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 CPP):

Solution:
#include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <algorithm>
#include <vector>

using namespace std;
typedef long long ll;
const int MAXN = 505;
int n,m,a[MAXN][MAXN];
vector<int> gr[MAXN][MAXN];
inline void addEdge(int u, int v, int c)
	{ gr[u][v].push_back(c), gr[v][u].push_back(c); }
int match[MAXN<<2];
bool vis[MAXN<<2];
inline bool dfs(int u)
{
	for(int i = n+1; i<=2*n; i++)
		if(!vis[i]&&!gr[u][i].empty())
		{
			vis[i] = true;
			if(match[i]<0||dfs(match[i]))
			{
				match[i] = u;
				return true;
			}
		}
	return false;
}
inline int calc(int x)
	{ return (x-1)/m+1; }
int ansb[MAXN][MAXN],tmp[MAXN],ansc[MAXN][MAXN];

int main()
{
	cin >> n >> m;
	for(int i = 1; i<=n; i++)
		for(int j = 1; j<=m; j++)
			cin >> a[i][j];
	for(int i = 1; i<=n; i++)
		for(int j = 1; j<=m; j++)
			addEdge(i,n+calc(a[i][j]),a[i][j]);
	for(int i = 1; i<=m; i++)
	{
		memset(match,-1,sizeof(match));
		for(int j = 1; j<=n; j++)
		{
			memset(vis,0,sizeof(vis));
			dfs(j);
		}
		for(int j = n+1; j<=2*n; j++)
		{	
			ansb[match[j]][i] = gr[j][match[j]][gr[j][match[j]].size()-1];
			gr[j][match[j]].pop_back(), gr[match[j]][j].pop_back();
		}
	}	
	for(int i = 1; i<=m; i++)
	{
		for(int j = 1; j<=n; j++)
			tmp[j] = ansb[j][i];
		sort(tmp+1,tmp+n+1);
		for(int j = 1; j<=n; j++)
			ansc[j][i] = tmp[j]; 
	}
	for(int i = 1; i<=n; i++)
	{
		for(int j = 1; j<=m; j++)
			cout << ansb[i][j] << " ";
		cout << endl;
	}
	for(int i = 1; i<=n; i++)
	{
		for(int j = 1; j<=m; j++)
			cout << ansc[i][j] << " ";
		cout << endl;	
	}
	return 0;
}