Problem: Let'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:

<image>

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

<image>

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

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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 ≤ n ≤ 20).

The second line contains n^2 integers a_1, a_2, ..., a_{n^2} (1 ≤ a_i ≤ 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.

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
import java.util.regex.*;

public class Codeforces{
	
	static class MyScanner{
		BufferedReader br;
		StringTokenizer st;
		
		MyScanner(FileReader fileReader){
			br = new BufferedReader(fileReader);
		}
		
		MyScanner(){
			br = new BufferedReader(new InputStreamReader(System.in));
		}
		
		String nn(){
			while(st == null || !st.hasMoreElements()){
				try{
					st = new StringTokenizer(br.readLine());
				}catch(IOException e){
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}
		
		char nc(){
			return nn().charAt(0);
		}
		
		int ni(){
			return Integer.parseInt(nn());
		}
		
		long nl(){
			return Long.parseLong(nn());
		}
		
		double nd(){
			return Double.parseDouble(nn());
		}
		
		int[] niArr0(int n){
			int[] ar = new int[n];
			for(int i = 0; i < n; i++) ar[i] = ni();
			return ar;
		}
		
		int[] niArr1(int n){
			int[] ar = new int[n + 1];
			for(int i = 1; i <= n; i++) ar[i] = ni();
			return ar;
		}
		
		long[] nlArr0(int n){
			long[] ar = new long[n];
			for(int i = 0; i < n; i++) ar[i] = nl();
			return ar;
		}
	}
	
	public static <T> void mprintln(T ... ar){
		for(T i: ar) out.print(i + " ");
		out.println();
	}
	
	private static PrintWriter out;
	
	public static void main(String[] args) throws FileNotFoundException{
		
		
		// Input from file
		// File inputFile = new File("JavaFile.txt");
		// File outputFile = new File("JavaOutputFile.txt");
		// FileReader fileReader = new FileReader(inputFile);
		// Here it ends
			
		MyScanner sc = new MyScanner();
		// MyScanner sc = new MyScanner(fileReader);
		
		out = new PrintWriter(new BufferedOutputStream(System.out)); // Output to console
		// out = new PrintWriter(new PrintStream(outputFile)); // Output to file
		
		getAns(sc);
		
		out.close();
	}
	
	private static void getAns(MyScanner sc){
		int n = sc.ni();
		int[] ar = sc.niArr0(n * n);
		int[] count = new int[1001];
		for(int i: ar) count[i]++;
		
		LinkedList<Integer> list = new LinkedList();
		int req = n / 2;
		req *= req;
		
		outer:
		for(int i = 1; i <= 1000; i++){
			while(count[i] >= 4){
				if(req == 0) break outer;
				req--;
				list.add(i);
				count[i] -= 4;
			}
		}
		
		if(req > 0){out.println("NO"); return;}
		
		// System.out.println(list);
		
		int[][] ans = new int[n][n];
		
		for(int i = 0; i < n / 2; i++) for(int j = 0; j < n / 2; j++)
			ans[i][j] = ans[n - 1 - i][j] = ans[i][n - 1 - j] = ans[n - 1 - i][n - 1 - j] = list.removeFirst();
		
		if(n % 2 == 0){
			out.println("YES");
		
			for(int[] cur: ans){
				for(int i: cur) out.print(i + " ");
				out.println();
			}
			return;
		}
		
		req = n / 2 * 2;
		
		outer:
		for(int i = 1; i <= 1000; i++){
			while(count[i] >= 2){
				if(req == 0) break outer;
				req--;
				list.add(i);
				count[i] -= 2;
			}
		}
		
		if(req > 0){out.println("NO"); return;}
		
		for(int i = 0; i < n / 2; i++) ans[i][n / 2] = ans[n - 1 - i][n / 2] = list.removeFirst();
		for(int j = 0; j < n / 2; j++) ans[n / 2][j] = ans[n / 2][n - 1 - j] = list.removeFirst();
		
		req = n % 2;
		
		outer:
		for(int i = 1; i <= 1000; i++){
			while(count[i] >= 1){
				if(req == 0) break outer;
				req--;
				list.add(i);
				count[i] -= 1;
			}
		}
		
		if(req > 0){out.println("NO"); return;}
		
		ans[n / 2][n / 2] = list.removeFirst();
		
		out.println("YES");
		
		for(int[] cur: ans){
			for(int i: cur) out.print(i + " ");
			out.println();
		}
	}
}