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We shall name a square matrix as spiral123 if it has the following properties:

· its elements are from the {0, 1, 2, 3} set; - · each row and column contains each of the values 1, 2 and 3, exactly once and all the other values are 0;

· starting from the upper-left corner going right, moving in spiral, the non-zero values will appear in the

following order 1, 2, 3, 1, 2, 3, ... , 1, 2, 3.

For example a 5x5 spiral123 matrix is the following:

0 1 0 2 3

0 2 3 0 1

1 3 0 0 2

3 0 2 1 0

2 0 1 3 0

Task

For a given natural number n, you should generate a n x n spiral123 matrix.

Description of input

The spiral123.in file contains only one natural number n on the first line.

Description of output

If there is solution, the spiral123.out file must contain n lines, each with n numbers separated

with one

space, representing the required matrix. If there is no solution, on the single line of the

output file, the -1 value

will be written.

Constrains

· 5 < n < 200;

· There can be many solutions, any of them can be written.

Example

spiral123.in spiral123.out remarks

5

0 1 0 2 3

0 2 3 0 1

1 3 0 0 2

3 0 2 1 0

2 0 1 3 0

another correct solution would be:

0 1 2 3 0

2 3 0 0 1

0 0 3 1 2

1 0 0 2 3

3 2 1 0 0