Problem:
Score : 1100 points

Problem Statement

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:

First, for each of the N rows, rearrange the numbers written in it as you like.

Second, for each of the M columns, rearrange the numbers written in it as you like.

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.

Sample Input 1

3 2
2 6
4 3
1 5

Sample Output 1

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

Sample Input 2

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

Sample Output 2

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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

//author: camypaper
using System;
using System.Linq;
using System.Collections.Generic;
using System.Text.RegularExpressions;
using Debug = System.Diagnostics.Debug;
using SB = System.Text.StringBuilder;
using System.Numerics;
using Point = System.Numerics.Complex;
using static System.Math;
using C = System.Int32;

namespace Program {
    public class Solver {
        Random rnd = new Random(0);
        public void Solve() {
            var n = ri;
            var m = ri;
            var a = Enumerate(n, x => new int[m]);
            var used = Enumerate(n, x => new bool[m]);
            var col = Enumerate(n, x => Enumerate(n, y => new Queue<int>()));
            for (int i = 0; i < n; i++)
                for (int j = 0; j < m; j++) {
                    a[i][j] = ri - 1;
                    col[i][a[i][j] / m].Enqueue(a[i][j] + 1);
                }

            var b = Enumerate(n, x => new List<int>());

            for (int T = 0; T < m; T++) {
                var mf = new MaxFlow(2 * n + 2);
                var src = 2 * n;
                var sink = src + 1;
                for (int i = 0; i < n; i++) {
                    mf.AddDirectedEdge(src, i, 1);
                    for (int j = 0; j < n; j++)
                        if (col[i][j].Count != 0)
                            mf.AddDirectedEdge(i, n + j, 1);
                }
                for (int j = 0; j < n; j++)
                    mf.AddDirectedEdge(n + j, sink, 1);
                var res = mf.Execute(src, sink, n);
                Debug.WriteLine(res);
                for (int i = 0; i < n; i++)
                    foreach (var e in mf.G[i])
                        if (e.To >= n && e.Cap != 1) {
                            b[i].Add(col[i][e.To - n].Dequeue());
                        }
            }
            foreach (var x in b)
                Console.WriteLine(x.AsJoinedString());
            var c = Enumerate(n, x => new int[m]);
            for (int i = 0; i < n; i++)
                for (int j = 0; j < m; j++)
                    c[(b[i][j] - 1) / m][j] = b[i][j];
            foreach (var x in c)
                Console.WriteLine(x.AsJoinedString());
        }
        const long INF = 1L << 60;
        int ri => sc.Integer();
        long rl => sc.Long();
        double rd => sc.Double();
        string rs => sc.Scan();
        public IO.StreamScanner sc = new IO.StreamScanner(Console.OpenStandardInput());

        static IEnumerable<int> Rep(int n) => Enumerable.Range(0, n);
        static IEnumerable<int> RRep(int n) => Enumerable.Range(0, n).Reverse();
        static T[] Enumerate<T>(int n, Func<int, T> f) {
            var a = new T[n];
            for (int i = 0; i < a.Length; ++i) a[i] = f(i);
            return a;
        }
        static public void Swap<T>(ref T a, ref T b) { var tmp = a; a = b; b = tmp; }
    }
}

#region main
static class Ex {
    static public string AsString(this IEnumerable<char> ie) { return new string(ie.ToArray()); }
    static public string AsJoinedString<T>(this IEnumerable<T> ie, string st = " ") {
        return string.Join(st, ie);
    }
    static public void Main() {
        Console.SetOut(new Program.IO.Printer(Console.OpenStandardOutput()) { AutoFlush = false });
        var solver = new Program.Solver();
        solver.Solve();
        Console.Out.Flush();
    }
}
#endregion
#region Ex
namespace Program.IO {
    using System.IO;
    using System.Text;
    using System.Globalization;

    public class Printer : StreamWriter {
        public override IFormatProvider FormatProvider => CultureInfo.InvariantCulture;
        public Printer(Stream stream) : base(stream, new UTF8Encoding(false, true)) { }
    }

    public class StreamScanner {
        public StreamScanner(Stream stream) { str = stream; }

        public readonly Stream str;
        private readonly byte[] buf = new byte[1024];
        private int len, ptr;
        public bool isEof = false;

        private byte read() {
            if (isEof) return 0;
            if (ptr >= len) {
                ptr = 0;
                if ((len = str.Read(buf, 0, 1024)) <= 0) {
                    isEof = true;
                    return 0;
                }
            }
            return buf[ptr++];
        }

        public char Char() {
            byte b = 0;
            do b = read(); while ((b < 33 || 126 < b) && !isEof);
            return (char)b;
        }
        public string Scan() {
            var sb = new StringBuilder();
            for (var b = Char(); b >= 33 && b <= 126; b = (char)read()) sb.Append(b);
            return sb.ToString();
        }
        public string ScanLine() {
            var sb = new StringBuilder();
            for (var b = Char(); b != '\n' && b != 0; b = (char)read()) if (b != '\r') sb.Append(b);
            return sb.ToString();
        }
        public long Long() { return isEof ? long.MinValue : long.Parse(Scan()); }
        public int Integer() { return isEof ? int.MinValue : int.Parse(Scan()); }
        public double Double() { return isEof ? double.NaN : double.Parse(Scan(), CultureInfo.InvariantCulture); }
    }
}

#endregion

#region Max Flow
/// <summary>
/// 辺の追加を行い，最大流を求めることが可能なグラフです．
/// </summary>
public class MaxFlow {
    public readonly List<Edge>[] G;
    readonly int[] lv, iter;
    /// <summary>
    /// 頂点数 <paramref name="V"/> で辺が存在しないグラフを構築します．
    /// </summary>
    /// <param name="V">頂点の数</param>
    /// <remarks>この操作は O(<paramref name="V"/>) で実行されます．</remarks>
    public MaxFlow(int V) {
        G = new List<Edge>[V];
        lv = new int[V];
        iter = new int[V];
        for (int i = 0; i < G.Length; i++)
            G[i] = new List<Edge>();
    }

    /// <summary>
    /// 頂点 <paramref name="from"/> から頂点 <paramref name="to"/> への容量 <paramref name="cap"/> の有向辺を追加します．
    /// </summary>
    /// <param name="from">始点となる頂点の 0-indexed での番号</param>
    /// <param name="to">終点となる頂点の 0-indexed での番号</param>
    /// <param name="cap">辺の容量</param>
    /// <remarks>この操作は O(1) で実行されます．</remarks>
    public void AddDirectedEdge(int from, int to, C cap) {
        addEdge(from, to, cap, 0);
    }

    /// <summary>
    /// 頂点 <paramref name="from"/> から頂点 <paramref name="to"/> への容量 <paramref name="cap"/> の無向辺を追加します．
    /// </summary>
    /// <param name="from">始点となる頂点の 0-indexed での番号</param>
    /// <param name="to">終点となる頂点の 0-indexed での番号</param>
    /// <param name="cap">辺の容量</param>
    /// <remarks>この操作は O(1) で実行されます．</remarks>
    public void AddUndirectedEdge(int from, int to, C cap) {
        addEdge(from, to, cap, cap);
    }
    void addEdge(int f, int t, C c1, C c2) {
        var a = new Edge(t, c1);
        var b = new Edge(f, c2);
        Edge.Link(a, b);
        G[f].Add(a);
        G[t].Add(b);
    }


    /// <summary>
    /// 頂点 <paramref name="src"/> から頂点 <paramref name="sink"/> へ最大で流量 <paramref name="f"/> だけフローを流します．
    /// </summary>
    /// <param name="src">ソースとなる頂点の 0-indexed での番号</param>
    /// <param name="sink">シンクとなる頂点の 0-indexed での番号</param>
    /// <param name="f">ソースからシンクへと流す最大の容量．-1を指定した場合，最大流を求める．</param>
    /// <remarks>この操作はDinic法に基づき，最悪計算量 O(EV^2) で実行されます．Vは頂点の数，Eは辺の数ｗ表します．</remarks>
    public C Execute(int src, int sink, C f = -1) {
        C flow = 0;
        if (f < 0) f = C.MaxValue;
        while (f > 0) {
            bfs(src);
            if (lv[sink] == 0) return flow;
            Array.Clear(iter, 0, iter.Length);
            C df;
            while ((df = dfs(src, sink, f)) > 0) { flow += df; f -= df; }
        }
        return flow;
    }

    void bfs(int s) {
        Array.Clear(lv, 0, lv.Length);
        var q = new Queue<int>();
        lv[s] = 1;
        q.Enqueue(s);
        while (q.Count > 0) {
            var v = q.Dequeue();
            foreach (var e in G[v])
                if (e.Cap > 0 && lv[e.To] == 0) {
                    lv[e.To] = lv[v] + 1;
                    q.Enqueue(e.To);
                }
        }

    }
    C dfs(int v, int t, C f) {
        if (v == t) return f;
        C ret = 0;
        for (; iter[v] < G[v].Count; iter[v]++) {
            var e = G[v][iter[v]];
            if (e.Cap <= 0 || lv[v] >= lv[e.To]) continue;
            C df = dfs(e.To, t, Math.Min(f, e.Cap));
            if (df <= 0) continue;
            e.Cap -= df;
            e.Rev.Cap += df;
            ret += df; f -= df;
            if (f == 0) break;
        }
        return ret;

    }
    public class Edge {
        public static void Link(Edge e1, Edge e2) {
            e1.Rev = e2; e2.Rev = e1;
        }
        public int To { get; private set; }
        public Edge Rev { get; private set; }
        public C Cap { get; set; }
        public Edge(int t, C c) {
            To = t;
            Cap = c;
        }
        public override string ToString() {
            return string.Format("to: {0}, cap: {1}", To, Cap);
        }
    }


}
#endregion