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;

const int N = 300;
bool occ[N][N];
int a[N][N], x[N][N];

struct graph {
  bool mark[N];
  int mat[N][N];
  int match[N];
  int n;

  graph(int x = 0) {
    n = x;
    memset(mat, 0, sizeof mat);
  }

  void add_edge(int u, int v) {
    ++mat[u][v];
    ++mat[v][u];
  }

  void remove_edge(int u, int v) {
    --mat[u][v];
    --mat[v][u];
  }

  bool dfs(int u) {
    mark[u] = true;
    for (int i = 0; i < n; i++) {
      if (!mat[u][i]) {
        continue;
      }
      if (match[i] == -1 || (!mark[match[i]] && dfs(match[i]))) {
        match[u] = i;
        match[i] = u;
        return true;
      }
    }
    return false;
  }

  vector<int> matching(int upper_size) {
    memset(match, -1, sizeof match);
    while (true) {
      memset(mark, false, sizeof mark);
      bool found = false;
      for (int i = 0; i < upper_size; i++) {
        if (match[i] == -1) {
          found |= dfs(i);
        }
      }
      if (!found) {
        break;
      }
    }
    vector<int> res;
    for (int i = 0; i < upper_size; i++) {
      assert(~match[i]);
      res.push_back(match[i] - upper_size);
    }
    return res;
  }
};

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n, m;
  cin >> n >> m;
  graph G(205);
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) {
      cin >> a[i][j];
      G.add_edge(i, (a[i][j] - 1) / m + n);
    }
  }
  for (int j = 0; j < m; j++) {
    vector<int> cur = G.matching(n);
    for (int i = 0; i < n; i++) {
      for (int c = 0; c < m; c++) {
        if ((a[i][c] - 1) / m == cur[i] && !occ[i][c]) {
          occ[i][c] = true;
          x[i][j] = a[i][c];
          break;
        }
      }
      G.remove_edge(i, cur[i] + n);
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) {
      cout << x[i][j] << " \n"[j == m - 1];
    }
  }
  for (int j = 0; j < m; j++) {
    vector<int> cur;
    for (int i = 0; i < n; i++) {
      cur.push_back(x[i][j]);
    }
    sort(cur.begin(), cur.end(), [&](int x, int y) { return (x - 1) / m < (y - 1) / m; });
    for (int i = 0; i < n; i++) {
      x[i][j] = cur[i];
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) {
      cout << x[i][j] << " \n"[j == m - 1];
    }
  }
  return 0;
}