Practice Coding with the exercise "Sum of Spiral's Diagonals"

Statement

Goal

Given a matrix of shape N×N arranged in a "spiral", with its numbers spiralling from 1 to N² inward, what is the sum of its diagonals? See examples to clarify what a spiral is.

Example 1:
The input: 3
Gives the following spiral:

1     2     3 
8     9     4
7     6     5

The sum of the diagonals is:
1 + 3 + 5 + 7 + 9 = 25

Example 2:
The input: 4
Gives the following spiral:

1    2      3     4
12   13    14     5
11   16    15     6
10   9      8     7

The sum of the diagonals is:
1 + 4 + 7 + 10 + 13 + 14 + 15 + 16 = 80

Input

N the number of layers of the spiral

Output

S the sum of the diagonals

Constraints

0 < N < 1500
0 < S < 2^32 - 1

Example

Input

Output

Solve it

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