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.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.PriorityQueue;
import java.util.HashMap;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.util.Map;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        ReaderFastIO in = new ReaderFastIO(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        CPalindromicMatrix solver = new CPalindromicMatrix();
        solver.solve(1, in, out);
        out.close();
    }

    static class CPalindromicMatrix {
        private static PrintWriter out;
        private int[][] m;
        private PriorityQueue<Pair> queue;

        public void solve(int testNumber, ReaderFastIO in, PrintWriter out) {

            this.out = out;
            int n = in.nextInt();
            m = new int[n][n];

            Map<Integer, Integer> map = new HashMap<Integer, Integer>();
            queue = new PriorityQueue<Pair>();

            for (int i = 0; i < n * n; i++) {
                int a = in.nextInt();
                map.put(a, map.getOrDefault(a, 0) + 1);
            }

            map.forEach((key, value) -> queue.add(new Pair(value, key)));

            boolean possible = true;

            for (int i = 0; i < n / 2; i++) {
                for (int j = 0; j < n / 2; j++) {
                    possible = possible && fill(new int[][]{{i, j}, {i, rev(j, n)}, {rev(i, n), j}, {rev(i, n), rev(j, n)}});
                }
            }

            if (n % 2 == 1) {
                for (int i = 0; i < n / 2; i++) {
                    possible = possible && fill(new int[][]{{i, (n - 1) / 2}, {rev(i, n), (n - 1) / 2}});
                    possible = possible && fill(new int[][]{{(n - 1) / 2, i}, {(n - 1) / 2, rev(i, n)}});
                }

                possible = possible && fill(new int[][]{{(n - 1) / 2, (n - 1) / 2}});
            }

            if (possible == false) {
                out.println("NO");
            } else {
                out.println("YES");
                print(m);
            }

        }

        public void print(int[][] m) {
            for (int i = 0; i < m.length; i++) {
                for (int j = 0; j < m[i].length; j++) {
                    out.print(m[i][j] + " ");
                }
                out.println();
            }
        }

        public boolean fill(int[][] coords) {

            Pair pair = queue.poll();

            if (pair.getKey() < coords.length) {
                return false;
            }

            for (int i = 0; i < coords.length; i++) {
                m[coords[i][0]][coords[i][1]] = pair.getValue();
            }

            queue.add(new Pair(pair.getKey() - coords.length, pair.getValue()));

            return true;
        }

        public int rev(int i, int n) {
            return n - 1 - i;
        }

    }

    static class Pair implements Comparable<Pair> {
        private int key;
        private int value;

        public Pair(int key, int value) {
            this.key = key;
            this.value = value;
        }

        public int getKey() {
            return key;
        }

        public int getValue() {
            return value;
        }

        public int compareTo(Pair p) {

            if (this.key == p.key) return Integer.compare(this.value, p.value);

            return -Integer.compare(this.key, p.key);
        }

    }

    static class ReaderFastIO {
        BufferedReader br;
        StringTokenizer st;

        public ReaderFastIO() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public ReaderFastIO(InputStream input) {
            br = new BufferedReader(new InputStreamReader(input));
        }

        public String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }
}