arnioxux

    lastJ = None
    def f(i, j):
        global lastJ
        if i != 0:
            return i * (lastJ + 1) + j
        else:
            lastJ = j
            return j


    N = 3
    M = 5
    seen = set()
    for i in range(N):
        for j in range(M):
            q = f(i, j)
            seen.add(q)
    assert sorted(seen) == list(range(N * M))

  def neighbors4(point): 
    "The four neighboring squares."
    x, y = point
    return (          (x, y-1),
            (x-1, y),           (x+1, y), 
                      (x, y+1))

  def neighbors8(point): 
    "The eight neighboring squares."
    x, y = point 
    return ((x-1, y-1), (x, y-1), (x+1, y-1),
            (x-1, y),             (x+1, y),
            (x-1, y+1), (x, y+1), (x+1, y+1))

  E[ln(X_1*...*X_N)] = sum E[ln(X)]

  E[sqrt(X_1*...*X_N)] = prod E[sqrt(X)]