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;
typedef long long ll;

int adj[100][100];
int a[100][100];
int b[100][100];
int c[100][100];
int val[100][100][100];

int n;
int matching[100], done[100];

int match(int i) {
  for (int j = 0; j < n; j++) {
    if (adj[i][j] && !done[j]++ && (matching[j] == -1 || match(matching[j]))) {
      matching[j] = i;
      return 1;
    }
  }
  return 0;
}

vector<pair<int,int>> maxmatch() {
  fill_n(matching, n, -1);
  for (int i = 0; i < n; i++) {
    fill_n(done, n, 0);
    assert(match(i));
  }
  vector<pair<int,int>> r;
  for (int i = 0; i < n; i++) {
    r.push_back({matching[i], i});
  }
  return r;
}

int main() {
  ios::sync_with_stdio(0); cin.tie(0);
  int h, w;
  cin >> h >> w;
  n = h;

  for (int i = 0; i < h; i++) {
    for (int j = 0; j < w; j++) {
      cin >> a[i][j];
      int y = (a[i][j]-1)/w;
      val[i][y][adj[i][y]++] = a[i][j];
    }
  }
  for (int j = 0; j < w; j++) {
    for (auto p : maxmatch()) {
      int i = p.first, y = p.second;
      b[i][j] = val[i][y][--adj[i][y]];
    }
  }
  for (int i = 0; i < h; i++) {
    for (int j = 0; j < w; j++) {
      cout << b[i][j] << ' ';
    }
    cout << endl;
  }
  for (int j = 0; j < w; j++) {
    vector<int> col(h);
    for (int i = 0; i < h; i++)
      col[i] = b[i][j];
    sort(col.begin(), col.end());
    for (int i = 0; i < h; i++)
      c[i][j] = col[i];
  }
  for (int i = 0; i < h; i++) {
    for (int j = 0; j < w; j++) {
      cout << c[i][j] << ' ';
    }
    cout << endl;
  }
}