Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

C. Palindromic Matrix

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputLet's call some square matrix with integer values in its cells palindromic if it doesn't change after the order of rows is reversed and it doesn't change after the order of columns is reversed.

For example, the following matrices are palindromic:

The following matrices are not palindromic because they change after the order of rows is reversed:

The following matrices are not palindromic because they change after the order of columns is reversed:

You are given $$$n^2$$$ integers. Put them into a matrix of $$$n$$$ rows and $$$n$$$ columns so that each number is used exactly once, each cell contains exactly one number and the resulting matrix is palindromic. If there are multiple answers, print any. If there is no solution, print "NO".

Input

The first line contains one integer $$$n$$$ ($$$1 \le n \le 20$$$).

The second line contains $$$n^2$$$ integers $$$a_1, a_2, \dots, a_{n^2}$$$ ($$$1 \le a_i \le 1000$$$) — the numbers to put into a matrix of $$$n$$$ rows and $$$n$$$ columns.

Output

If it is possible to put all of the $$$n^2$$$ numbers into a matrix of $$$n$$$ rows and $$$n$$$ columns so that each number is used exactly once, each cell contains exactly one number and the resulting matrix is palindromic, then print "YES". Then print $$$n$$$ lines with $$$n$$$ space-separated numbers — the resulting matrix.

If it's impossible to construct any matrix, then print "NO".

You can print each letter in any case (upper or lower). For example, "YeS", "no" and "yES" are all acceptable.

Examples

Input

4 1 8 8 1 2 2 2 2 2 2 2 2 1 8 8 1

Output

YES 1 2 2 1 8 2 2 8 8 2 2 8 1 2 2 1

Input

3 1 1 1 1 1 3 3 3 3

Output

YES 1 3 1 3 1 3 1 3 1

Input

4 1 2 1 9 8 4 3 8 8 3 4 8 9 2 1 1

Output

NO

Input

1 10

Output

YES 10

Note

Note that there exist multiple answers for the first two examples.

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Sep/20/2020 18:23:07 (h3).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|