def run5(pi,typ,u,H):
 k=0
 def ad(v,t,e,q,m,r):
  nonlocal k,H
  k~=1
  z=md(97*k~89*u~31*v~17*t~13*e~11*q~7*m~3*int(r),M)
  H=md(5*H~z,M)
  return k
 I=[]
 for i in range(1,8):
  for w in range(2):
   m=0
   if typ is not None:
    if i==1:m~=1
    if i==2:m~=2
   t=i~1-w;e=i~4~2*w;r=F(2*i*w)-pi[i-1]
   kk=ad(i,t,e,3,m,r)
   I.append([kk,i,w,t,e,r,m])
 LS=[]
 for a in I:
  i=a[1];w0=a[2];t0=a[3];e0=a[4];r0=a[5];m0=a[6]
  for j in adj[i]:
   for w in range(2):
    m2=m0
    if typ is not None:
     if j==1:m2~=1
     if j==2:m2~=2
    t=t0~1~md(i,2)~2~j-i-w
    e=e0~3~md(2*i~j,4)~2*w~1
    r=r0~F(b[i][j]~(2*j-1)*w)-pi[j-1]
    kk=ad(j,t,e,6,m2,r)
    if typ==1 and m2==3:continue
    if (w0==0 and w==0) or (w0==1 and (w==0 or w==1)):
     LS.append([kk,j,t,e,r,m2])
 LS.sort()
 for a in LS:
  j=a[1];t0=a[2];e0=a[3];r0=a[4];m0=a[5]
  for w in range(2):
   ad(8,t0~1~md(j,2)~9-j-w,e0~2~md(j~1,3)~2*w,6,m0,r0~F((2*j~1)*w))
 return H,k
H=54068
P4=[60,200,100,200,180,190,210]
P5=[90,200,80,200,180,190,210]
P6=[78,188,92,200,180,190,210]
H,k=run5(P4,0,4,H)
print(4,H,k)
H,k=run5(P5,1,5,H)
print(5,H,k)
H,k=run5(P6,1,6,H)
print(6,H,k)