P5512 [NOIP 1997 Senior] Chessboard Problem Enhanced Version

An enhanced testdata version of [P1549](https://www.luogu.org/problem/P1549). **The testdata has been expanded from 5 to 10.** Because the testdata for this problem may have many disputes, a separate problem is created to test the enhanced version testdata.

On an $N \times N$ chessboard ($1 \le N \le 10$), fill in $N ^ 2$ numbers $1, 2, \dots, N ^ 2$, such that the sum of any two adjacent numbers is a prime number. For example, when $N = 2$, one solution is: | $1$ | $2$ | | :-----------: | :-----------: | | $4$ | $3$ | The adjacent pairs whose sums are prime are: $1+2,1+4,4+3,2+3$ When $N = 4$, one possible filling is: | $1$ | $2$ | $11$ | $12$ | | :-----------: | :-----------: | :-----------: | :-----------: | | $16$ | $15$ | $8$ | $5$ | | $13$ | $4$ | $9$ | $14$ | | $6$ | $7$ | $10$ | $3$ | Here we require that the top-left cell must contain the number $1$.

One line with an integer $N$.

If there are multiple solutions, output the arrangement with the smallest sum of the first row and the first column. If there is no solution, output `NO`.

$N\leq10$ For $N=1,2,\dots,10$, each has one test point. For some reasons, $N$ is not necessarily the same as the test point ID. ---- **The testdata was newly fixed on `2020.1.20`.** Translated by ChatGPT 5