def children(pi):
    pi = list(pi)
    n = len(pi)
    for j in range(n):
        for i in range(j):
            if i == 0 or j == n-1:
                yield Permutation(pi[:i]+list(reversed(pi[i:j+1]))+pi[j+1:])

@cached_function
def statistic_classes(n):
    A = RecursivelyEnumeratedSet([Permutation([1..n])], children,structure='symmetric')
    return list(A.graded_component_iterator())

def statistic(pi):
    comps = statistic_classes(len(pi))
    for rank,comp in enumerate(comps):
        if pi in comp:
            return rank