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:
//package sept;

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



public class TimePass implements Runnable {
    InputStream is;
    PrintWriter out;
    String INPUT = "";
    //boolean debug=false;
    boolean debug=true;
    static long mod=998244353;
    static long mod2=1000000007;
    
    void solve() throws IOException
	{
	    int n=ni();
	    int[] a=na(n*n);
	    int[][] mat=new int[n][n];
	    int cnt4=n*n;
	    if(n%2!=0)cnt4-=(n-1)*2+1;
	    cnt4/=4;
	    int[] cnt=new int[1001];
	    for(int i=0;i<n*n;i++)
	    {
	        cnt[a[i]]++;
	    }
	    ArrayList<Integer> l1=new ArrayList<>();
	    ArrayList<Integer> l2=new ArrayList<>();
	    for(int i=0;i<=1000;i++)
	    {
	        if(cnt[i]>=4)
	        {
	            int c=cnt[i];
	            for(int j=0;j<c/4;j++)
	            {
	                if(l1.size()==cnt4)break;
	                l1.add(i);
	                cnt[i]-=4;
	            }
	            if(l1.size()==cnt4)break;
	        }
	    }
	    int cnt2=0;
	    if(n%2!=0)cnt2=n-1;
	    for(int i=0;i<=1000;i++)
	    {
	        if(cnt[i]>=2)
	        {
	            int c=cnt[i];
	            for(int j=0;j<c/2;j++)
	            {
	                if(l2.size()==cnt2)break;
	                l2.add(i);
	                cnt[i]-=2;
	            }
	            if(l2.size()==cnt2)break;
	        }
	    }
	    if(cnt4!=l1.size())
	    {
	        out.println("NO");
	        return;
	    }
	    if(n%2!=0 && cnt2!=l2.size())
	    {
	        out.println("NO");
	        return;
	    }
	    int ind=0;
        for(int i=0;i<n/2;i++)
        {
            for(int j=0;j<n/2;j++)
            {
                mat[i][j]=l1.get(ind);
                mat[i][n-1-j]=mat[i][j];
                mat[n-1-i][j]=mat[i][j];
                mat[n-1-i][n-1-j]=mat[i][j];
                ind++;
            }
        }
	    if(n%2!=0)
	    {
	        ind=0;
	        for(int i=0;i<(n-1)/2;i++)
	        {
	            mat[n/2][i]=l2.get(ind);
	            ind++;
	            mat[n/2][n-1-i]=mat[n/2][i];
	        }
	        for(int i=0;i<(n-1)/2;i++)
	        {
	            mat[i][n/2]=l2.get(ind);
	            ind++;
	            mat[n-1-i][n/2]=mat[i][n/2];
	        }
	        for(int i=0;i<=1000;i++)
	        {
	            if(cnt[i]!=0)
	            {
	                mat[n/2][n/2]=i;
	                break;
	            }
	        }
	    }
	    
	    out.println("YES");
        for(int i=0;i<n;i++)
        {
            for(int j=0;j<n;j++)
            {
                out.print(mat[i][j]+" ");
            }
            out.println();
        }
	}
	
	static int comp(char[] a,int st,int end)
	{
	    int len=end-st+1;
	    if(len==3)return 2;
	    if(len==2)return -1;
	    int mid=(st+end)/2;
	    if(len%2!=0)mid--;
	    int ch2=1;
	    for(int i=0;i<len;i++)
	    {
	        if(a[st+i]!=a[len-1])
	        {
	            ch2=0;
	            break;
	        }
	    }
	    if(ch2==1)
	    {
	        return -1;
	    }
	    int ch=1;
	    for(int i=0;i<len/4;i++)
	    {
	        if(a[i+st]!=a[mid-i])
	        {
	            ch=0;
	            break;
	        }
	    }
	    if(ch==1)return 2*comp(a,st,mid);
	    if(len%2==0)return 1;
	    return 2;
	}
    
    static int[] xor;
    
    static void dfs(int u,int[] a,int[][] g,int[] vis)
    {
    	xor[u]=a[u];
    	
    	vis[u]=1;
    	for(int v:g[u])
    	{
    		if(vis[v]==0)
    		{
    			dfs(v,a,g,vis);
    			xor[u]=xor[u]^xor[v];
    		}
    	}
    }

	static int[][] packD(int n,int[] from,int[] to)
	{
		int[][] g=new int[n][];
		int[] p=new int[n];
		for(int f:from)
		{
			p[f]++;
		}
		int m=from.length;
		for(int i=0;i<n;i++)
		{
			g[i]=new int[p[i]];
		}
		for(int i=0;i<m;i++)
		{
			g[from[i]][--p[from[i]]]=to[i];
		}
		return g;
	}
	    
    static class Pair
    {
        int a,b;
        public Pair(int a,int b)
        {
            this.a=a;
            this.b=b;
            //this.ind=ind;
        }
    }
    
    static long lcm(int a,int b)
    {
        long val=a;
        val*=b;
        return (val/gcd(a,b));
    }
    
    static long gcd(long a,long b)
    {
        if(a==0)return b;
        return gcd(b%a,a);
    }
    
    static int pow(int a, int b, int p)
    {
        long ans = 1, base = a;
        while (b!=0)
        {
            if ((b & 1)!=0)
            {
                ans *= base;
                ans%= p;
            }
            base *= base;
            base%= p;
            b >>= 1;
        }
        return (int)ans;
    }

    static int inv(int x, int p)
    {
        return pow(x, p - 2, p);
    }
    
    public static long[] radixSort(long[] f){ return radixSort(f, f.length); }
	public static long[] radixSort(long[] f, int n)
	{
		long[] to = new long[n];
		{
			int[] b = new int[65537];
			for(int i = 0;i < n;i++)b[1+(int)(f[i]&0xffff)]++;
			for(int i = 1;i <= 65536;i++)b[i]+=b[i-1];
			for(int i = 0;i < n;i++)to[b[(int)(f[i]&0xffff)]++] = f[i];
			long[] d = f; f = to;to = d;
		}
		{
			int[] b = new int[65537];
			for(int i = 0;i < n;i++)b[1+(int)(f[i]>>>16&0xffff)]++;
			for(int i = 1;i <= 65536;i++)b[i]+=b[i-1];
			for(int i = 0;i < n;i++)to[b[(int)(f[i]>>>16&0xffff)]++] = f[i];
			long[] d = f; f = to;to = d;
		}
		{
			int[] b = new int[65537];
			for(int i = 0;i < n;i++)b[1+(int)(f[i]>>>32&0xffff)]++;
			for(int i = 1;i <= 65536;i++)b[i]+=b[i-1];
			for(int i = 0;i < n;i++)to[b[(int)(f[i]>>>32&0xffff)]++] = f[i];
			long[] d = f; f = to;to = d;
		}
		{
			int[] b = new int[65537];
			for(int i = 0;i < n;i++)b[1+(int)(f[i]>>>48&0xffff)]++;
			for(int i = 1;i <= 65536;i++)b[i]+=b[i-1];
			for(int i = 0;i < n;i++)to[b[(int)(f[i]>>>48&0xffff)]++] = f[i];
			long[] d = f; f = to;to = d;
		}
		return f;
	}

    
    public void run()
    {
        if(debug)oj=true;
        is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        out = new PrintWriter(System.out);
        
        long s = System.currentTimeMillis();
        try {
			solve();
		} catch (IOException e) {
			// TODO Auto-generated catch block
			e.printStackTrace();
		}
        out.flush();
        tr(System.currentTimeMillis()-s+"ms");
    }
    
    public static void main(String[] args) throws Exception {new Thread(null,new TimePass(),"Main",1<<26).start();}
    
    private byte[] inbuf = new byte[1024];
    public int lenbuf = 0, ptrbuf = 0;
    
    private int readByte()
    {
        if(lenbuf == -1)throw new InputMismatchException();
        if(ptrbuf >= lenbuf){
            ptrbuf = 0;
            try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
            if(lenbuf <= 0)return -1;
        }
        return inbuf[ptrbuf++];
    }
    
    private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
    private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
    
    private double nd() { return Double.parseDouble(ns()); }
    private char nc() { return (char)skip(); }
    
    private String ns()
    {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    
    private char[] ns(int n)
    {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while(p < n && !(isSpaceChar(b))){
            buf[p++] = (char)b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }
    
    private char[][] nm(int n, int m)
    {
        char[][] map = new char[n][];
        for(int i = 0;i < n;i++)map[i] = ns(m);
        return map;
    }
    
    private int[] na(int n)
    {
        int[] a = new int[n];
        for(int i = 0;i < n;i++)a[i] = ni();
        return a;
    }
    
    private int ni()
    {
        int num = 0, b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }
        
        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    private long nl()
    {
        long num = 0;
        int b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }
        
        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
    private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}