from itertools import permutations
from math import factorial

for N in range(4, 21, 2):
    perms = factorial(N)
    zeros = 0
    for tail in permutations(range(2, N+1)):
        order = (1,) + tail
        lefts = (order[-1],) + order
        rights = tail + (order[0],)
        for left, n, right in zip(lefts, order, rights):
            # if n in between:
            if (left < n) == (n < right):
                break
        else:
            zeros += 1
    zeros *= N

    print(f'N = {N}:\t {zeros} / {perms} \t= {zeros / perms}')