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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace test
{
    class Program
    {
        static void Main(string[] args)
        {
            string[] h2 = Console.ReadLine().Split(' ');
            int N = int.Parse(h2[0]);
            int M = int.Parse(h2[1]);
            int[,] A = new int[M, N];
            int[,] B = new int[M, N];
            int[] T = new int[M];
            int[] U = new int[N];
            int[,] C = new int[M, N];
            for (var i = 0; i < N; i++)
            {
                string[] input = Console.ReadLine().Split(' ');
                for (var j = 0; j < input.Length; j++)
                {
                    T[j] = int.Parse(input[j]);
                }
                var S = T.ToList();
                S.Sort();
                for (var j = 0; j < S.Count(); j++)
                {
                    A[j, i] = S[j];
                    B[j, i] = (S[j]-1)/M;
                }
            }
            for (var i = 0; i < N; i++)
            {
                for (var j = 0; j < M; j++)
                {
                    C[j, B[j, i]]++;
                }
            }
            for (var k0 = 0; k0 < N; k0++)
            {
                bool complete = true;
                for (var j = 0; j < M; j++)
                {
                    for (var k = 0; k < N; k++)
                    {
                        if (C[j, k] == 0)
                        {
                            bool hit = false;
                            for (var j2 = j + 1; j2 < M && !hit; j2++)
                            {
                                if (C[j2, k] > 1)
                                {
                                    for (var k2 = 0; k2 < N; k2++)
                                    {
                                        if (B[j2, k2] == k)
                                        {
                                            var tmpA = A[j, k2];
                                            A[j, k2] = A[j2, k2];
                                            A[j2, k2] = tmpA;
                                            var tmpB = B[j, k2];
                                            B[j, k2] = B[j2, k2];
                                            B[j2, k2] = tmpB;
                                            C[j, k]++;
                                            C[j2, k]--;
                                            C[j, tmpB]--;
                                            C[j2, tmpB]++;
                                            hit = true;
                                            break;
                                        }
                                    }
                                }
                            }
                            if (!hit)
                            {
                                complete = false;
                            }
                        }
                    }
                }
                if (complete) break;
            }
            for (var k = 0; k < N; k++)
            {
                for (var j = 0; j < M; j++)
                {
                    T[j] = A[j, k];
                }
                string l = string.Join(" ", T);
                Console.WriteLine(l);
            }
            for (var j = 0; j < M; j++)
            {
                for (var k = 0; k < N; k++)
                {
                    U[k] = A[j, k];
                }
                var S = U.ToList();
                S.Sort();
                for (var k = 0; k < N; k++)
                {
                    A[j, k] = S[k];
                }
            }
            for (var k = 0; k < N; k++)
            {
                for (var j = 0; j < M; j++)
                {
                    T[j] = A[j, k];
                }
                string l = string.Join(" ", T);
                Console.WriteLine(l);
            }
        }
    }
}