def DecoratedPermutations(n):
    for sigma in Permutations(n):
        F = sigma.fixed_points()
        for X in Subsets(F):
            tau = list(sigma)
            for i in X:
                tau[i-1] = -tau[i-1]
            yield list(SignedPermutations(n)(tau))

def element_repr(pi):
    pi = list(pi)
    for i,a in enumerate(pi):
        if a == i+1:
            pi[i] = 0
        elif -a == i+1:
            pi[i] = -1
    return str(pi).replace(" ","").replace("0","+").replace("-1","-")

def statistic(d):
    e = 0
    for i in range(len(d)):
        if d[i] >= i+1:
            e += 1
    return e