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 maxn 510
#define pii pair<int,int>
#define fi first
#define se second

using namespace std;

int a[maxn][maxn],b[maxn][maxn],c[maxn][maxn],n,m,p[maxn],fre[maxn],cnt=0,been[maxn][maxn];
pii g[maxn][maxn];

bool visit(int u) {
    if (fre[u]!=cnt) fre[u]=cnt;
    else return false;
    for (int v=0;v<n;v++)
        if (g[u][v].fi==1) {
            if (p[v]==-1||visit(p[v])) {
                p[v]=u;
                return true;
            }
        }
    return false;
}

int main() {
    ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
   // freopen("in.txt","r",stdin);
    cin>>n>>m;
    for (int i=0;i<n;i++)
        for (int j=0;j<m;j++) {
            cin>>a[i][j];
            a[i][j]--;
        }
    for (int col=0;col<m;col++) {
        for (int i=0;i<n;i++) {
            for (int j=0;j<n;j++) g[i][j]=pii(-1,-1);
            p[i]=-1;
        }
        for (int i=0;i<n;i++)
            for (int j=0;j<m;j++)
                if (!been[i][j]) g[i][a[i][j]/m]=pii(1,j);
        for (int i=0;i<n;i++) {
            cnt++;
            visit(i);
        }
        for (int i=0;i<n;i++) {
            int row = p[i];
            b[row][col] = a[row][g[row][i].se]+1;
            c[i][col] = a[row][g[row][i].se]+1;
            been[row][g[row][i].se]=1;
        }
    }
    for (int i=0;i<n;i++) {
        for (int j=0;j<m;j++) cout<<b[i][j]<<" ";
        cout<<endl;
    }
    for (int i=0;i<n;i++) {
        for (int j=0;j<m;j++) cout<<c[i][j]<<" ";
        cout<<endl;
    }
    //for (int i=0;i<n;i++) {
     //   for (int j=0;j<m;j++) if ((c[i][j]-1)/m!=i) cout<<"fuck "<<c[i][j]<<" "<<i<<endl;
   // }
    return 0;
}