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>
        using namespace std;
   #define int long long
   #define PP pair<int,pair<int,int>>
const int MAX = 510000;
const int MOD =  998244353;
const int INV2 = (MOD+1)/2;

     signed main(){
       int n,m;
       cin>>n>>m;
       int a[n][m];pair<int,int>ichi[n*m+1];
       for(int i=0;i<n;i++)for(int j=0;j<m;j++){
         cin>>a[i][j];
        ichi[a[i][j]]=make_pair(i,j);
       }
       int ten[n][m];
       for(int i=1;i<=n*m;i++){
         ten[(i-1)/m][(i-1)%m]=ichi[i].first;
         int i0=a[ichi[i].first][(i-1)%m],j=ichi[i].second,i1=ichi[i].first;
         if(j==(i-1)%m)continue;
         swap(a[ichi[i].first][(i-1)%m],a[ichi[i].first][ichi[i].second]);
         while((i0-1)/m<(i-1)/m){
           swap(a[ten[(i0-1)/m][j]][j],a[ten[(i0-1)/m][j]][(i-1)%m]);
           i1=ten[(i0-1)/m][j];
           swap(ten[(i0-1)/m][j],ten[(i0-1)/m][(i-1)%m]);
           
          i0=a[ten[(i0-1)/m][(i-1)%m]][j];
         }
        // cerr<<i0<<' '<<i1<<endl;
         ichi[i0]=make_pair(i1,j);
        
       
       }
       for(int i=0;i<n;i++){
         for(int j=0;j<m;j++)cout<<a[i][j]<<' ';
         cout<<endl;
       }
       int b[m][n];for(int i=0;i<n;i++)for(int j=0;j<m;j++)b[j][i]=a[i][j];
       for(int i=0;i<m;i++)sort(b[i],b[i]+n);
       for(int i=0;i<n;i++){
         for(int j=0;j<m;j++)cout<<b[j][i]<<' ';
         cout<<endl;
       }

                  
}