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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.Scanner;
//import java.util.ArrayList;
class Main {

    static int n;
    static int m;
    public static void main(String[] args) {
        Scanner stdIn = new Scanner(System.in);
        
        n = stdIn.nextInt();
        m = stdIn.nextInt();
        int[][] a = new int[n][m];

        for(int i = 0;i < n ;i++){
            for(int j = 0;j<m;j++){
                a[i][j] = stdIn.nextInt();
            }
        }

        for(int j = 0;j < m;j++) {
            int[] g = new int[n];
            for(int i = 0;i < n;i++){
                g[i] = gyou(a[i][j]);
            }
            for(int i = 0;i < n;i++) {
                for(int k = 0;k < i;k++){
                    if(g[i] == g[k]){
                        //a[i][j]をa[i][h]と入れ替える gyou(a[i][h])がg[k]のいずれでもないように(h > j)
                        for(int h = j+1;h < m;h++){
                            int check = 0;
                            for(int l = 0;l <= k;l++){
                                if(gyou(a[i][h]) == g[l]){
                                    break;
                                }
                                if(l == k) {
                                    int x = a[i][j];
                                    a[i][j] = a[i][h];
                                    a[i][h] = x;
                                    g[i] = gyou(a[i][j]);
                                    check = 1;
                                }
                            }
                            if(check == 1){
                                break;
                            }
                        }
                    }
                }
            }
        }

        for(int i = 0;i < n;i++) {
            for(int j = 0;j < m;j++) {
                System.out.println(a[i][j]);
            }
        }

        for(int j = 0;j < m;j++){
            int g[] = new int[n];
            for(int i = 0;i < n;i++) {
                g[i] = gyou(a[i][j]);
            }
            for(int i = 0;i < n;i++){
                if(g[i] != i){
                    for(int h = i+1;h < n;h++){
                        if(g[h] == i){
                            int x = a[i][j];
                            a[i][j] = a[h][j];
                            a[h][j] = x;
                            //break;
                        }
                    }
                }
            }
        }

        for(int i = 0;i < n;i++) {
            for(int j = 0;j < m;j++) {
                System.out.println(a[i][j]);
            }
        }
    }

    static int gyou(int n){
        int count = 0;
        while(n > m){
            n -= m;
            count++;
        }
        return count;
    }

}