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++14 (Clang 3.8.0) (judge verdict: Time Limit Exceeded)

#include<iostream>
#include<vector>
#include<cstring>
#include<algorithm>
#include<cmath>
#include<random>
#include<ctime>
#define ll long long
#define mp make_pair
using namespace std;
int n,m;
int a[111][111];
vector<int>nbel[111];
int bgst;
inline int geth(int x){return (x-1)/m+1;}
int main(){
	cin>>n>>m;
	srand(time(NULL));
	int mxsz=0;
	for(int i=1;i<=n;++i)for(int j=1;j<=m;++j){
		cin>>a[i][j];
		if(geth(a[i][j])!=i)nbel[i].push_back(a[i][j]),mxsz=max(mxsz,int(nbel[i].size()));
	}
//	cout<<"###  "<<smaller(1,6)<<endl;
	for(int k=2;k<=n;++k){
		while(1){
			bool ok=1;
			random_shuffle(a[k]+1,a[k]+m+1);
			for(int j=1;j<=m;++j){
				for(int i=1;i<k;++i)if(geth(a[i][j])==geth(a[k][j])){
					ok=0;
					break;
				}
			}
			if(ok)break;
		}
	}
	for(int i=1;i<=n;++i){
		for(int j=1;j<=m;++j)cout<<a[i][j]<<' ';
		cout<<endl;
	}
	for(int j=1;j<=m;++j){
		for(int i=1;i<=n;++i){
			for(int k=i+1;k<=n;++k){
				if(a[k][j]<a[i][j])swap(a[i][j],a[k][j]);
			}
		}
	}
	for(int i=1;i<=n;++i){
		for(int j=1;j<=m;++j)cout<<a[i][j]<<' ';
		cout<<endl;
	}
}
/*
3 3
1 6 2
3 9 5
4 7 8
*/