from math import factorial
from random import shuffle

def loop(k, n, string):
    if k > 0:
        for i in range(n-k):
            loop(k-1, n, string)
            seg = string[-n:-n+k]
            seg1 = list(reversed(seg[-2:]))
            seg2 = seg[:-2]
            shuffle(seg2)
            string += seg1 + seg2
        loop(k-1, n, string)

def find_string(alphabet):
    n = len(alphabet)
    string = list(alphabet)
    loop(n-1, n, string)
    return string

def check_string(string, alphabet):
    n = len(alphabet)
    perm_list = set()
    for i in range(len(string)-n+1):
        perm = string[i:i+n]
        if sorted(perm) == sorted(alphabet):
            perm_list.add(tuple(perm))
    return len(perm_list) == factorial(n)

alphabet = [1,2,3,4,5,6]
for i in range(20):
    string = find_string(alphabet)
    print(''.join(str(n) for n in string), check_string(string, alphabet))