bracketinfo

#!/usr/bin/env python3
import sys, itertools
import urllib.parse
from collections import defaultdict, Counter

try:
    import primesieve
except ImportError as e:
    sys.exit("primesieve is required. See https://pypi.python.org/pypi/primesieve")

def factorize(n):
    factors = []
    i = 2
    while i * i <= n:
        while n % i == 0:
            n = n // i
            factors.append(i)
        i = i + 1
    factors.append(n)
    return [factor for factor in factors if factor != 1]

def get_brackets(n):
    factors = factorize(n)
    if len(factors) == 1:
        return '<' + get_brackets(primesieve.count_primes(n)) + '>'
    else:
        return ''.join(get_brackets(x) for x in factors)

def get_ordinal(n, latex=True):
    omega = r'\omega' if latex else 'ω'
    factors = factorize(n)
    if len(factors) == 1:
        if n == 3:
            return omega
        else:
            ordinal = get_ordinal(primesieve.count_primes(n), latex=latex)
            if latex:
                return omega + '^{' + ordinal + '}'
            else:
                if '+' in ordinal:
                    return omega + '^(' + ordinal + ')'
                else:
                    return omega + '^(' + ordinal + ')'
    else:
        terms = []
        for factor, times in sorted(Counter(factors).items(), reverse=True):
            if factor == 2:
                terms.append(str(times))
            else:
                terms.append(get_ordinal(factor, latex=latex) + (str(times) if times > 1 else ''))
        return '+'.join(terms)

def full_ordinal(n):
    return r'\mathfrak{p}(' + get_ordinal(n) + ')'

def is_symmetrical(n):
    factors = factorize(n)
    if len(factors) == 1:
        return is_symmetrical(primesieve.count_primes(n))
    found_odd = False
    for factor, times in Counter(factors).items():
        if times % 2 == 1:
            if found_odd:
                return False
            if not is_symmetrical(factor):
                return False
            found_odd = True
    return True


def get_info(n):
    info = {}
    brackets = get_brackets(n)
    factors = factorize(n)

    info["bracket_notation"] = brackets

    abc = brackets.replace('<>', 'a')
    for letter in 'abcdefghij':
        abc = abc.replace('<'+letter+'>', chr(ord(letter)+1))
    info["abc_notation"] = abc

    p = abc.replace('<', 'p<')
    for letter in 'abcdefghij':
        p = p.replace(letter, 'p'*(ord(letter)-96)+'1')
    info["p_notation"] = p

    digits_list = []
    last_bracket = ''
    for char in brackets:
        if char == last_bracket:
            digits_list[-1] += 1
        else:
            digits_list.append(1)
        last_bracket = char
    digits = ''.join(map(str,digits_list))
    info["digit_notation"] = digits

    depth = []
    current_depth = 0
    max_depth = 0
    add = True
    for digit in digits_list[:-1]:
        if add:
            current_depth += digit
        else:
            current_depth -= digit
        depth.append('*' * current_depth)
        add = not add
        if current_depth > max_depth:
            max_depth = current_depth
    info["depth_notation"] = '\n'.join(''.join(row) for row in itertools.zip_longest(*depth, fillvalue=' '))
    ordinal_escaped = urllib.parse.quote(full_ordinal(n))
    info["ordinal"] = '[img]http://latex.codecogs.com/gif.latex?' + ordinal_escaped + '[/img]'

    info["is_prime"] = len(factors) == 1
    info["is_symmetrical"] = is_symmetrical(n)
    info["is_alphabetical"] = not ('<' in abc)

    info["length"] = len(brackets)
    info["reversals"]= len(digits_list) - 1
    info["max_depth"] = max_depth
    info["factors"] = len(factors)
    info["smoothness"] = max(factors)
    info["necessary_brackets"] = abc.count('<')*2

    return info

def info_string(number):
    info = get_info(number)
    return '\n'.join([
        str(number),
        info["bracket_notation"],
        info["abc_notation"],
        info["p_notation"],
        info["digit_notation"],
        '[code]',
        info["depth_notation"],
        '[/code]' +
        info["ordinal"],
        '',
        'Prime: {0}'.format('Yes' if info["is_prime"] else 'No'),
        'Symmetrical: {0}'.format('Yes' if info["is_symmetrical"] else 'No'),
        'Alphabetical: {0}'.format('Yes' if info["is_alphabetical"] else 'No'),
        '',
        'Length: {0}'.format(info["length"]),
        'Reversals: {0}'.format(info["reversals"]),
        'Max Depth: {0}'.format(info["max_depth"]),
        'Factors: {0}'.format(info["factors"]),
        'Smoothness: {0}'.format(info["smoothness"]),
        'Necessary Brackets: {0}'.format(info["necessary_brackets"])
    ])

if __name__ == '__main__':
    n = int(sys.argv[1] if len(sys.argv) > 1 else sys.stdin.read())
    print(info_string(n))