# idx_permu_plus.py

# idx_permu_plus.py

import math

def idx_permu(idx, length=8):
    elements = list(range(length))
    result = []
    for i in range(length - 1, -1, -1):
        facto = math.factorial(i)
        pos = idx // facto
        result.append(elements.pop(pos))
        idx %= facto
    return result

length = 6
facto = math.factorial(length)
step = int(facto * 0.99)

while step > 2:
    while math.gcd(step, facto) != 1:
        step -= 1

    i = 0
    count = 0
    while count < facto:
        result = idx_permu(i, length)
        print(result, step, f'{count + 1}/{facto}')
        i = (i + step) % facto
        count += 1
    step -= 1