"Ulam's spiral is a plot in which positive integers are arranged in a spiral. It was discovered by the mathematician Stanislaw Ulam in 1963, while he was doodling during the presentation of a "long and very boring paper" at a scientific meeting. ...Ulam constructed the spiral by writing down a regular rectangular grid of numbers, starting with 1 at the center, and spiraling out." [adapted from Wikipedia]

You are a student who, like Ulam, also doodles during the presentation of a "long and very boring" lesson. However, there is a finite amount of space on your doodling surface (paper), and you have gotten bored of drawing the spiral. The solution to this would be to write a program to draw the spiral for you.

Given an integer , output the Ulam spiral for an square. Please refer to the sample output for more details.

#### Input Format

The input will contain exactly one line with one integer, .

#### Output Format

The output should contain the integer matrix representing the spiral. Each number in the spiral should be padded with spaces until it is three characters long. For example, `16`

should be printed as `X16`

and `1`

should be printed as `XX1`

, where spaces are represented by `X`

. On top of this, there should be 1 space between each number. As can be seen in sample output 1, there are 3 spaces between `5`

and `4`

(1 from the spacing, 2 from the padding). There should not be any trailing spaces at the end of each row.

#### Constraints

Subtask 1 (0%): Sample Testcases.

Subtask 2 (37%): .

Subtask 3 (63%): .

#### Sample Input 1

`4`

#### Sample Output 1

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

#### Sample Input 1

`5`

#### Sample Output 2

```
17 16 15 14 13
18 5 4 3 12
19 6 1 2 11
20 7 8 9 10
21 22 23 24 25
```

## Comments