Snake#847

Snake

1 second
64 megabytes
Very easy

Print a square consisting of N \times N cells filled with the numbers from to N^2 in a "snake" order (see examples).

Input

The first line contains a single integer (2 \leq N \leq 100).

Output

Print rows with numbers in each, separated by spaces. Starting the snake from another corner or changing its direction is not allowed.

Examples

Example 1

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