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.*;
import java.util.*;
import java.math.*;
import java.lang.*;
import static java.lang.Math.*;
 
public class fast implements Runnable {
    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private SpaceCharFilter filter;
        private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
 
        public InputReader(InputStream stream) {
            this.stream = stream;
        }
        
        public int read() {
            if (numChars==-1) 
                throw new InputMismatchException();
            
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                }
                catch (IOException e) {
                    throw new InputMismatchException();
                }
                
                if(numChars <= 0)               
                    return -1;
            }
            return buf[curChar++];
        }
     
        public String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            }
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
        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 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 double nextDouble() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }
        
        public String readString() {
            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 boolean isSpaceChar(int c) {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
     
        public String next() {
            return readString();
        }
        
        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }
    
    class pair implements Comparable<pair>{
        int x;
        int y;
        pair(int xi, int yi){
            x=xi;
            y=yi;
        }
        @Override
        public int compareTo(pair other){
            if(this.x>other.x){return 1;}
            if(this.x<other.x){return -1;}
            return 0;
        }    
    }
 
    class dist{
        int x;
        int y;
        int z;
        dist(int xi, int yi, int zi){
            x=xi;
            y=yi;
            z=zi;
        }
    } 
    
    public static void main(String args[]) throws Exception {
        new Thread(null, new fast(),"fast",1<<26).start();
    }
    
    public void sortbyColumn(int arr[][], final int col){ 
        // Using built-in sort function Arrays.sort 
        Arrays.sort(arr, new Comparator<int[]>() { 
            
          @Override              
          // Compare values according to columns 
          public int compare(final int[] entry1, final int[] entry2) { 
  
            // To sort in descending order revert  
            // the '>' Operator 
            if (entry1[col] > entry2[col]) 
                return 1; 
            if(entry1[col] < entry2[col])
                return -1;
            return 0;
          } 
        });  // End of function call sort(). 
    }
    
    public void sortbyColumn(long arr[][], final int col){ 
        // Using built-in sort function Arrays.sort 
        Arrays.sort(arr, new Comparator<long[]>() { 
            
          @Override              
          // Compare values according to columns 
          public int compare(final long[] entry1, final long[] entry2) { 
  
            // To sort in descending order revert  
            // the '>' Operator 
            if (entry1[col] > entry2[col]) 
                return 1; 
            if(entry1[col] < entry2[col])
                return -1;
            return 0;
          } 
        });  // End of function call sort(). 
    }
	
	public void sort(int ar[]){
		int n=ar.length;
		Integer arr[]=new Integer[n];
		for(int i=0;i<n;i++){
			arr[i]=ar[i];
		}
		Arrays.sort(arr); 
		for(int i=0;i<n;i++){
			ar[i]=arr[i].intValue();
		}
	}
	
	public void sort(long ar[]){
		int n=ar.length;
		Long arr[]=new Long[n];
		for(int i=0;i<n;i++){
			arr[i]=ar[i];
		}
		Arrays.sort(arr); 
		for(int i=0;i<n;i++){
			ar[i]=arr[i].longValue();
		}
	}
    
    long power(long x, long y, long p){  
        long res = 1;      
        x = x % p;  
        while (y > 0) 
        { 
            if((y & 1)==1) 
                res = (res * x) % p; 
            y = y >> 1;  
            x = (x * x) % p;  
        } 
        return res; 
    }
	
	long gcd(long a, long b){
		if(a>b){
			long temp=a;
			a=b;
			b=temp;
		}
		if(b%a==0){return a;}
		return gcd(b%a,a);
	}
    
    public void run(){
        InputReader s = new InputReader(System.in);
        PrintWriter w = new PrintWriter(System.out);

		int n=s.nextInt(),a[]=new int[n*n],freq[]=new int[1001],mat[][]=new int[n][n],flag=0;
		for(int i=0;i<n*n;i++){
			a[i]=s.nextInt();
			freq[a[i]]++;
		}
		if(n==1){
			w.println("YES");
			w.println(a[0]);
		}
		else if(n%2==0){
			int k;
				for(int i=0;i<n/2;i++){
					for(int j=0;j<n/2;j++){
						for(k=1;k<1001;k++){
							if(freq[k]>3){
								mat[i][j]=k;
								mat[n-i-1][j]=k;
								mat[n-i-1][n-j-1]=k;
								mat[i][n-j-1]=k;
								freq[k]-=4;
								break;
							}
						}
						if(k==1001){
							flag=1;
						}
					}
				}
				if(flag==1){
					w.println("NO");
				}
				else{
					w.println("YES");
					for(int i=0;i<n;i++){
						for(int j=0;j<n;j++){
							w.print(mat[i][j]+" ");
						}w.println();
					}
				}
				
		}
		else{
			int k;
				for(int i=0;i<n/2;i++){
					for(int j=0;j<n/2;j++){
						for(k=1;k<1001;k++){
							if(freq[k]>3){
								//w.println(k);
								mat[i][j]=k;
								mat[n-i-1][j]=k;
								mat[n-i-1][n-j-1]=k;
								mat[i][n-j-1]=k;
								freq[k]-=4;
								break;
							}
						}
						if(k==1001){
							flag=1;
							break;
						}
					}
				}
				
				for(int i=0;i<n/2;i++){
					for(k=1;k<1001;k++){
						if(freq[k]>1){
							mat[i][n/2]=k;
							mat[n-i-1][n/2]=k;
							freq[k]-=2;
							break;
						}
					}
					if(k==1001){
						flag=1;
					}
				}
				
				for(int i=0;i<n/2;i++){
					for(k=1;k<1001;k++){
						if(freq[k]>1){
							mat[n/2][i]=k;
							mat[n/2][n-i-1]=k;
							freq[k]-=2;
							break;
						}
					}
					if(k==1001){
						flag=1;
				}
				}
				for(k=1;k<1001;k++){
					if(freq[k]>0){
						mat[n/2][n/2]=k;
						freq[k]-=1;
						break;
					}
				}
				if(k==1001){
					flag=1;
				}
				if(flag==1){
					w.println("NO");
				}
				else{
					w.println("YES");
					for(int i=0;i<n;i++){
						for(int j=0;j<n;j++){
							w.print(mat[i][j]+" ");
						}w.println();
					}
				}
				
			
		}
        
        w.close();
    }
}