Symmetric Number Triangle

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem Statement

Given $n$, print $n$ rows. Row $i$ contains $1,2,\ldots,i$ followed by $i-1,i-2,\ldots,1$. Print the central $i$ once and separate consecutive numbers by one space without trailing spaces.

Input

One line contains integer $n$.

Output

Print exactly $n$ rows in order.

Subtasks

• Subtask 1 (20%): $1\le n\le 3$.

• Subtask 2 (30%): $1\le n\le 7$.

• Subtask 3 (50%): $1\le n\le 12$.

Examples

Example 1

Input:

3

Output:

1
1 2 1
1 2 3 2 1

Explanation:

Print 3 rows; row i increases to i, then decreases to 1 without repeating i.

Example 2

Input:

1

Output:

1

Explanation:

Print 1 rows; row i increases to i, then decreases to 1 without repeating i.