# Modulo Test
from prbraid.math import *
from prbraid.color import *

import sys
from math import gcd
from time import sleep

PROMPT = '[n]: '

'''
Modify the body of this function, it will be run
against every prime number ascending.
'''
def test_function(p: int, phi: int):
    p_color = Color.Green
    result_color = Color.Yellow
    
    result = phi / gcd(p, phi) - 1
    if result < 0 or not is_prime(result):
        p_color = Color.Red
        result_color = Color.Red
    uprint(p, color=p_color, style=Color.Bold, end=' -> ', flush=False)
    uprint(result, color=result_color, flush=True)
    sleep(0.1)
    

def main():
    n = -1
    while True:
        n += 1

        # calculate phi of n
        phi = totient(n)
        # determine if n is prime
        prime = n - 1 == phi
        if not prime:
            continue
        
        # # primitive root values
        # proot_v = []
        # # primitive root count
        # proot_c = 0
        # # cumulative sum of primitive root orbits
        # prorb_cum = []       
  
        # # 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 

        #     if proot:
        #         proot_v.append(a)
        #         if not prorb_cum:
        #             prorb_cum = orb
        #         else:
        #             orb_cum(prorb_cum, orb)
        #         print(a)            
        # 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)
        test_function(n, phi)

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