import math

def avg (ns):
    s = 0
    for n in ns:
        s = s+n
    return s/len(ns)

def reflection(ns):
    mu = avg(ns)
    n = len(ns)
    ns2 = [None]*n
    for i in range(n):
        ns2[i] = 2 * mu - ns[i]
    return ns2

def gen_amplitude(n):
    a = [1/math.sqrt(2**n)] * (2 ** n)
    # for i in range(2 ** n):
    #     a[i] = 1/math.sqrt(2**n)
    return a

def flip(ns, i):
    ns[i] = -1 * ns[i]
    return ns

def iter_ref(l, ns, j):
    for i in range(l):
        ns = flip(ns, j)
        ns = reflection(ns)
    return ns