#!/usr/bin/env python

test_list = [ 21,9,17,10 ]

def fibonacci_sequence(test_number):
    # test_number represent the number that sequence should stop at.

    # Initialize the sequence with the first two numbers
    sequence = [0, 1]

    # keep_find setup to let while loop keep find the number sequence 
    # unless the last generated number (next_num) is greater than the number 
    # need to be tested.
    keep_find = True

    # initialize to true to run the while loop at the very first execution
    while keep_find:
        # after the very first execution, the keep_find may not keep true anymore.

        # 1st, 2nd, 3rd, 4th
        # 0,   1,   1,   2
        # at the first execution, the next_num is the 3rd number
        # at the first execution, the sequence[-1] is the 2rd number
        # at the first execution, the sequence[-2] is the 1st number

        # at the second execution, the next_num is the 4th number
        # at the second execution, the sequence[-1] is the 3rd number
        # at the second execution, the sequence[-2] is the 2nd number
        next_num = sequence[-1] + sequence[-2]

        # append the number to the sequence
        # append means extend the list to with the value given
        # [0,1].append(2) => [0,1,2]
        # at the first execution the number appended is at 3rd place
        # at the second execution the number appended is at 4th place
        sequence.append(next_num)

        # test if:
        # the last number(next_num) calculated is already larger than the number need to be tested
        keep_find = (next_num < test_number)
    
    # test the number if it exist in fibonacci sequence
    # return true if the next_num is equal to the test_number
    # it is because there are two possibilities of next_num
    # next_num > test_number => means the number is not in sequence
    # next_num = test_number => means the number is in sequence
    return next_num == test_number

def triangular_sequence(test_number):
    # Initialize the sequence with the first number
    sequence = [1]
    
    # Generate the Triangular sequence
    keep_find = True
    i = 2
    while keep_find:
        next_num = sequence[-1] + i
        keep_find = next_num < test_number
        sequence.append(next_num)        
        i = i + 1
    return next_num == test_number

def square_number_sequence(test_number):
    # Initialize the sequence with the first number
    sequence = [1]
    
    keep_find = True
    i = 2
    while keep_find:
        next_num = i * i
        keep_find = next_num < test_number
        i = i + 1

    return next_num == test_number

def check_mathematical_series(n: int) -> str:
    all_result = []
    
    f_result = fibonacci_sequence(n)
    t_result = triangular_sequence(n)
    s_result = square_number_sequence(n)
    
    if (f_result):
        all_result.append('Fibonacci')
    if (t_result):
        all_result.append('Triangular')
    if (s_result):
        all_result.append('Square')
        
    if (all_result == []):
        print(f'n = {n}: None')
    else:
        print(f'n = {n}: '+', '.join(all_result))

for n in test_list:
    check_mathematical_series(n)