#!/usr/bin/env python3
import sys
import readline

from noether.math import *
from noether.cli import *


PROMPT = '[n]: '

'''
Pairwise orbit cumulative summation (cum orb) 
'''
def orb_cum(cum, orb):
    for i in range(len(cum)):
        cum[i] += orb[i]

def main():
    while True:
        n = None
        strlen_n = None
        try:
            uprint(PROMPT, color=Color.Blue, end='')
            n = input()
            strlen_n = len(n)
            n = int(n)
        except ValueError:
            continue

        # calculate phi of n
        phi = totient(n)
        # determine if n is prime
        prime = n - 1 == phi
        if prime:
            uprint('', moveup=1, end='', flush=False)
            column = len(PROMPT) + strlen_n + 1
            sys.stdout.write(f'\033[{column}C')
            uprint('[PRIME]', color=Color.Magenta, style=Color.Bold, flush=True)
        # primitive root values
        proot_v = []
        # primitive root count
        proot_c = 0
        # cumulative sum of primitive root orbits
        prorb_cum = []
        
        # calculate left padding to align i values
        # lpadded = strlen_n
        # calculate right padding to align len(orb) values
        rpadded = len(str(phi))
    
        # find all invertible elements (skipped for now)
        for a in range(n):
            orb, ord = orbit(a, n)

            # check if `a` is a primitive root
            proot = (ord + 1 == n)
            proot_c += proot 

            # calculate padding
            lpad = ' ' * (strlen_n - len(str(a)))
            rpad = ' ' * (rpadded - len(str(ord)))
            # calculate coloring
            color_a = Color.Red
            color_ord = None
            color_orb = None
            style_ord = None
            style_orb = None                
            if proot:
                color_a = Color.Green
                color_ord = Color.Yellow
                color_orb = Color.Green
                style_ord = Color.Bold
                style_orb = Color.Bold
                proot_v.append(a)
                if not prorb_cum:
                    prorb_cum = orb
                else:
                    orb_cum(prorb_cum, orb)
            elif gcd(a, n) == 1:
                color_a = Color.Yellow
            
            uprint(f'{lpad}{a}', color=color_a, style=Color.Bold, end=' ', flush=False)
            uprint('->', end=' ', flush=False)
            uprint(f'{ord}{rpad}', color=color_ord, style=style_ord, end=' ', flush=False)
            uprint('|', end=' ', flush=False)
            uprint(f'{orb}', color=color_orb, style=style_orb, flush=True)
        uprint('Cum Orb:   ', end='', color=Color.Cyan)
        uprint(f'{prorb_cum}', flush=True)
        prorb_cum_mod = [x % n for x in prorb_cum]
        uprint(f'           {prorb_cum_mod}', flush=True)

        uprint('Roots:     ', end='', color=Color.Cyan)
        uprint(proot_v, flush=True)
        root_delta = [proot_v[i+1] - proot_v[i] for i in range(proot_c - 1)]
        uprint('Delta:     ', end='', color=Color.Cyan)
        uprint(root_delta, flush=True)
        
        uprint('Roots/Phi: ', end='', color=Color.Cyan)
        uprint(f'{proot_c}/{phi}\n', flush=True)

if __name__ == '__main__':
    try:
        main()
    except (KeyboardInterrupt, EOFError):
        pass