def countonly(zdelta):
    largestenclosing={zdelta[0]:set([zdelta[0]])}
    count = 1
    n = len(zdelta)
    for delta_i in zdelta[1:n-1]:
        Left = largestenclosing.get( ( (delta_i-1) % n),set([]) )
        Right = largestenclosing.get( ( (delta_i+1) % n),set([]) )
        if Left or Right:
            newlargest = set([delta_i]).union(Right).union(Left)
            largestenclosing[delta_i]=newlargest
            for  delta_j in newlargest:
                largestenclosing[delta_j] = newlargest
            if Left and Right:
                count*=choose(len(Right)+len(Left),len(Right))
        else:
            largestenclosing[delta_i]=set([delta_i])
    return count

def cycCount(data):
    return countonly(zdeltaof(data))

def deltaof(li):
    decorated = zip(li,range(1,len(li)+1))
    decorated.sort()
    decorated.reverse()
    return [d[1] for d in decorated]

def zdeltaof(li):
    """descent vector with numbering from zero """
    decorated = zip(li,range(len(li)))
    decorated.sort()
    decorated.reverse()
    return [d[1] for d in decorated]

    
fac=lambda n: n<=0 or reduce(lambda a,b: long(a)*long(b),xrange(1,n+1))

# n*(n-1)* ... *(n-k+1)
def facto(n,k):
    if k==0: return 1
    return(reduce(lambda a,b: long(a)*long(b),xrange(n-k+1,n+1)))

def choose(n,k):
    return(facto(n,k)/fac(k))