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++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>

using namespace std;

using int64 = long long;
const int mod = 998244353;

const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;


template< typename T1, typename T2 >
ostream &operator<<(ostream &os, const pair< T1, T2 > &p) {
  os << p.first << " " << p.second;
  return os;
}

template< typename T1, typename T2 >
istream &operator>>(istream &is, pair< T1, T2 > &p) {
  is >> p.first >> p.second;
  return is;
}

template< typename T >
ostream &operator<<(ostream &os, const vector< T > &v) {
  for(int i = 0; i < (int) v.size(); i++) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template< typename T >
istream &operator>>(istream &is, vector< T > &v) {
  for(T &in : v) is >> in;
  return is;
}

template< typename T1, typename T2 >
inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }

template< typename T1, typename T2 >
inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); }

template< typename T = int64 >
vector< T > make_v(size_t a) {
  return vector< T >(a);
}

template< typename T, typename... Ts >
auto make_v(size_t a, Ts... ts) {
  return vector< decltype(make_v< T >(ts...)) >(a, make_v< T >(ts...));
}

template< typename T, typename V >
typename enable_if< is_class< T >::value == 0 >::type fill_v(T &t, const V &v) {
  t = v;
}

template< typename T, typename V >
typename enable_if< is_class< T >::value != 0 >::type fill_v(T &t, const V &v) {
  for(auto &e : t) fill_v(e, v);
}

template< typename F >
struct FixPoint : F {
  FixPoint(F &&f) : F(forward< F >(f)) {}

  template< typename... Args >
  decltype(auto) operator()(Args &&... args) const {
    return F::operator()(*this, forward< Args >(args)...);
  }
};

template< typename F >
inline decltype(auto) MFP(F &&f) {
  return FixPoint< F >{forward< F >(f)};
}

struct HopcroftKarp {
  vector< vector< int > > graph;
  vector< int > dist, match;
  vector< bool > used, vv;

  HopcroftKarp(int n, int m) : graph(n), match(m, -1), used(n) {}

  void add_edge(int u, int v) {
    graph[u].push_back(v);
  }

  void bfs() {
    dist.assign(graph.size(), -1);
    queue< int > que;
    for(int i = 0; i < graph.size(); i++) {
      if(!used[i]) {
        que.emplace(i);
        dist[i] = 0;
      }
    }

    while(!que.empty()) {
      int a = que.front();
      que.pop();
      for(auto &b : graph[a]) {
        int c = match[b];
        if(c >= 0 && dist[c] == -1) {
          dist[c] = dist[a] + 1;
          que.emplace(c);
        }
      }
    }
  }

  bool dfs(int a) {
    vv[a] = true;
    for(auto &b : graph[a]) {
      int c = match[b];
      if(c < 0 || (!vv[c] && dist[c] == dist[a] + 1 && dfs(c))) {
        match[b] = a;
        used[a] = true;
        return (true);
      }
    }
    return (false);
  }

  int bipartite_matching() {
    int ret = 0;
    while(true) {
      bfs();
      vv.assign(graph.size(), false);
      int flow = 0;
      for(int i = 0; i < graph.size(); i++) {
        if(!used[i] && dfs(i)) ++flow;
      }
      if(flow == 0) return (ret);
      ret += flow;
    }
  }

  void output() {
    for(int i = 0; i < match.size(); i++) {
      if(~match[i]) {
        cout << match[i] << "-" << i << endl;
      }
    }
  }
};


int main() {
  int N, M;
  cin >> N >> M;
  auto A = make_v< int >(N, M);
  cin >> A;
  for(auto &vs : A) for(auto &p : vs) --p;
  auto B = make_v< int >(N, M);
  fill_v(B, -1);
  for(int i = 0; i < M; i++) {
    HopcroftKarp bm(N, N);
    auto pre = make_v< int >(N, N);
    fill_v(pre, -1);
    for(int j = 0; j < N; j++) {
      for(int k = 0; k < M; k++) {
        if(A[j][k] == -1) continue;
        if(pre[j][A[j][k] / M] != -1) continue;
        bm.add_edge(j, A[j][k] / M);
        pre[j][A[j][k] / M] = k;
      }
    }
    bm.bipartite_matching();
    vector< int > rev(N);
    for(int j = 0; j < N; j++) {
      rev[bm.match[j]] = j;
    }
    for(int j = 0; j < N; j++) {
      B[j][i] = A[j][pre[j][rev[j]]];
      A[j][pre[j][rev[j]]] = -1;
    }
  }

  for(auto &vs : B) {
    for(auto &p : vs) ++p;
    cout << vs << endl;
  }

  auto C = make_v< int >(N, M);
  for(int i = 0; i < M; i++) {
    vector< int > be;
    for(int j = 0; j < N; j++) {
      be.emplace_back(B[j][i]);
    }
    sort(begin(be), end(be));
    for(int j = 0; j < N; j++) {
      C[j][i] = be[j];
    }
  }

  for(auto &vs : C) {
    cout << vs << endl;
  }


}