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 <cstdio>
#include <cstdlib>
#include <cstring>
#include <vector>
#include <algorithm>

#define fin stdin
#define fout stdout
//FILE *fin = fopen("a.in", "r"), *fout = fopen("a.out", "w");

#define MAXN 109

std::vector < int > a[MAXN][MAXN], g[MAXN], mat[MAXN], ans[MAXN];
int n, fata[MAXN], baiat[MAXN];
bool viz[MAXN];

bool gasim(int x) {
    if (viz[x])
        return 0;
    viz[x] = 1;

    for (auto &y : g[x]) {
        if (baiat[y] == 0) {
            fata[x] = y;
            baiat[y] = x;
            return 1;
        }
    }

    for (auto &y : g[x]) {
        if (gasim(baiat[y])) {
            fata[x] = y;
            baiat[y] = x;
            return 1;
        }
    }

    return 0;
}

inline void cuplaj() {
    memset(fata, 0, sizeof fata);
    memset(baiat, 0, sizeof baiat);
    bool f = 1;
    for (int i = 1; i <= n; i++) {
        g[i].clear();
        for (int j = 1; j <= n; j++)
            if (!a[i][j].empty())
                g[i].push_back(j);
    }
    while (f) {
        f = 0;
        memset(viz, 0, sizeof viz);
        for (int i = 1; i <= n; i++)
            if (fata[i] == 0)
                f |= gasim(i);
    }
}

int main() {
    int m;
    fscanf(fin, "%d%d", &n, &m);

    for (int i = 1; i <= n; i++) {
        for (int j = 1; j <= m; j++) {
            int x;
            fscanf(fin, "%d", &x);

            a[i][(x - 1) / m + 1].push_back(x);
        }
    }

    for (int i = 1; i <= m; i++) {
        cuplaj();
        for (int j = 1; j <= n; j++) {
            if (fata[j] == 0)
                exit(1);
            mat[j].push_back(a[j][fata[j]].back());
            a[j][fata[j]].pop_back();
        }
    }

    for (int i = 1; i <= n; i++, fprintf(fout, "\n"))
        for (auto &x : mat[i])
            fprintf(fout, "%d ", x);

    for (int i = 1; i <= m; i++) {
        std::vector < int > avem;
        for (int l = 1; l <= n; l++)
            avem.push_back(mat[l][i - 1]);
        std::sort(avem.begin(), avem.end());
        for (int l = 0; l < n; l++)
            ans[l].push_back(avem[l]);
    }

    for (int i = 0; i < n; i++, fprintf(fout, "\n"))
        for (auto &x : ans[i])
            fprintf(fout, "%d ", x);

    fclose(fin);
    fclose(fout);
    return 0;
}