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 128
using namespace std;

int n,m;
int a[maxn][maxn];

void read()
{
    cin>>n>>m;

    int i,j;

    for(i=0;i<n;i++)
        for(j=0;j<m;j++)
            cin>>a[i][j];
}

vector<int>v[maxn*maxn];
bool used[maxn*maxn];
bool tused[maxn*maxn];
int match[maxn*maxn];

void clearr()
{
    int i;
    for(i=0;i<maxn;i++)
        v[i].clear();
}

/*void build()
{
    int i,j;
    for(i=0;i<n;i++)
     {
        int sz=v[i].size();
        for(j=0;j<v[i].size();j++)
        {
            int nb=v[i][j];
            if(!match[nb])
            {
                match[nb]=i;
                break;
            }
        }
     }
}*/

bool khun(int i)
{
    //cout<<i<<" ";
    if(tused[i])return false;
    tused[i]=true;
    int j,sz=v[i].size();
    for(j=0;j<sz;j++)
    {
        int t=v[i][j];
        if(match[t]==-1||khun(match[t]))
        {
            match[t]=i;
            match[i]=t;
            return true;
        }
    }
    return false;
}

int ans[maxn][maxn];
void solve()
{
    int i,j,k;
    for(i=0;i<m;i++)
    {
        clearr();
        for(j=0;j<n;j++)
            for(k=0;k<m;k++)
                if(!used[a[j][k]])
                {
                    v[j].push_back((a[j][k]-1)/m+n);
                    v[(a[j][k]-1)/m+n].push_back(j);
                }
        memset(match,-1,sizeof(match));
        for (j=0;j<n;j++)
        {
            memset(tused,0,sizeof(tused));
            khun(j);
        }

        for(j=0;j<n;j++)
        {
            if(match[j]!=-1)
            {
                for(k=0;k<m;k++)
                {
                    if((a[j][k]-1)/m+n==match[j]&&!used[a[j][k]])
                    {
                        used[a[j][k]]=true;
                        ans[j][i]=a[j][k];
                        break;
                    }
                }
            }
        }
    }

    for(i=0;i<n;i++)
    {
        for(j=0;j<m;j++)
            cout<<ans[i][j]<<" ";
        cout<<endl;
    }
}

//bool ans[maxn][maxn];
int main()
{
    int i,j,k;
	read();
	solve();

    for(i=0;i<n;i++)
    {
        for(j=0;j<m;j++)
            for(k=0;k<n;k++)
                if((ans[k][j]-1)/m==i)
                {cout<<ans[k][j]<<" ";break;}

        cout<<endl;
    }
	return 0;
}

/*
3 4
1 4 7 10
2 5 8 11
3 6 9 12
*/