2 - n*f)*x + (2*n*k - (n*g + f*k))*y + (k^2 - k*g)*z)>;
    sum := a+b+c;
    pro := a*b*c;

    startk := [];
    startn := [];

    L := MakeCon(a,b,c);
    max := LargestElement(L);
    den := Sqrt(pro) - sum;

    if den le 0 then
        // Unsafe region — nothing reliable to search
        return startk, startn;
    end if;

    MaxN := Floor((i + max) * (2*pro / den));
    if MaxN lt 1 then
        return startk, startn;
    end if;

    for n in [1..MaxN] do 
        k := Floor(n/Sqrt(pro) + 1);
        if h1(n, -k) + L[n mod pro + 1] eq 1 - i and n^2/(a*b*c) - k^2 le 0 then
            Append(~startk, k);
            Append(~startn, n);
        end if;
    end for;

    return startk, startn;
end function;

// Prepare for the function DesiredCurves(a, b, c, def_i) that goes through the list of n and k, and checks whethere there is a curve that has degree n and pass through the blowup Points //with multiplicity k. 

function ExponentTriples(N, wa, wb, wc)
    triples := [];
    maxA := N div wa;
    for aExp in [0..maxA] do
        rem1 := N - wa*aExp;
        maxB := rem1 div wb;
        for bExp in [0..maxB] do
            rem2 := rem1 - wb*bExp;
            if rem2 mod wc eq 0 then
                cExp := rem2 div wc;
                Append(~triples, <aExp, bExp, cExp>);
            end if;
        end for;
    end for;
    return triples;
end function;

function RowTriples(d)
    rows := [];
    for u in [0..d-1] do
        for v in [0..d-1-u] do
            w := d - 1 - u - v;
            Append(~rows, <u, v, w>);
        end for;
    end for;
    return rows;
end function;

// ---------- Memory-safe DesiredCurves ----------
procedure DesiredCurves(a, b, c, def_i)

    printf "WPS: P%o\n------------------\n", [a,b,c];

    Pair := Eff(a,b,c);
    if &*Pair ne 1 then
        printf "Output of Eff function: %o\n--------------------\n", Pair;
        printf "================================================= i=%o\n", def_i;
        return;
    end if;

    M, N := SEff(a,b,c,def_i);
    if #N eq 0 then
        printf "================================================= i=%o\n", def_i;
        return;
    end if;

    // Guard to avoid gigantic dense matrices (entries count r*n)
    // Tune as you like; 2e6 entries is typically safe on modest RAM.
    LIMIT := 2000000;

    for idx in [1..#N] do
        d := M[idx];
        Ndeg := N[idx];

        rowTriples := RowTriples(d);
        r := #rowTriples;

        cols := ExponentTriples(Ndeg, a, b, c);
        n := #cols;

        if r*n gt LIMIT then
            // Skip instead of risking a crash
            printf "Skipping (k=%o, n=%o): r*n=%o exceeds %o\n", d, Ndeg, r*n, LIMIT;
            continue;
        end if;

        // Build integer matrix X (r x n) with entries:
        // X[(u,v,w),(A,B,C)] = binom(A,u) * binom(B,v) * binom(C,w) * u! v! w!
        X := ZeroMatrix(Integers(), r, n);
        rowFactors := [ Factorial(rowTriples[j][1]) * Factorial(rowTriples[j][2]) * Factorial(rowTriples[j][3]) : j in [1..r] ];

        for j in [1..r] do
            u := rowTriples[j][1];
            v := rowTriples[j][2];
            w := rowTriples[j][3];
            uf := rowFactors[j];
            for col in [1..n] do
                Aexp := cols[col][1];
                Bexp := cols[col][2];
                Cexp := cols[col][3];
                X[j, col] := uf * Binomial(Aexp, u) * Binomial(Bexp, v) * Binomial(Cexp, w);
            end for;
        end for;

        // Solve XT * vec = 0 ⇒ Nullspace(XT) over Q
        XT := Transpose(X);
        XTrat := ChangeRing(XT, Rationals());
        K := Nullspace(XTrat);

        if Dimension(K) eq 1 then
            printf "Desired Curve may appear for Deficiency: %o, k=%o, n=%o\n", def_i, d, Ndeg;
        end if;
    end for;

    printf "================================================= i=%o\n", def_i;
end procedure;

//The following vector gives all triples where X(a,b,c) do not contain negative curves of deficiency 0.
// Number of distinct elements: 3771
L := [<5,33,49>,<5,37,61>,<5,41,68>,<5,48,79>,<5,56,83>,<5,56,93>,<5,59,97>,<7,11,20>,<7,13,16>,<7,13,23>,<7,13,24>,<7,15,19>,<7,16,17>,<7,16,29>,<7,16,31>,<7,17,33>,<7,18,19>,<7,19,34>,<7,20,23>,<7,20,37>,<7,22,39>,<7,23,24>,<7,23,43>,<7,23,45>,<7,24,29>,<7,24,43>,<7,24,47>,<7,24,85>,<7,25,26>,<7,25,27>,<7,25,44>,<7,25,48>,<7,25,51>,<7,27,52>,<7,29,31>,<7,29,33>,<7,29,53>,<7,29,54>,<7,30,31>,<7,30,59>,<7,31,36>,<7,31,57>,<7,31,61>,<7,32,33>,<7,32,41>,<7,32,65>,<7,33,62>,<7,34,37>,<7,34,65>,<7,36,67>,<7,37,38>,<7,37,45>,<7,37,66>,<7,37,71>,<7,37,73>,<7,38,43>,<7,38,71>,<7,38,75>,<7,39,40>,<7,39,41>,<7,39,76>,<7,39,79>,<7,41,44>,<7,41,51>,<7,41,72>,<7,41,73>,<7,41,79>,<7,41,80>,<7,43,45>,<7,43,47>,<7,43,54>,<7,43,81>,<7,43,82>,<7,44,45>,<7,44,85>,<7,44,87>,<7,45,82>,<7,45,89>,<7,46,47>,<7,46,83>,<7,46,93>,<7,47,50>,<7,47,53>,<7,47,60>,<7,47,83>,<7,47,88>,<7,47,90>,<7,50,61>,<7,50,89>,<7,51,52>,<7,51,59>,<7,51,92>,<7,51,94>,<7,52,57>,<7,52,99>,<7,53,54>,<7,53,55>,<7,53,62>,<7,53,93>,<7,53,97>,<7,53,100>,<7,54,67>,<7,54,95>,<7,54,97>,<7,55,58>,<7,57,59>,<7,57,61>,<7,58,59>,<7,58,73>,<7,59,64>,<7,59,71>,<7,60,61>,<7,61,64>,<7,61,67>,<7,61,74>,<7,62,65>,<7,62,79>,<7,65,69>,<7,65,73>,<7,66,71>,<7,67,69>,<7,67,76>,<7,67,83>,<7,68,71>,<7,69,79>,<7,69,86>,<7,71,73>,<7,71,75>,<7,71,82>,<7,71,89>,<7,73,78>,<7,73,85>,<7,73,92>,<7,74,83>,<7,76,79>,<7,76,81>,<7,76,93>,<7,78,89>,<7,79,83>,<7,80,99>,<7,81,83>,<7,82,85>,<7,82,95>,<7,83,86>,<7,83,88>,<7,83,93>,<7,83,100>,<7,85,87>,<7,85,89>,<7,85,96>,<7,87,92>,<7,89,92>,<7,89,95>,<7,93,97>,<7,94,99>,<7,95,97>,<7,97,100>,<8,15,43>,<9,10,13>,<9,10,23>,<9,11,17>,<9,11,28>,<9,13,16>,<9,13,55>,<9,16,19>,<9,16,67>,<9,17,23>,<9,17,40>,<9,17,74>,<9,19,22>,<9,19,31>,<9,19,50>,<9,19,79>,<9,22,25>,<9,22,91>,<9,23,29>,<9,23,38>,<9,23,52>,<9,23,61>,<9,23,98>,<9,25,28>,<9,25,37>,<9,25,62>,<9,26,41>,<9,26,67>,<9,28,31>,<9,29,35>,<9,29,44>,<9,29,73>,<9,31,34>,<9,31,43>,<9,31,52>,<9,31,74>,<9,31,83>,<9,32,47>,<9,34,37>,<9,34,55>,<9,34,89>,<9,35,41>,<9,35,59>,<9,35,94>,<9,37,40>,<9,37,49>,<9,37,58>,<9,37,86>,<9,37,95>,<9,38,53>,<9,38,91>,<9,40,43>,<9,40,61>,<9,41,47>,<9,41,56>,<9,41,65>,<9,41,97>,<9,43,46>,<9,43,55>,<9,43,64>,<9,43,73>,<9,43,98>,<9,44,59>,<9,46,49>,<9,46,67>,<9,47,53>,<9,47,62>,<9,47,71>,<9,47,80>,<9,49,52>,<9,49,61>,<9,49,79>,<9,50,83>,<9,52,55>,<9,53,59>,<9,53,68>,<9,53,77>,<9,53,86>,<9,55,58>,<9,55,67>,<9,55,76>,<9,55,94>,<9,56,71>,<9,56,89>,<9,58,61>,<9,58,79>,<9,58,97>,<9,59,65>,<9,59,74>,<9,59,92>,<9,61,64>,<9,61,73>,<9,61,82>,<9,61,91>,<9,61,100>,<9,62,77>,<9,62,95>,<9,64,67>,<9,64,85>,<9,65,71>,<9,65,89>,<9,65,98>,<9,67,70>,<9,67,79>,<9,67,88>,<9,67,97>,<9,68,83>,<9,70,73>,<9,71,77>,<9,71,86>,<9,71,95>,<9,73,76>,<9,73,85>,<9,73,94>,<9,74,89>,<9,76,79>,<9,76,97>,<9,77,83>,<9,77,92>,<9,79,82>,<9,79,91>,<9,79,100>,<9,82,85>,<9,83,89>,<9,83,98>,<9,85,88>,<9,85,97>,<9,88,91>,<9,89,95>,<9,91,94>,<9,94,97>,<9,97,100>,<10,11,17>,<10,13,61>,<10,17,19>,<10,17,49>,<10,17,79>,<10,19,23>,<10,19,53>,<10,19,93>,<10,21,97>,<10,23,31>,<10,23,61>,<10,27,79>,<10,29,33>,<10,29,43>,<10,29,73>,<10,29,83>,<10,31,37>,<10,31,47>,<10,31,87>,<10,33,41>,<10,33,91>,<10,37,49>,<10,37,59>,<10,37,99>,<10,39,53>,<10,41,47>,<10,41,57>,<10,43,51>,<10,43,61>,<10,47,59>,<10,47,69>,<10,49,73>,<10,51,67>,<10,51,77>,<10,53,61>,<10,53,71>,<10,53,81>,<10,57,79>,<10,57,89>,<10,59,73>,<10,59,83>,<10,59,93>,<10,61,77>,<10,61,87>,<10,61,97>,<10,63,71>,<10,67,79>,<10,67,89>,<10,67,99>,<10,69,83>,<10,71,87>,<10,71,97>,<10,73,91>,<10,77,89>,<10,79,93>,<10,81,97>,<11,12,19>,<11,12,41>,<11,13,16>,<11,13,21>,<11,13,27>,<11,13,38>,<11,13,49>,<11,15,31>,<11,15,32>,<11,15,43>,<11,15,46>,<11,16,29>,<11,16,51>,<11,17,24>,<11,17,26>,<11,17,30>,<11,17,37>,<11,17,47>,<11,17,48>,<11,17,59>,<11,17,75>,<11,18,23>,<11,18,35>,<11,18,53>,<11,18,67>,<11,19,31>,<11,19,40>,<11,19,42>,<11,19,53>,<11,19,59>,<11,19,64>,<11,20,39>,<11,20,61>,<11,21,29>,<11,21,47>,<11,21,58>,<11,21,80>,<11,21,92>,<11,23,30>,<11,23,38>,<11,23,41>,<11,23,49>,<11,23,52>,<11,23,72>,<11,23,74>,<11,23,85>,<11,24,43>,<11,24,49>,<11,24,67>,<11,24,71>,<11,25,34>,<11,25,46>,<11,25,48>,<11,25,73>,<11,25,79>,<11,26,43>,<11,26,53>,<11,26,79>,<11,26,87>,<11,27,40>,<11,27,47>,<11,27,58>,<11,27,85>,<11,27,95>,<11,28,37>,<11,28,59>,<11,28,81>,<11,29,39>,<11,29,45>,<11,29,56>,<11,29,57>,<11,29,86>,<11,29,89>,<11,29,100>,<11,30,43>,<11,30,53>,<11,30,97>,<11,31,39>,<11,31,50>,<11,31,56>,<11,31,61>,<11,31,67>,<11,31,87>,<11,31,94>,<11,31,98>,<11,32,47>,<11,32,61>,<11,32,69>,<11,32,91>,<11,32,93>,<11,34,63>,<11,34,71>,<11,35,71>,<11,35,76>,<11,36,59>,<11,36,79>,<11,37,49>,<11,37,54>,<11,37,64>,<11,37,65>,<11,37,75>,<11,37,76>,<11,38,53>,<11,38,69>,<11,38,73>,<11,39,59>,<11,39,70>,<11,39,74>,<11,39,85>,<11,40,67>,<11,40,79>,<11,40,89>,<11,41,53>,<11,41,54>,<11,41,64>,<11,41,73>,<11,41,75>,<11,41,84>,<11,41,86>,<11,42,67>,<11,42,83>,<11,42,89>,<11,43,62>,<11,43,69>,<11,43,72>,<11,43,80>,<11,43,83>,<11,43,91>,<11,43,94>,<11,45,59>,<11,45,74>,<11,45,82>,<11,46,63>,<11,46,71>,<11,46,87>,<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9,59,94>,<49,59,96>,<49,61,78>,<49,61,89>,<49,61,100>,<49,62,83>,<49,64,71>,<49,64,73>,<49,64,99>,<49,65,72>,<49,65,79>,<49,65,86>,<49,66,73>,<49,67,68>,<49,67,81>,<49,68,93>,<49,69,83>,<49,69,86>,<49,71,75>,<49,71,78>,<49,71,99>,<49,71,100>,<49,72,79>,<49,73,80>,<49,73,94>,<49,74,83>,<49,74,89>,<49,76,97>,<49,78,85>,<49,79,80>,<49,79,86>,<49,79,93>,<49,79,97>,<49,79,100>,<49,80,87>,<49,80,99>,<49,81,95>,<49,83,97>,<49,85,87>,<49,85,92>,<49,85,96>,<49,86,93>,<49,87,94>,<49,87,100>,<49,92,99>,<49,93,100>,<50,53,77>,<50,59,61>,<50,61,69>,<50,61,73>,<50,67,81>,<50,73,89>,<50,77,83>,<50,79,91>,<50,79,97>,<50,81,83>,<50,87,91>,<50,93,97>,<51,52,59>,<51,52,71>,<51,53,86>,<51,55,74>,<51,55,91>,<51,56,59>,<51,56,67>,<51,58,89>,<51,58,97>,<51,59,64>,<51,59,74>,<51,59,89>,<51,59,92>,<51,61,64>,<51,61,67>,<51,61,83>,<51,61,100>,<51,65,76>,<51,67,77>,<51,67,92>,<51,71,77>,<51,71,83>,<51,71,94>,<51,73,76>,<51,73,83>,<51,76,91>,<51,82,89>,<51,82,95>,<51,83,92>,<51,89,100>,<52,53,75>,<52,55,69>,<52,55,93>,<52,59,75>,<52,61,89>,<52,63,79>,<52,63,97>,<52,67,79>,<52,67,85>,<52,69,79>,<52,69,89>,<52,71,77>,<52,73,81>,<52,75,83>,<52,77,85>,<52,77,89>,<52,77,97>,<52,79,93>,<52,81,95>,<52,81,97>,<52,83,89>,<52,83,95>,<53,54,61>,<53,55,62>,<53,55,78>,<53,55,84>,<53,56,61>,<53,56,69>,<53,56,73>,<53,56,83>,<53,57,64>,<53,57,71>,<53,58,71>,<53,58,89>,<53,59,64>,<53,59,69>,<53,59,80>,<53,59,85>,<53,61,75>,<53,61,78>,<53,61,89>,<53,61,95>,<53,61,100>,<53,63,71>,<53,63,100>,<53,64,91>,<53,65,86>,<53,65,97>,<53,66,85>,<53,67,100>,<53,68,77>,<53,68,81>,<53,69,89>,<53,70,83>,<53,71,81>,<53,71,86>,<53,71,96>,<53,72,79>,<53,73,85>,<53,73,89>,<53,73,90>,<53,73,98>,<53,75,82>,<53,77,86>,<53,77,97>,<53,79,87>,<53,79,98>,<53,80,91>,<53,82,93>,<53,82,95>,<53,85,94>,<53,85,97>,<53,87,100>,<53,89,99>,<53,89,100>,<54,55,97>,<54,59,73>,<54,67,79>,<54,73,83>,<54,79,95>,<54,85,97>,<55,56,71>,<55,56,79>,<55,57,64>,<55,57,73>,<55,57,92>,<55,57,94>,<55,58,63>,<55,59,73>,<55,59,96>,<55,61,82>,<55,61,89>,<55,63,73>,<55,63,82>,<55,64,81>,<55,64,89>,<55,67,81>,<55,67,82>,<55,69,74>,<55,71,89>,<55,71,91>,<55,74,87>,<55,78,97>,<55,83,93>,<55,91,96>,<56,57,73>,<56,57,89>,<56,57,97>,<56,59,75>,<56,59,83>,<56,59,99>,<56,61,85>,<56,61,93>,<56,65,81>,<56,65,89>,<56,65,97>,<56,67,83>,<56,67,87>,<56,69,85>,<56,71,83>,<56,71,87>,<56,71,95>,<56,73,89>,<56,73,97>,<56,79,95>,<56,81,97>,<56,83,99>,<57,58,65>,<57,58,79>,<57,59,82>,<57,61,82>,<57,61,97>,<57,61,100>,<57,62,65>,<57,64,65>,<57,65,79>,<57,65,86>,<57,67,73>,<57,67,79>,<57,67,91>,<57,68,71>,<57,68,83>,<57,70,97>,<57,71,73>,<57,71,80>,<57,71,97>,<57,73,86>,<57,73,100>,<57,74,79>,<57,79,85>,<57,79,94>,<57,83,97>,<57,83,100>,<57,85,89>,<57,91,100>,<57,92,97>,<58,59,75>,<58,59,95>,<58,61,75>,<58,61,85>,<58,63,85>,<58,65,67>,<58,67,81>,<58,67,95>,<58,69,73>,<58,71,75>,<58,71,93>,<58,79,81>,<58,79,85>,<58,81,97>,<58,89,95>,<58,93,95>,<59,60,77>,<59,61,77>,<59,61,86>,<59,61,95>,<59,61,100>,<59,62,67>,<59,62,69>,<59,63,86>,<59,63,92>,<59,64,67>,<59,64,85>,<59,65,79>,<59,65,81>,<59,65,86>,<59,65,97>,<59,66,67>,<59,67,85>,<59,67,90>,<59,68,89>,<59,69,97>,<59,70,89>,<59,71,86>,<59,71,98>,<59,71,99>,<59,73,75>,<59,73,79>,<59,73,86>,<59,73,96>,<59,74,93>,<59,74,95>,<59,74,97>,<59,75,98>,<59,76,77>,<59,78,83>,<59,80,83>,<59,80,89>,<59,81,82>,<59,81,100>,<59,85,89>,<59,87,91>,<59,87,92>,<59,89,100>,<59,93,95>,<59,94,97>,<59,94,99>,<59,95,96>,<60,67,71>,<60,71,73>,<60,77,79>,<60,79,83>,<60,79,97>,<60,89,97>,<61,62,75>,<61,62,79>,<61,62,97>,<61,63,79>,<61,63,88>,<61,63,97>,<61,64,81>,<61,64,83>,<61,64,91>,<61,65,83>,<61,66,73>,<61,67,84>,<61,67,88>,<61,67,94>,<61,68,69>,<61,69,94>,<61,71,79>,<61,71,85>,<61,71,90>,<61,71,100>,<61,72,91>,<61,72,95>,<61,73,94>,<61,75,77>,<61,76,97>,<61,77,97>,<61,79,92>,<61,79,99>,<61,79,100>,<61,81,97>,<61,82,85>,<61,82,87>,<61,83,84>,<61,86,87>,<61,89,93>,<61,91,95>,<61,96,97>,<61,99,100>,<62,63,89>,<62,67,71>,<62,69,71>,<62,69,95>,<62,71,95>,<62,73,75>,<62,75,79>,<62,77,89>,<62,79,89>,<62,83,89>,<62,83,99>,<62,85,87>,<62,85,91>,<63,65,92>,<63,67,94>,<63,67,97>,<63,68,95>,<63,73,100>,<63,76,79>,<63,89,95>,<63,97,100>,<64,65,73>,<64,65,79>,<64,65,89>,<64,67,75>,<64,67,77>,<64,69,73>,<64,69,95>,<64,71,73>,<64,73,81>,<64,73,97>,<64,75,83>,<64,79,91>,<64,79,97>,<64,81,89>,<64,81,95>,<64,83,91>,<64,83,93>,<64,85,89>,<64,85,91>,<64,87,89>,<64,89,97>,<64,91,99>,<65,67,74>,<65,67,82>,<65,67,83>,<65,67,94>,<65,69,83>,<65,69,94>,<65,71,82>,<65,71,98>,<65,74,81>,<65,77,92>,<65,79,83>,<65,83,88>,<65,83,97>,<66,67,95>,<66,79,83>,<66,83,95>,<66,91,97>,<67,68,93>,<67,68,97>,<67,69,76>,<67,69,98>,<67,70,97>,<67,71,76>,<67,71,85>,<67,71,98>,<67,72,83>,<67,73,86>,<67,73,89>,<67,73,100>,<67,75,89>,<67,76,81>,<67,77,85>,<67,77,90>,<67,78,83>,<67,78,85>,<67,79,92>,<67,79,94>,<67,79,100>,<67,80,97>,<67,81,85>,<67,81,89>,<67,86,93>,<67,89,99>,<67,93,100>,<67,94,99>,<67,96,97>,<68,69,77>,<68,69,79>,<68,73,79>,<68,75,97>,<68,83,95>,<68,83,97>,<69,71,88>,<69,71,100>,<69,76,79>,<69,79,95>,<69,82,85>,<69,82,89>,<69,83,86>,<69,83,89>,<69,83,95>,<69,85,94>,<69,86,97>,<69,91,100>,<70,71,79>,<70,71,97>,<70,73,81>,<71,73,80>,<71,73,90>,<71,73,91>,<71,74,97>,<71,75,82>,<71,76,89>,<71,79,89>,<71,79,93>,<71,81,89>,<71,81,95>,<71,81,100>,<71,82,85>,<71,83,100>,<71,84,89>,<71,85,89>,<71,85,93>,<71,86,87>,<71,89,100>,<71,90,91>,<71,94,97>,<73,75,82>,<73,75,92>,<73,77,82>,<73,78,85>,<73,79,92>,<73,79,95>,<73,81,82>,<73,83,90>,<73,83,91>,<73,83,95>,<73,83,97>,<73,83,100>,<73,86,95>,<73,87,91>,<73,87,92>,<73,87,97>,<73,87,100>,<73,89,90>,<73,89,91>,<73,95,98>,<73,95,99>,<73,97,100>,<74,79,83>,<74,81,83>,<74,93,97>,<75,77,94>,<75,79,86>,<75,79,92>,<75,79,98>,<75,83,86>,<75,88,89>,<75,89,92>,<75,89,97>,<75,91,92>,<75,91,94>,<75,91,97>,<75,97,98>,<76,81,85>,<76,83,85>,<77,78,95>,<77,79,97>,<77,83,100>,<77,85,86>,<77,93,95>,<77,94,95>,<78,83,97>,<78,85,89>,<79,80,97>,<79,81,100>,<79,82,89>,<79,82,95>,<79,83,96>,<79,85,99>,<79,86,89>,<79,87,88>,<79,89,90>,<79,93,94>,<79,95,97>,<79,96,97>,<81,82,91>,<81,83,92>,<81,85,94>,<81,88,91>,<81,91,100>,<81,97,100>,<82,87,95>,<82,89,93>,<82,89,95>,<82,97,99>,<83,85,94>,<83,86,93>,<83,87,94>,<83,88,95>,<83,91,94>,<83,93,100>,<83,97,100>,<84,89,95>,<85,89,98>,<85,92,97>,<85,93,98>,<86,89,97>,<86,93,97>,<87,88,97>,<87,89,98>,<89,91,100>,<89,92,99>,<89,93,100>,<89,97,100>];

for I in L do 
a, b, c := Explode(I);
DesiredCurves(a,b,c,1);
end for;

for I in L do 
a,b,c:= Explode(I);
DesiredCurves(a,b,c,2);
end for;

for I in L do 
a,b,c:= Explode(I);
DesiredCurves(a,b,c,3);
end for;

//For the skipping cases, an extra round of checks has been carried out. See file For the skipping cases on the website.