'''
There exists an infinitely large two-dimensional grid of uncolored unit cells. You are given a positive integer n, indicating that you must do the following routine for n minutes:

At the first minute, color any arbitrary unit cell blue.
Every minute thereafter, color blue every uncolored cell that touches a blue cell.
Below is a pictorial representation of the state of the grid after minutes 1, 2, and 3.


Return the number of colored cells at the end of n minutes.

 

Example 1:

Input: n = 1
Output: 1
Explanation: After 1 minute, there is only 1 blue cell, so we return 1.
Example 2:

Input: n = 2
Output: 5
Explanation: After 2 minutes, there are 4 colored cells on the boundary and 1 in the center, so we return 5. 
 

Constraints:

1 <= n <= 105
'''
import unittest

from typing import *

class Solution:
    def coloredCells(self, n: int) -> int:
        return 2 * (n - 1) * n + 1


class TestSolution(unittest.TestCase):

    def test_case(self):
        examples = (
            ((2,),5),
        )
        for first, second in examples:
            self.assert_function(first, second)

    def assert_function(self, first, second):
        self.assertEqual(Solution().coloredCells(*first), second,
                         msg="first: {}; second: {}".format(first, second))


unittest.main()
