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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

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

    static class CPalindromicMatrix {
        public void solve(int testNumber, InputReader in, OutputWriter out) {

            int n = in.nextInt();

            int[] a = in.nextIntArray(n * n);

            int[] h = new int[1001];

            for (int val : a) {
                h[val]++;
            }

            int[][] ans = new int[n][n];

            if (n % 2 == 1) {
                int val = -1;
                for (int i = 1; i <= 1000; i++) {
                    if (h[i] % 4 == 1) {
                        val = i;
                        break;
                    } else if (h[i] % 4 == 3) {
                        val = i;
                        break;
                    }
                }

                if (val != -1) {
                    ans[n / 2][n / 2] = val;
                    h[val]--;
                } else {
                    out.println("NO");
                    return;
                }

                //row n/2
                for (int i = 0; i < n / 2; i++) {
                    val = -1;
                    for (int j = 1; j <= 1000; j++) {
                        if (h[j] % 4 == 2) {
                            val = j;
                            break;
                        } else if (h[j] % 4 == 0 && h[j] >= 2) {
                            if (val == -1) {
                                val = j;

                            }
                        }
                    }

                    if (val != -1) {
                        ans[n / 2][i] = val;
                        int d = n / 2 - i;
                        ans[n / 2][n / 2 + d] = val;
                        h[val] -= 2;
                    } else {
                        out.println("NO");
                        return;
                    }
                }


                //col n/2
                for (int i = 0; i < n / 2; i++) {
                    val = -1;
                    for (int j = 1; j <= 1000; j++) {
                        if (h[j] % 4 == 2) {
                            val = j;
                            break;
                        } else if (h[j] % 4 == 0 && h[j] >= 2) {
                            if (val == -1) {
                                val = j;

                            }
                        }
                    }

                    if (val != -1) {
                        ans[i][n / 2] = val;
                        int d = n / 2 - i;
                        ans[n / 2 + d][n / 2] = val;
                        h[val] -= 2;
                    } else {
                        out.println("NO");
                        return;
                    }
                }

                for (int i = 0; i < n / 2; i++) {
                    for (int j = 0; j < n / 2; j++) {
                        boolean f = false;
                        for (int k = 1; k <= 1000; k++) {
                            if (h[k] >= 4) {
                                f = true;
                                ans[i][j] = k;
                                int dx = n / 2 - i;
                                int dy = n / 2 - j;

                                ans[i][n / 2 + dy] = k;
                                ans[n / 2 + dx][j] = k;
                                ans[n / 2 + dx][n / 2 + dy] = k;
                                h[k] -= 4;
                                break;
                            }
                        }
                        if (!f) {
                            out.println("NO");
                            return;
                        }
                    }
                }
            } else {

                for (int i = 0; i < n / 2; i++) {
                    for (int j = 0; j < n / 2; j++) {
                        boolean f = false;
                        for (int k = 1; k <= 1000; k++) {
                            if (h[k] >= 4) {
                                f = true;
                                ans[i][j] = k;
                                int dx = n / 2 - i;
                                int dy = n / 2 - j;

                                ans[i][n / 2 + dy - 1] = k;
                                ans[n / 2 + dx - 1][j] = k;
                                ans[n / 2 + dx - 1][n / 2 + dy - 1] = k;
                                h[k] -= 4;
                                break;
                            }
                        }
                        if (!f) {
                            out.println("NO");
                            return;
                        }
                    }
                }
            }

            out.println("YES");

            for (int i = 0; i < n; i++) {
                for (int j = 0; j < n; j++) {
                    out.print(ans[i][j] + " ");
                }
                out.println();
            }
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        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 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 boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

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

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static class OutputWriter {
        private final PrintWriter writer;

        public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }

        public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
        }

        public void print(Object... objects) {
            for (int i = 0; i < objects.length; i++) {
                if (i != 0) {
                    writer.print(' ');
                }
                writer.print(objects[i]);
            }
        }

        public void println() {
            writer.println();
        }

        public void println(Object... objects) {
            print(objects);
            writer.println();
        }

        public void close() {
            writer.close();
        }

    }
}