from copy import deepcopy

def sum_squared(nlist, power):
    mysum = 0
    for x in nlist:
        mysum += x ** power
    return mysum



def power(x, n, counter_list , solutions_list):
    counter = int(x ** (1/n))

    mysum = sum_squared(counter_list, n)

    if mysum == x:
        solution_list = deepcopy(counter_list)
        return solution_list
    else:
        old_counter = deepcopy(counter_list)

        i = counter

        while len(solutions_list) == 0 and i >= 0 and mysum <= x and len(counter_list) <= x:

            if i  == 0 or (counter_list and i not in counter_list and i > max(counter_list)):

                counter_list.append(i)

                solutions_list = power(x, n, counter_list, solutions_list)

                counter_list = deepcopy(old_counter)

            i -= 1

        return solutions_list

for x in range(20):
    for n in range(5):
        print("x, n", x + 1, n + 1)
        sl = power(x + 1, n + 1, [], [])
        print(sl)
        print(len(sl) - 1)