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:

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

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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 static java.lang.Math.*;
public class Main {
    static final long MOD = 1_000_000_007, INF = 1_000_000_000_000_000_000L;
    static final int INf = 1_000_000_000;
    static FastReader reader;
    static PrintWriter writer;
    public static void main(String[] args) {
        Thread t = new Thread(null, new O(), "Integer.MAX_VALUE", 100000000);
        t.start();
    }
    static class O implements Runnable {
        public void run() {
            try {
                magic();
            }
            catch (Exception e) {
                e.printStackTrace();
                System.exit(1);
            }
        }
    }
    static class FastReader {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

        public FastReader() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public FastReader(String file_name) throws IOException {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public String readLine() throws IOException {
            byte[] buf = new byte[1000000];
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n') break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public int nextInt() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ') c = read();
            boolean neg = (c == '-');
            if (neg) c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg) return -ret;
            return ret;
        }

        public long nextLong() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ') c = read();
            boolean neg = (c == '-');
            if (neg) c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg) return -ret;
            return ret;
        }

        public double nextDouble() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ') c = read();
            boolean neg = (c == '-');
            if (neg) c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (c == '.') while ((c = read()) >= '0' && c <= '9') ret += (c - '0') / (div *= 10);
            if (neg) return -ret;
            return ret;
        }

        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1) buffer[0] = -1;
        }

        private byte read() throws IOException {
            if (bufferPointer == bytesRead) fillBuffer();
            return buffer[bufferPointer++];
        }

        public void close() throws IOException {
            if (din == null) return;
            din.close();
        }
    }
    static int n, freq[] = new int[1001];
    static LinkedList<Integer> freq_multiple_of_4, freq_multiple_of_2, freq_odd;
    static LinkedList<Pair> odd_pos, pos_2, pos_4;
    static void magic() throws IOException{
        reader = new FastReader();
        writer = new PrintWriter(System.out, true);
        n = reader.nextInt();
        int N = n*n;
        for(int i=0;i<N;++i) {
            ++freq[reader.nextInt()];
        }
        freq_multiple_of_4 = new LinkedList<>();
        freq_multiple_of_2 = new LinkedList<>();
        freq_odd = new LinkedList<>();
        odd_pos = new LinkedList<>();
        pos_2 = new LinkedList<>();
        pos_4 = new LinkedList<>();
        for(int i=0;i<=1000;++i) {
            if(freq[i]==0) {
                continue;
            }
            if(freq[i]%4==0) {
                freq_multiple_of_4.add(i);
            }
            else if(freq[i]%2==0) {
                freq_multiple_of_2.add(i);
            }
            else {
                freq_odd.add(i);
            }
        }
        boolean done[][] = new boolean[n][n];
        int ans[][] = new int[n][n];
        for(int i=0;i<n;++i) {
            for(int j=0;j<n;++j) {
                if(done[i][j]) {
                    continue;
                }
                done[i][j] = true;
                int iska = 1;
                if(n-1-i!=i) {
                    iska++;
                }
                if(n-1-j!=j) {
                    iska*=2;
                }
                done[i][n-1-j] = true;
                done[n-1-i][n-1-j] = true;
                done[n-1-i][j] = true;
                if(iska==4) {
                    pos_4.add(new Pair(i,j));
                }
                else if(iska==2) {
                    pos_2.add(new Pair(i,j));
                }
                else {
                    odd_pos.add(new Pair(i,j));
                }
            }
        }
        while(!odd_pos.isEmpty()) {
            Pair curr = odd_pos.pollFirst();
            int x = curr.x, y = curr.y;
            if(!freq_odd.isEmpty()) {
                int val = freq_odd.pollFirst();
                freq[val]--;
                ans[x][y] = ans[x][n-1-y] = ans[n-1-x][y] = ans[n-1-x][n-1-y] = val;
                add(val);
            }
            else if(!freq_multiple_of_2.isEmpty()) {
                int val = freq_multiple_of_2.pollFirst();
                freq[val]--;
                ans[x][y] = ans[x][n-1-y] = ans[n-1-x][y] = ans[n-1-x][n-1-y] = val;
                add(val);
            }
            else if(!freq_multiple_of_4.isEmpty()) {
                int val = freq_multiple_of_4.pollFirst();
                freq[val]--;
                ans[x][y] = ans[x][n-1-y] = ans[n-1-x][y] = ans[n-1-x][n-1-y] = val;
                add(val);
            }
            else {
                writer.println("No");
                System.exit(0);
            }
        }
        while(!pos_2.isEmpty()) {
            Pair curr = pos_2.pollFirst();
            int x = curr.x, y = curr.y;
            if(!freq_multiple_of_2.isEmpty()) {
                int val = freq_multiple_of_2.pollFirst();
                freq[val]-=2;
                ans[x][y] = ans[x][n-1-y] = ans[n-1-x][y] = ans[n-1-x][n-1-y] = val;
                add(val);
            }
            else if(!freq_multiple_of_4.isEmpty()) {
                int val = freq_multiple_of_4.pollFirst();
                freq[val]-=2;
                ans[x][y] = ans[x][n-1-y] = ans[n-1-x][y] = ans[n-1-x][n-1-y] = val;
                add(val);
            }
            else {
                writer.println("No");
                System.exit(0);
            }
        }
        while(!pos_4.isEmpty()) {
            Pair curr = pos_4.pollFirst();
            int x = curr.x, y = curr.y;
            if(!freq_multiple_of_4.isEmpty()) {
                int val = freq_multiple_of_4.pollFirst();
                freq[val]-=4;
                ans[x][y] = ans[x][n-1-y] = ans[n-1-x][y] = ans[n-1-x][n-1-y] = val;
                add(val);
            }
            else {
                writer.println("No");
                System.exit(0);
            }
        }
        writer.println("Yes");
        for(int i=0;i<n;++i) {
            for(int j=0;j<n;++j) {
                writer.print(ans[i][j]+" ");
            }
            writer.println();
        }
    }
    static void add(int val) {
        if(freq[val]==0) {
            return;
        }
        if(freq[val]%4==0) {
            freq_multiple_of_4.add(val);
        }
        else if(freq[val]%2==0) {
            freq_multiple_of_2.add(val);
        }
        else {
            freq_odd.add(val);
        }
    }
    static class Pair {
        int x,y;
        Pair(int x, int y) {
            this.x = x;
            this.y = y;
        }
    }
}