Problem: We have a grid with N rows and M columns of squares. Each integer from 1 to NM is written in this grid once. The number written in the square at the i-th row from the top and the j-th column from the left is A_{ij}.

You need to rearrange these numbers as follows:

1. First, for each of the N rows, rearrange the numbers written in it as you like.
2. Second, for each of the M columns, rearrange the numbers written in it as you like.
3. Finally, for each of the N rows, rearrange the numbers written in it as you like.



After rearranging the numbers, you want the number written in the square at the i-th row from the top and the j-th column from the left to be M\times (i-1)+j. Construct one such way to rearrange the numbers. The constraints guarantee that it is always possible to achieve the objective.

Constraints

* 1 \leq N,M \leq 100
* 1 \leq A_{ij} \leq NM
* A_{ij} are distinct.

Input

Input is given from Standard Input in the following format:


N M
A_{11} A_{12} ... A_{1M}
:
A_{N1} A_{N2} ... A_{NM}


Output

Print one way to rearrange the numbers in the following format:


B_{11} B_{12} ... B_{1M}
:
B_{N1} B_{N2} ... B_{NM}
C_{11} C_{12} ... C_{1M}
:
C_{N1} C_{N2} ... C_{NM}


Here B_{ij} is the number written in the square at the i-th row from the top and the j-th column from the left after Step 1, and C_{ij} is the number written in that square after Step 2.

Examples

Input

3 2
2 6
4 3
1 5


Output

2 6
4 3
5 1
2 1
4 3
5 6


Input

3 4
1 4 7 10
2 5 8 11
3 6 9 12


Output

1 4 7 10
5 8 11 2
9 12 3 6
1 4 3 2
5 8 7 6
9 12 11 10

Solution (in JAVA):

Solution:

import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.nio.charset.Charset;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;

public class Main {
    public static void main(String[] args) throws Exception {
        boolean local = false;
        boolean async = false;

        Charset charset = Charset.forName("ascii");

        FastIO io = local ? new FastIO(new FileInputStream("D:\\DATABASE\\TESTCASE\\Code.in"), System.out, charset) : new FastIO(System.in, System.out, charset);
        Task task = new Task(io, new Debug(local));

        if (async) {
            Thread t = new Thread(null, task, "dalt", 1 << 27);
            t.setPriority(Thread.MAX_PRIORITY);
            t.start();
            t.join();
        } else {
            task.run();
        }

        if (local) {
            io.cache.append("\n\n--memory -- \n" + ((Runtime.getRuntime().totalMemory() - Runtime.getRuntime().freeMemory()) >> 20) + "M");
        }

        io.flush();
    }

    public static class Task implements Runnable {
        final FastIO io;
        final Debug debug;
        int inf = (int) 1e8;

        public Task(FastIO io, Debug debug) {
            this.io = io;
            this.debug = debug;
        }

        @Override
        public void run() {
            solve();
        }

        int n;
        int m;

        public void solve() {
            n = io.readInt();
            m = io.readInt();
            int[][] grids = new int[n][m];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    grids[i][j] = io.readInt();
                }
            }

            KMAlgo km = new KMAlgo(n, n);
            for (int c = 0; c < m; c++) {
                km.reset();
                for (int i = 0; i < n; i++) {
                    for (int j = c; j < m; j++) {
                        km.edges[i][rowIdOf(grids[i][j])] = true;
                    }
                }
                for (int i = 0; i < n; i++) {
                    km.matchLeft(i);
                }
                for (int i = 0; i < n; i++) {
                    int rowId = km.leftSides[i].partner.id;
                    for (int j = c; j < m; j++) {
                        if (rowIdOf(grids[i][j]) == rowId) {
                            int tmp = grids[i][j];
                            grids[i][j] = grids[i][c];
                            grids[i][c] = tmp;
                            break;
                        }
                    }
                }
            }

            printGrid(grids);

            int[][] second = new int[n][m];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    second[rowIdOf(grids[i][j])][j] = grids[i][j];
                }
            }

            printGrid(second);
        }

        public void printGrid(int[][] grids) {
            for (int[] row : grids) {
                for (int col : row) {
                    io.cache.append(col).append(' ');
                }
                io.cache.append('\n');
            }
        }

        public int rowIdOf(int x) {
            return (x - 1) / m;
        }
    }

    public static class KMAlgo {
        public static class Node {
            List<Node> nodes = new ArrayList(2);
            int visited;
            Node partner;
            int id;

            @Override
            public String toString() {
                return "" + id;
            }
        }

        Node[] leftSides;
        Node[] rightSides;
        int version;
        boolean[][] edges;

        int l;
        int r;

        public void reset() {
            for (int i = 0; i < l; i++) {
                for (int j = 0; j < r; j++) {
                    edges[i][j] = false;
                }
            }
            for (int i = 0; i < l; i++) {
                leftSides[i].partner = null;
            }
            for (int i = 0; i < r; i++) {
                rightSides[i].partner = null;
            }
        }

        public KMAlgo(int l, int r) {
            this.l = l;
            this.r = r;
            leftSides = new Node[l];
            for (int i = 0; i < l; i++) {
                leftSides[i] = new Node();
                leftSides[i].id = i;
            }
            rightSides = new Node[r];
            for (int i = 0; i < r; i++) {
                rightSides[i] = new Node();
                rightSides[i].id = i;
            }
            edges = new boolean[l][r];
        }

        public void addEdge(int lId, int rId) {
            leftSides[lId].nodes.add(rightSides[rId]);
            rightSides[rId].nodes.add(leftSides[lId]);
        }

        private void init() {
            version++;
        }

        /**
         * Determine can we find a partner for a left node to enhance the matching degree.
         */
        public boolean matchLeft(int id) {
            if (leftSides[id].partner != null) {
                return false;
            }
            init();
            return findPartner(leftSides[id]);
        }


        private boolean findPartner(Node src) {
            if (src.visited == version) {
                return false;
            }
            src.visited = version;
            for (int i = 0; i < r; i++) {
                Node node = rightSides[i];
                if (!edges[src.id][i]) {
                    continue;
                }
                if (!tryRelease(node)) {
                    continue;
                }
                node.partner = src;
                src.partner = node;
                return true;
            }
            return false;
        }

        private boolean tryRelease(Node src) {
            if (src.visited == version) {
                return false;
            }
            src.visited = version;
            if (src.partner == null) {
                return true;
            }
            if (findPartner(src.partner)) {
                src.partner = null;
                return true;
            }
            return false;
        }

        @Override
        public String toString() {
            StringBuilder builder = new StringBuilder();
            for (int i = 1; i < leftSides.length; i++) {
                if (leftSides[i].partner == null) {
                    continue;
                }
                builder.append(leftSides[i].id).append(" - ").append(leftSides[i].partner.id).append(" || ");
            }
            if (builder.length() > 0) {
                builder.setLength(builder.length() - 4);
            }
            return builder.toString();
        }
    }

    public static class FastIO {
        public final StringBuilder cache = new StringBuilder(1 << 13);
        private final InputStream is;
        private final OutputStream os;
        private final Charset charset;
        private StringBuilder defaultStringBuf = new StringBuilder(1 << 13);
        private byte[] buf = new byte[1 << 13];
        private int bufLen;
        private int bufOffset;
        private int next;

        public FastIO(InputStream is, OutputStream os, Charset charset) {
            this.is = is;
            this.os = os;
            this.charset = charset;
        }

        public FastIO(InputStream is, OutputStream os) {
            this(is, os, Charset.forName("ascii"));
        }

        private int read() {
            while (bufLen == bufOffset) {
                bufOffset = 0;
                try {
                    bufLen = is.read(buf);
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
                if (bufLen == -1) {
                    return -1;
                }
            }
            return buf[bufOffset++];
        }

        public void skipBlank() {
            while (next >= 0 && next <= 32) {
                next = read();
            }
        }

        public int readInt() {
            int sign = 1;

            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+' ? 1 : -1;
                next = read();
            }

            int val = 0;
            if (sign == 1) {
                while (next >= '0' && next <= '9') {
                    val = val * 10 + next - '0';
                    next = read();
                }
            } else {
                while (next >= '0' && next <= '9') {
                    val = val * 10 - next + '0';
                    next = read();
                }
            }

            return val;
        }

        public long readLong() {
            int sign = 1;

            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+' ? 1 : -1;
                next = read();
            }

            long val = 0;
            if (sign == 1) {
                while (next >= '0' && next <= '9') {
                    val = val * 10 + next - '0';
                    next = read();
                }
            } else {
                while (next >= '0' && next <= '9') {
                    val = val * 10 - next + '0';
                    next = read();
                }
            }

            return val;
        }

        public double readDouble() {
            boolean sign = true;
            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+';
                next = read();
            }

            long val = 0;
            while (next >= '0' && next <= '9') {
                val = val * 10 + next - '0';
                next = read();
            }
            if (next != '.') {
                return sign ? val : -val;
            }
            next = read();
            long radix = 1;
            long point = 0;
            while (next >= '0' && next <= '9') {
                point = point * 10 + next - '0';
                radix = radix * 10;
                next = read();
            }
            double result = val + (double) point / radix;
            return sign ? result : -result;
        }

        public String readString(StringBuilder builder) {
            skipBlank();

            while (next > 32) {
                builder.append((char) next);
                next = read();
            }

            return builder.toString();
        }

        public String readString() {
            defaultStringBuf.setLength(0);
            return readString(defaultStringBuf);
        }

        public int readLine(char[] data, int offset) {
            int originalOffset = offset;
            while (next != -1 && next != '\n') {
                data[offset++] = (char) next;
                next = read();
            }
            return offset - originalOffset;
        }

        public int readString(char[] data, int offset) {
            skipBlank();

            int originalOffset = offset;
            while (next > 32) {
                data[offset++] = (char) next;
                next = read();
            }

            return offset - originalOffset;
        }

        public int readString(byte[] data, int offset) {
            skipBlank();

            int originalOffset = offset;
            while (next > 32) {
                data[offset++] = (byte) next;
                next = read();
            }

            return offset - originalOffset;
        }

        public char readChar() {
            skipBlank();
            char c = (char) next;
            next = read();
            return c;
        }

        public void flush() throws IOException {
            os.write(cache.toString().getBytes(charset));
            os.flush();
            cache.setLength(0);
        }

        public boolean hasMore() {
            skipBlank();
            return next != -1;
        }
    }

    public static class Debug {
        private boolean allowDebug;

        public Debug(boolean allowDebug) {
            this.allowDebug = allowDebug;
        }

        public void assertTrue(boolean flag) {
            if (!allowDebug) {
                return;
            }
            if (!flag) {
                fail();
            }
        }

        public void fail() {
            throw new RuntimeException();
        }

        public void assertFalse(boolean flag) {
            if (!allowDebug) {
                return;
            }
            if (flag) {
                fail();
            }
        }

        private void outputName(String name) {
            System.out.print(name + " = ");
        }

        public void debug(String name, int x) {
            if (!allowDebug) {
                return;
            }

            outputName(name);
            System.out.println("" + x);
        }

        public void debug(String name, long x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println("" + x);
        }

        public void debug(String name, double x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println("" + x);
        }

        public void debug(String name, int[] x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println(Arrays.toString(x));
        }

        public void debug(String name, long[] x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println(Arrays.toString(x));
        }

        public void debug(String name, double[] x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println(Arrays.toString(x));
        }

        public void debug(String name, Object x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println("" + x);
        }

        public void debug(String name, Object... x) {
            if (!allowDebug) {
                return;
            }
            outputName(name);
            System.out.println(Arrays.deepToString(x));
        }
    }
}