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Description

Fill an $n \times n$ matrix with numbers $1$, $2$, $3$, ..., $n \times n$ in a snake-like pattern. For example, when $n=4$, the matrix looks like:

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

Input Format

Input $n$.

Output Format

Output the matrix as described. $n$ lines, with numbers in each line separated by a single space.

Sample

4

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