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#!/usr/bin/env python3
#
# A "sieve of Eratosthenes" for integer vectors of length N.
#
# The original usage of this was for studying pythagorean triples and
# filtering out those that were simply multiples of smaller ones, e.g.
#
#    (5, 12, 13) as a "fundamental" Pythagorean triple vs
#   (10, 24, 26) as a multiple of (5, 12, 13)
#

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// The MIT License
// 
// Copyright (c) 2015 Neil Webber
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:

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# The MIT License
#
# Copyright (c) 2019 Neil Webber
#
# Permission is hereby granted, free of charge, to any person obtaining a copy
# of this software and associated documentation files (the "Software"), to deal
# in the Software without restriction, including without limitation the rights
# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
# copies of the Software, and to permit persons to whom the Software is
# furnished to do so, subject to the following conditions:

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# Python support for argument parsing of list-like things (usually comma separated).
# For example:
#     def commapair(s):
#         return argtuple(s, n=2)
# can then be used as: 
#      type=commapair 
# in argparse for arguments like "--blah 17,42"
#
def argtuple(s, *dflts, n=None, seps=(',',), type=int):
    """Return tuple of 'type' from a,b,c,d... format.                           

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import functools


__IGX_SENTINEL = object()     # sentinel for a "default argument" see below


def IgnoreExceptionsDecorator(excepts, *, exception_result=__IGX_SENTINEL):
    """Decorator - catch exceptions and convert to a return value.

    'excepts' - exceptions (as a tuple, or a single exception) to catch

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import functools
from collections import ChainMap


def tuplify(arg, *, keep=str):
    """Return tuple from an iterable or a naked single object.

    If arg is a non-iterable object, returns: (arg,)
    If arg is iterable, returns: tuple(arg)

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def iskeith(n):
    """Return True if n is a Keith number - https://oeis.org/A007629"""

    if n < 10:
        return False          # by definition

    # initial sequence seeding is the digits of n
    kl = [int(d) for d in str(n)]      # crude, but easy. Speed not relevant.
    ksum = sum(kl)

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#!/usr/bin/env python3

def collatz_sequence(n):
    """Generate the collatz sequence for n (see OEIS A006577)."""

    c = int(n)
    if c < 1 or c != n:
        raise ValueError(f"Argument n ({n}) must be a positive integer")

    while c != 1:

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# toy example re-implementing C3 method resolution order
# (MRO, as used for python multi-inheritance)
#
# Algorithm snippets in comments come from:
#      https://www.python.org/download/releases/2.3/mro/
# and are notated as [2.3MRO]
#

# A Hier represents a class hierarchy, with a name, and a possibly-empty
# list of bases (each base itself also a Hier).

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from functools import lru_cache

@lru_cache
def _powA046253(i, n):
    """Return i**n for two integers i and n. Defines 0**0 to be ZERO."""
    r = i
    while n > 1:
        r *= i
        n -= 1
    return r