from operator import mul

def calc_combos(nums):
    """
    Calculate the number of possible ways a string of numbers can be decoded
    using the scheme 1 -> a, 2 -> b, ... , 26 -> z.

    Parameters
    ----------
    num : str
        String of numeric characters. It is assumed that the string
        has at least one valid decoding.

    Returns
    -------
    combos : int
        The number of ways `num` can be decoded.

    """
    return reduce(mul, (calc_substring_combos(chunk) for chunk in chunk_numbers(nums)))

def chunk_numbers(nums):
    """
    Separate a string of numbers into a list of substrings.
    Returned substrings are as small as possible (e.g. one or two characters)
    except where numbers are grouped such that they have multiple
    decodings.

    Parameters
    ----------
    num : str
        String of numeric characters. It is assumed that the string
        has at least one valid decoding.

    Returns
    -------
    subnums : list of str
        List of substrings broken down as much as possible.

    """
    subnums = ['']
    
    for i, n in enumerate(nums[:-1]):
        subnums[-1] += n
        if n == '1':
            continue
        elif n == '2' and nums[i + 1] in '0123456':
            continue
        else:
            subnums.append('')
            
    subnums[-1] += nums[-1]

    return subnums

def series(n):
    """
    Return the n-th member of the series 1, 2, 3, 5, 8, 13...
    (Which is actually the Fibonacci series minus the first 1.)

    """
    r0 = 1
    r1 = 1
    
    for _ in xrange(n):
        r0, r1 = r1, r0 + r1
    
    return r0

def calc_substring_combos(subnums):
    """
    For a given string of numbers, return the number
    of possible cominations for decoding that string.
    
    Parameters
    ----------
    subnums : str
        String of digits. Should be irreducable if passed through
        check_numbers. Assumed to have a valid decoding.

    Returns
    -------
    combos : int
        The number of possible decodings for this substring.

    """
    if len(subnums) == 1 or (len(subnums) == 2 and subnums[1] == '0'):
        return 1
    else:
        return series(len(subnums))

# tests for calc_combos
assert calc_combos('9') == 1, calc_combos('9')
assert calc_combos('999') == 1, calc_combos('999')
assert calc_combos('1111') == series(4), calc_combos('1111')
assert calc_combos('11911') == 6, calc_combos('11911')
assert calc_combos('119119') == 9, calc_combos('119119')
assert calc_combos('119119119') == 27, calc_combos('119119119')
assert calc_combos('12911') == 4, calc_combos('12911')
assert calc_combos('1211') == series(4), calc_combos('1211')
assert calc_combos('101010') == 1, calc_combos('101010')
assert calc_combos('202020') == 1, calc_combos('202020')
assert calc_combos('212121') == series(6), calc_combos('212121')

# tests for calc_substring_combos
assert calc_substring_combos('1') == series(1), calc_substring_combos('1')
assert calc_substring_combos('11') == series(2), calc_substring_combos('11')
assert calc_substring_combos('212121') == series(6), calc_substring_combos('212121')

# tests for series
assert series(1) == 1, series(1)
assert series(2) == 2, series(2)
assert series(3) == 3, series(3)
assert series(4) == 5, series(4)
assert series(5) == 8, series(5)
assert series(6) == 13, series(6)
assert series(7) == 21, series(7)

# tests for chunk_numbers
assert chunk_numbers('1') == ['1'], chunk_numbers('1')
assert chunk_numbers('10') == ['10'], chunk_numbers('10')
assert chunk_numbers('567') == ['5', '6', '7'], chunk_numbers('567')
assert chunk_numbers('1111') == ['1111'], chunk_numbers('1111')
assert chunk_numbers('11911') == ['119', '11'], chunk_numbers('11911')
assert chunk_numbers('12911') == ['12', '9', '11'], chunk_numbers('12911')
assert chunk_numbers('123') == ['123'], chunk_numbers('123')