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<bits/stdc++.h>
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define SZ(x) ((int)x.size())
#define ref(i,x,y)for(int i=x;i<=y;++i)
using namespace std;
typedef long long LL;
typedef pair<int,int> PII;
int n,m,a[101][101],id[10010];int vis[101];
int s[101][101],link[101],LK[101];
bool dfs(int x){
	if(vis[x])return 0;vis[x]=1;
	ref(i,1,n)if(s[x][i]){
		if(!link[i]||dfs(link[i])){
			link[i]=x;
			return 1;
		}
	}
	return 0;
}
int main(){
	scanf("%d%d",&n,&m);
	ref(i,1,n)ref(j,1,m)scanf("%d",&a[i][j]);
	ref(i,1,n*m)id[i]=(i-1)/m+1;
	ref(i,1,m){
		memset(s,0,sizeof s);
		ref(I,1,n)ref(J,i,m)s[I][id[a[I][J]]]++;
		memset(link,0,sizeof link);
		ref(I,1,n){
			memset(vis,0,sizeof vis);
			dfs(I);
		}
		ref(I,1,n)LK[link[I]]=I;
		ref(I,1,n){
			ref(J,i,m)if(LK[I]==id[a[I][J]]){
				swap(a[I][i],a[I][J]);
				break;
			}
		}
	}
	ref(i,1,n){
		ref(j,1,m)cout<<a[i][j]<<" ";
		cout<<endl;
	}
	ref(i,1,m){
		ref(j,1,n){
			ref(k,j,n)if(id[a[k][i]]==j){
				swap(a[j][i],a[k][i]);
				break;
			}
		}
	}
	ref(i,1,n){
		ref(j,1,m)cout<<a[i][j]<<" ";
		cout<<endl;
	}
}