python3 - <<'PY'
p=996979
d=14641
g=379153
J=[(22716,22810),(397695,397787),(731292,731385)]
K=J+[(a+p,b+p) for a,b in J]
W=[b-a for a,b in K]
patterns=[]
k=48
def gen(pos,cost,arr,D):
    if pos==k-1:
        patterns.append(tuple(arr))
        return
    w=1 if pos in (0,k-2) else 2
    for e in range((D-cost)//w+1):
        arr.append(e)
        gen(pos+1,cost+w*e,arr,D)
        arr.pop()
sol=set()
for m,(L,U) in enumerate(K):
    D=W[m]-(2*k-4)
    if D<0: continue
    patterns.clear()
    gen(0,0,[],D)
    for e in patterns:
        delta=2*k-4+2*sum(e[1:k-2])+e[0]+e[k-2]
        lo=(L-e[0])//2
        hi=(U-delta-1-e[0])//2
        for y1 in range(lo,hi+1):
            ys=[y1]
            y=y1
            for gg in e:
                y+=1+gg
                ys.append(y)
            y1=ys[0]
            yk=ys[-1]
            A=[]
            B=[]
            for li,ui in K:
                a0=max(0,li-y1)
                a1=min(y1-1,ui-yk)
                if a0<=a1: A.append((a0,a1))
                b0=max(yk+1,li-y1)
                b1=min(p-1,ui-yk)
                if b0<=b1: B.append((b0,b1))
            for a0,a1 in A:
                for b0,b1 in B:
                    for a in range(a0,a1+1):
                        for lk,uk in K:
                            ll=max(b0,lk-a)
                            hh=min(b1,uk-a)
                            for b in range(ll,hh+1):
                                if b<=yk: continue
                                X=tuple([a]+ys+[b])
                                ok=True
                                for i1 in range(50):
                                    for j1 in range(i1+1,50):
                                        ss=X[i1]+X[j1]
                                        if not(22716<=ss<=22810 or 397695<=ss<=397787 or 731292<=ss<=731385 or 1019695<=ss<=1019789 or 1394674<=ss<=1394766 or 1728271<=ss<=1728364):
                                            ok=False
                                if ok: sol.add(X)
print('Ncliques',len(sol))
print('distinct interiors',len(set(X[1:-1] for X in sol)))
print('distinct a,b',len(set((X[0],X[-1]) for X in sol)))
C2=C3=0
S2=S3=0
for X in sol:
    for x in X:
        S2=(S2+x*x)%983
        S3=(S3+x*x*x)%983
        aa=(d*x)%p
        C2=(C2+aa*aa)%983
        C3=(C3+aa*aa*aa)%983
print('C2,C3',C2,C3,'S2,S3',S2,S3)
X=list(sol)[0]
orig=[(d*x)%p for x in X]
print('example X',X)
print('orig',orig)
bad=0
for i in range(50):
    for j in range(i+1,50):
        aa=orig[i]; bb=orig[j]
        lam=(g*(aa+bb)+123801)%p
        if not(146517<=lam<=146611 or 521496<=lam<=521588 or 855093<=lam<=855186): bad+=1
print('badlambda',bad)
PY