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:

<image>

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.io.IOException;
import java.util.*;

public class Codechef2 {
	static FasterScanner in = new FasterScanner();

	static class nodem{
		int ban, cnt;
		nodem(int b, int c){
			this.ban=b; this.cnt=c;
		}
	}
	public static void main(String[] args) throws Exception {
		int n = in.nextInt();
		int [] arr = in.nextIntArray(n*n);
		int [] their = new int [1006];
		int ct=0;
		for(int i=0; i<n*n; i++){
			if(their[arr[i]]==0)ct++;
			their[arr[i]]++;
		}
		nodem [] uskarr = new nodem[ct];
		int ad=0;
		for(int i=0; i<=1000; i++){
			if(their[i]!=0){
				uskarr[ad]=new nodem(i, their[i]);
				ad++;
			}
		}
		int [][] a = new int [n][n];
		int an=0;
		for(int i=0; i<n; i++){
			for(int j=0; j<n; j++)a[i][j]=an++;
		}
		int [][] rowc = new int [n][n];
		int [][] colc = new int [n][n];
		for(int i=0,d=n-1; i<n; i++, d--){
			for(int j=0; j<n; j++){
				rowc[i][j]=a[d][j];
			}
		}
		for(int i=0; i<n; i++){
			for(int j=0,d=n-1; j<n; j++,d--){
				colc[i][j]=a[i][d];
			}
		}
		int [] val = new int [500];
		int ac=1;
		for(int i=0; i<n; i++){
			for(int j=0; j<n; j++){
				if(val[a[i][j]]!=0){
					int pt=val[a[i][j]];
					val[rowc[i][j]]=pt;
					val[colc[i][j]]=pt;
				}else if(val[rowc[i][j]]!=0){
					int pt=val[rowc[i][j]];
					val[a[i][j]]=pt;
					val[colc[i][j]]=pt;
				}else if(val[colc[i][j]]!=0){
					int pt=val[colc[i][j]];
					val[rowc[i][j]]=pt;
					val[a[i][j]]=pt;
				}else{
					val[rowc[i][j]]=ac;
					val[a[i][j]]=ac;
					val[colc[i][j]]=ac;
					ac++;
				}
			}
		}
		int [] mine = new int [ac+4];
		for(int i=0; i<405; i++){
			mine[val[i]]++;
		}
		nodem [] merarr = new nodem[ac+1];
		for(int i=1; i<=ac; i++){
			merarr[i] = new nodem(i, mine[i]);
		}
		
		PriorityQueue<nodem> meri = new PriorityQueue<>(new Comparator<nodem>() {
			@Override
			public int compare(nodem o1, nodem o2) {
				// TODO Auto-generated method stub
				if(o1.cnt<o2.cnt)return 1;
				else if(o1.cnt>o2.cnt) return -1;
				else return 0;
			}
		});
		PriorityQueue<nodem> uski = new PriorityQueue<>(new Comparator<nodem>() {

			@Override
			public int compare(nodem o1, nodem o2) {
				// TODO Auto-generated method stub
				if(o1.cnt<o2.cnt)return 1;
				else if(o1.cnt>o2.cnt) return -1;
				else return 0;
			}
			
		});
		for(int i=0; i<ct; i++){
			uski.add(uskarr[i]);
		}
		for(int i=1; i<ac; i++){
			meri.add(merarr[i]);
//			System.out.println(merarr[i].cnt);
		}
		int [] place = new int [ac+1];
//		System.out.println(meri.size());
		while(meri.size()!=0){
			nodem us = uski.peek();
			nodem me = meri.peek();
//			System.out.println(us.ban + " " + me.ban);
			if(us.cnt<me.cnt){
				System.out.println("NO");
				return;
			}else{
				place[me.ban]=us.ban;
			}
			if(us.cnt==me.cnt){
				uski.remove();
			}else{
				nodem add = new nodem(us.ban, us.cnt-me.cnt);
				uski.remove();
				uski.add(add);
			}
			meri.remove();
		}
		System.out.println("YES");
		int [][] ans = new int [n][n];
		for(int i=0; i<n; i++){
			for(int j=0; j<n; j++){
				int g = (i*n) + j;
				ans[i][j] = place[val[g]];
				System.out.print(ans[i][j] + " ");
			}
			System.out.println();
		}
		
		
	}

	static class FasterScanner {
		private byte[] buf = new byte[1024];
		private int curChar;
		private int snumChars;

		public int read() {
			if (snumChars == -1)
				throw new InputMismatchException();
			if (curChar >= snumChars) {
				curChar = 0;
				try {
					snumChars = System.in.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (snumChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		public String nextLine() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndOfLine(c));
			return res.toString();
		}

		public String nextString() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		public long nextLong() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public int nextInt() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public int[] nextIntArray(int n) {
			int[] arr = new int[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nextInt();
			}
			return arr;
		}

		public long[] nextLongArray(int n) {
			long[] arr = new long[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nextLong();
			}
			return arr;
		}

		private boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		private boolean isEndOfLine(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}
	}
}