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;
bool edges[100][100];
int n, m;
vector<int> mt;
vector<char> used;
 
bool try_kuhn (int v) {
	if (used[v])  return false;
	used[v] = true;
	for (int i=0; i < n; i++) {
		if (!edges[v][i]) continue;
		if (mt[i] == -1 || try_kuhn (mt[i])) {
			mt[i] = v;
			return true;
		}
	}
	return false;
}
vector<int> find_matching(){
	mt.assign(n, -1);
	for (int v=0; v<n; ++v) {
		used.assign (n, false);
		bool res = try_kuhn (v);
		assert(res);
	}
	vector<int> res(n);
	for (int i=0; i < n; i++) res[mt[i]] = i;
	return res;
}
signed main() {
	#ifdef LOCAL
		freopen("H_input.txt", "r", stdin);
		//freopen("C_output.txt", "w", stdout);
	#endif
    ios_base::sync_with_stdio(0); cin.tie(0);
    cin >> n >> m;
    int matrix[n][m];
    for (int i=0; i < n;i++) for (int j=0; j < m; j++) cin >> matrix[i][j];
    for (int i=0; i < n;i++) for (int j=0; j < m; j++) matrix[i][j]--;
    int groups[n][m];
	for (int i=0; i < n; i++) for (int j=0; j < m; j++) groups[i][j] = matrix[i][j]/m;
	bool taken[n][m];
	for (int i=0; i < n; i++) for (int j=0; j < m; j++) taken[i][j] = false;
	int ans[n][m];
	for (int i=0; i < m; i++){
		for (int j=0; j < n; j++) for (int k=0; k < n; k++) edges[j][k] = false;
		for (int j=0; j < n; j++){
			for (int k=0; k < m; k++){
				if (taken[j][k]) continue;
				edges[j][groups[j][k]] = true;
			}
		}
		vector<int> res = find_matching();
		for (int j=0; j < n; j++){
			for (int k=0; k < m; k++){
				if (taken[j][k] || groups[j][k] != res[j]) continue;
				ans[j][i] = matrix[j][k];
				taken[j][k] = true;
				break;
			}
		}
	}
	for (int i=0; i < n; i++){
		for (int j=0; j < m; j++)cout << ans[i][j]+1 << " ";
		cout << "\n";
	}
	for (int j=0; j < m; j++){
		for (int i=0; i < n; i++){
			int G = ans[i][j] / m;
			matrix[G][j] = ans[i][j];
		}
	}
	for (int i=0; i < n; i++){
		for (int j=0; j < m; j++)cout << matrix[i][j]+1 << " ";
		cout << "\n";
	}
}