Problem:
Score : 1100 points

Problem Statement

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:

First, for each of the N rows, rearrange the numbers written in it as you like.

Second, for each of the M columns, rearrange the numbers written in it as you like.

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.

Sample Input 1

3 2
2 6
4 3
1 5

Sample Output 1

2 6
4 3
5 1
2 1
4 3
5 6

Sample Input 2

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

Sample Output 2

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 C (GCC 5.4.1) (judge verdict: Wrong Answer)

//set many funcs template
//Ver.20190714
#include<stdio.h>
#include<string.h>
#include<stdlib.h>
#include<stdbool.h>
#include<time.h>
#define inf 1072114514
#define llinf 4154118101919364364
#define mod 1000000007
#define pi 3.1415926535897932384

int max(int a,int b){if(a>b){return a;}return b;}
int min(int a,int b){if(a<b){return a;}return b;}
int zt(int a,int b){return max(a,b)-min(a,b);}
int round(int a,int b){if((a%b)*2 >= b){return (a/b)+1;}return a/b;}
int ceil(int a,int b){if(a%b==0){return a/b;}return (a/b)+1;}
int gcd(int a,int b){int c;while(b!=0){c=a%b;a=b;b=c;}return a;}
int lcm(int a,int b){int c=gcd(a,b);a/=c;return a*b;}
int nCr(int a,int b){int i,r=1;for(i=1;i<=b;i++){r*=(a+1-i);r/=i;}return r;}
int nHr(int a,int b){return nCr(a+b-1,b);}
int fact(int a){int i,r=1;for(i=1;i<=a;i++){r*=i;}return r;}
int pow(int a,int b){int i,r=1;for(i=1;i<=b;i++){r*=a;}return r;}
int dsum(int x){int r=0;while(x){r+=(x%10);x/=10;}return r;}
int dsumb(int x,int b){int r=0;while(x){r+=(x%b);x/=b;}return r;}
int sankaku(int x){return ((1+x)*x)/2;}
void swap(int *a,int *b){int c;c=(*a);(*a)=(*b);(*b)=c;}
long long llmax(long long a,long long b){if(a>b){return a;}return b;}
long long llmin(long long a,long long b){if(a<b){return a;}return b;}
long long llzt(long long a,long long b){return llmax(a,b)-llmin(a,b);}
long long llround(long long a,long long b){if((a%b)*2 >= b){return (a/b)+1;}return a/b;}
long long llceil(long long a,long long b){if(a%b==0){return a/b;}return (a/b)+1;}
long long llgcd(long long a,long long b){long long c;while(b!=0){c=a%b;a=b;b=c;}return a;}
long long lllcm(long long a,long long b){long long c=llgcd(a,b);a/=c;return a*b;}
long long llnCr(long long a,long long b){long long i,r=1;for(i=1;i<=b;i++){r*=(a+1-i);r/=i;}return r;}
long long llnHr(long long a,long long b){return llnCr(a+b-1,b);}
long long llfact(long long a){long long i,r=1;for(i=1;i<=a;i++){r*=i;}return r;}
long long llpow(long long a,long long b){long long i,r=1;for(i=1;i<=b;i++){r*=a;}return r;}
long long lldsum(long long x){long long r=0;while(x){r+=(x%10);x/=10;}return r;}
long long lldsumb(long long x,long long b){long long r=0;while(x){r+=(x%b);x/=b;}return r;}
long long llsankaku(long long x){return ((1+x)*x)/2;}
void llswap(long long *a,long long *b){long long c;c=(*a);(*a)=(*b);(*b)=c;}
double dbmax(double a,double b){if(a>b){return a;}return b;}
double dbmin(double a,double b){if(a<b){return a;}return b;}
double dbzt(double a,double b){return dbmax(a,b)-dbmin(a,b);}
void dbswap(double *a,double *b){double c;c=(*a);(*a)=(*b);(*b)=c;}
void chswap(char *a,char *b){char c;c=(*a);(*a)=(*b);(*b)=c;}
int sortfncsj(const void *a,const void *b){if(*(int *)a>*(int *)b){return 1;}if(*(int *)a==*(int *)b){return 0;}return -1;}
int sortfnckj(const void *a,const void *b){if(*(int *)a<*(int *)b){return 1;}if(*(int *)a==*(int *)b){return 0;}return -1;}
int llsortfncsj(const void *a,const void *b){if(*(long long *)a>*(long long *)b){return 1;}if(*(long long *)a==*(long long *)b){return 0;}return -1;}
int llsortfnckj(const void *a,const void *b){if(*(long long *)a<*(long long *)b){return 1;}if(*(long long *)a==*(long long *)b){return 0;}return -1;}
int dbsortfncsj(const void *a,const void *b){if(*(double *)a>*(double *)b){return 1;}if(*(double *)a==*(double *)b){return 0;}return -1;}
int dbsortfnckj(const void *a,const void *b){if(*(double *)a<*(double *)b){return 1;}if(*(double *)a==*(double *)b){return 0;}return -1;}
int strsortfncsj(const void *a,const void *b){return strcmp((char *)a,(char *)b);}
int strsortfnckj(const void *a,const void *b){return strcmp((char *)b,(char *)a);}
int chsortfncsj(const void *a,const void *b){if(*(char *)a>*(char *)b){return 1;}if(*(char *)a==*(char *)b){return 0;}return -1;}
int chsortfnckj(const void *a,const void *b){if(*(char *)a<*(char *)b){return 1;}if(*(char *)a==*(char *)b){return 0;}return -1;}

void shuffledget(int x[],int n){
    srand(time(0));
    int i,b[524288],p,c;
    for(i=0;i<n;i++){
        b[i]=i;
    }
    for(i=n;i>=1;i--){
        p=rand()%i;
        c=b[i-1];b[i-1]=b[p];b[p]=c;
    }
    for(i=0;i<n;i++){
        scanf("%d",&x[b[i]]);
    }
}

int dx4[4]={1,-1,0,0};
int dy4[4]={0,0,1,-1};
int dx8[8]={-1,-1,-1,0,0,1,1,1};
int dy8[8]={-1,0,1,-1,1,-1,0,1};

int search(int x,int a[],int n){
    int st=0,fi=n-1,te;
    while(st<=fi){
        te=(st+fi)/2;
        if(a[te]<x){st=te+1;}else{fi=te-1;}
    }
    return st;
}

void prarr(long long arr[],long long n){
  long long i;
  for(i=0;i<n;i++){
    if(i){printf(" ");}
    printf("%lld",arr[i]+1);
  }
  printf("\n");
  return;
}

typedef struct{
long long val;
long long node;
}sd;

int sdsortfnc(const void *a,const void *b){
if(((sd*)a)->val < ((sd*)b)->val){return -1;}
if(((sd*)a)->val > ((sd*)b)->val){return 1;}
return 0;
}

void coordinate_comp(int a[],int n){
  int i,c=0;
  sd dat[524288];
  for(i=0;i<n;i++){
    dat[i].val=a[i];
    dat[i].node=i;
  }
  qsort(dat,n,sizeof(dat[0]),sdsortfnc);
  a[dat[0].node]=c;
  for(i=1;i<n;i++){
    if(dat[i-1].val!=dat[i].val){c++;}
    a[dat[i].node]=c;
  }
}

sd q[1048576];
long long qp=0,qqp=0,qsize=1048576;

void qpush(sd x){
    qp++;
    qp%=qsize;
    q[qp]=x;
}

sd qpop(){
    qqp++;
    qqp%=qsize;
    return q[qqp];
}

typedef struct{
    long long st;
    long long fi;
    long long cap;
    long long id;
    long long rev;
}rs;

typedef struct{
    long long st;
    long long kz;
}mkj;

int sortfnc(const void *a,const void *b){
if(((rs*)a)->st > ((rs*)b)->st){return 1;}
if(((rs*)a)->st < ((rs*)b)->st){return -1;}
if(((rs*)a)->fi > ((rs*)b)->fi){return 1;}
if(((rs*)a)->fi < ((rs*)b)->fi){return -1;}
return 0;
}

int revsortfnc(const void *a,const void *b){
long long p,q,r,s,t;
p=((rs*)a)->st;
q=((rs*)a)->fi;
r=((rs*)b)->st;
s=((rs*)b)->fi;
if(p>q){t=p;p=q;q=t;}
if(r>s){t=r;r=s;s=t;}
if(p<r){return -1;}
if(p>r){return 1;}
if(q<s){return -1;}
if(q>s){return 1;}
return 0;
}

void makemkj(rs g[],mkj x[],long long n){
    long long i,ms=0,nst=g[0].st;
    for(i=1;i<n;i++){
        if(g[i].st!=g[i-1].st){
            x[nst].kz=i-ms;
            x[nst].st=ms;
            nst=g[i].st;ms=i;
        }
    }
    x[nst].kz=n-ms;
    x[nst].st=ms;
}

long long rep(long long vst,long long vfi,long long nf,rs g[],mkj x[],long long dist[],long long ptr[]){
  long long d;
  if(vst==vfi){return nf;}
  while(ptr[vst]<x[vst].kz){
    if(g[x[vst].st+ptr[vst]].cap>0 && dist[vst] < dist[g[x[vst].st+ptr[vst]].fi]){
      d=rep(g[x[vst].st+ptr[vst]].fi,vfi,llmin(nf,g[x[vst].st+ptr[vst]].cap),g,x,dist,ptr);
      if(d>0){
        g[x[vst].st+ptr[vst]].cap-=d;
        g[g[x[vst].st+ptr[vst]].rev].cap+=d;
        return d;
      }
    }
    ptr[vst]++;
  }
  return 0;
}

long long dinic(long long vst,long long vfi,long long vc,long long ec,rs g[],mkj x[]){
  long long nv,i,j,res=0,fl,dist[524288],ptr[524288],f;
  sd pd,od;
  while(1){
    qp=0;qqp=0;
    pd.val=0;
    pd.node=vst;
    qpush(pd);
    for(i=0;i<=vc;i++){
      dist[i]=llinf;
    }
    while(qp!=qqp){
      od=qpop();
      if(dist[od.node]!=llinf){continue;}
      dist[od.node]=od.val;
      nv=od.node;
      for(i=x[nv].st;i<x[nv].st+x[nv].kz;i++){
        if(dist[g[i].fi]==llinf && g[i].cap>0){
          pd.node=g[i].fi;
          pd.val=od.val+1;
          qpush(pd);
        }
      }
    }
    if(dist[vfi]==llinf){return res;}
    for(i=0;i<=ec;i++){
      ptr[i]=0;
    }
    while(1){
      f=rep(vst,vfi,llinf,g,x,dist,ptr);
      if(f==0){break;}
      res+=f;
    }
  }
}

int main(void){
  long long i,j,n,m,k,a[128][128],b[128],c,h,w,r=0,l,t;
  long long cnt=0;
  long long mm[128];
  rs g[524288];
  mkj x[524288];
  scanf("%lld%lld",&n,&m);
  for(i=0;i<n;i++){
    for(j=0;j<m;j++){
      scanf("%lld",&a[i][j]);a[i][j]--;
    }
  }

  for(i=m-1;i>=0;i--){
    cnt=0;
    for(j=0;j<n;j++){
      for(k=0;k<=i;k++){
        g[cnt].st=j;
        g[cnt].fi=n+a[j][k]/m;
        g[cnt].cap=1;
        cnt++;
        g[cnt].st=g[cnt-1].fi;
        g[cnt].fi=g[cnt-1].st;
        g[cnt].cap=0;
        cnt++;
      }
    }
    for(j=0;j<n;j++){
      g[cnt].st=2*n;
      g[cnt].fi=j;
      g[cnt].cap=1;
      cnt++;
      g[cnt].st=g[cnt-1].fi;
      g[cnt].fi=g[cnt-1].st;
      g[cnt].cap=0;
      cnt++;
      g[cnt].st=n+j;
      g[cnt].fi=2*n+1;
      g[cnt].cap=1;
      cnt++;
      g[cnt].st=g[cnt-1].fi;
      g[cnt].fi=g[cnt-1].st;
      g[cnt].cap=0;
      cnt++;
    }
    qsort(g,cnt,sizeof(g[0]),sortfnc);
    for(j=0;j<cnt;j++){
      g[j].id=j;
    }
    qsort(g,cnt,sizeof(g[0]),revsortfnc);
    for(j=0;j<cnt;j+=2){
      g[j].rev=g[j+1].id;
      g[j+1].rev=g[j].id;
    }
    qsort(g,cnt,sizeof(g[0]),sortfnc);
    makemkj(g,x,cnt);
    //for(j=0;j<cnt;j++){
    //  printf("%lld -> %lld : %lld\n",g[j].st,g[j].fi,g[j].cap);
    //}
    r=dinic(2*n,2*n+1,2*n+2,cnt,g,x);
    for(j=0;j<cnt;j++){
      if(0<=g[j].st && g[j].st<n && n<=g[j].fi && g[j].fi<2*n && g[j].cap==0){
        mm[g[j].st]=g[j].fi-n;
        //printf("[%lld]",g[j].fi-n);
      }
    }//printf("\n");
    for(j=0;j<n;j++){
      for(k=0;k<i;k++){
        if(a[j][k]/m == mm[j]){
          llswap(&a[j][k],&a[j][i]);
        }
      }
    }//printf("\n");
  }
  
  for(i=0;i<n;i++){prarr(a[i],m);}
  for(i=0;i<m;i++){
    for(j=0;j<n;j++){
      b[j]=a[j][i];
    }
    qsort(b,n,sizeof(long long),sortfncsj);
    for(j=0;j<n;j++){
      a[j][i]=b[j];
    }
  }
  for(i=0;i<n;i++){prarr(a[i],m);}
  
  return 0;
}