Problem: Koa the Koala has a matrix A of n rows and m columns. Elements of this matrix are distinct integers from 1 to n ⋅ m (each number from 1 to n ⋅ m appears exactly once in the matrix).

For any matrix M of n rows and m columns let's define the following:

  * The i-th row of M is defined as R_i(M) = [ M_{i1}, M_{i2}, …, M_{im} ] for all i (1 ≤ i ≤ n). 
  * The j-th column of M is defined as C_j(M) = [ M_{1j}, M_{2j}, …, M_{nj} ] for all j (1 ≤ j ≤ m). 



Koa defines S(A) = (X, Y) as the spectrum of A, where X is the set of the maximum values in rows of A and Y is the set of the maximum values in columns of A.

More formally:

  * X = \{ max(R_1(A)), max(R_2(A)), …, max(R_n(A)) \} 
  * Y = \{ max(C_1(A)), max(C_2(A)), …, max(C_m(A)) \}



Koa asks you to find some matrix A' of n rows and m columns, such that each number from 1 to n ⋅ m appears exactly once in the matrix, and the following conditions hold:

  * S(A') = S(A) 
  * R_i(A') is bitonic for all i (1 ≤ i ≤ n) 
  * C_j(A') is bitonic for all j (1 ≤ j ≤ m) 

An array t (t_1, t_2, …, t_k) is called bitonic if it first increases and then decreases.

More formally: t is bitonic if there exists some position p (1 ≤ p ≤ k) such that: t_1 < t_2 < … < t_p > t_{p+1} > … > t_k.

Help Koa to find such matrix or to determine that it doesn't exist.

Input

The first line of the input contains two integers n and m (1 ≤ n, m ≤ 250) — the number of rows and columns of A.

Each of the ollowing n lines contains m integers. The j-th integer in the i-th line denotes element A_{ij} (1 ≤ A_{ij} ≤ n ⋅ m) of matrix A. It is guaranteed that every number from 1 to n ⋅ m appears exactly once among elements of the matrix.

Output

If such matrix doesn't exist, print -1 on a single line.

Otherwise, the output must consist of n lines, each one consisting of m space separated integers — a description of A'.

The j-th number in the i-th line represents the element A'_{ij}.

Every integer from 1 to n ⋅ m should appear exactly once in A', every row and column in A' must be bitonic and S(A) = S(A') must hold.

If there are many answers print any.

Examples

Input


3 3
3 5 6
1 7 9
4 8 2


Output


9 5 1
7 8 2
3 6 4


Input


2 2
4 1
3 2


Output


4 1
3 2


Input


3 4
12 10 8 6
3 4 5 7
2 11 9 1


Output


12 8 6 1
10 11 9 2
3 4 5 7

Note

Let's analyze the first sample:

For matrix A we have:

    * Rows: 
      * R_1(A) = [3, 5, 6]; max(R_1(A)) = 6 
      * R_2(A) = [1, 7, 9]; max(R_2(A)) = 9 
      * R_3(A) = [4, 8, 2]; max(R_3(A)) = 8 

    * Columns: 
      * C_1(A) = [3, 1, 4]; max(C_1(A)) = 4 
      * C_2(A) = [5, 7, 8]; max(C_2(A)) = 8 
      * C_3(A) = [6, 9, 2]; max(C_3(A)) = 9 

  * X = \{ max(R_1(A)), max(R_2(A)), max(R_3(A)) \} = \{ 6, 9, 8 \} 
  * Y = \{ max(C_1(A)), max(C_2(A)), max(C_3(A)) \} = \{ 4, 8, 9 \} 
  * So S(A) = (X, Y) = (\{ 6, 9, 8 \}, \{ 4, 8, 9 \}) 



For matrix A' we have:

    * Rows: 
      * R_1(A') = [9, 5, 1]; max(R_1(A')) = 9 
      * R_2(A') = [7, 8, 2]; max(R_2(A')) = 8 
      * R_3(A') = [3, 6, 4]; max(R_3(A')) = 6 

    * Columns: 
      * C_1(A') = [9, 7, 3]; max(C_1(A')) = 9 
      * C_2(A') = [5, 8, 6]; max(C_2(A')) = 8 
      * C_3(A') = [1, 2, 4]; max(C_3(A')) = 4 

  * Note that each of this arrays are bitonic. 
  * X = \{ max(R_1(A')), max(R_2(A')), max(R_3(A')) \} = \{ 9, 8, 6 \} 
  * Y = \{ max(C_1(A')), max(C_2(A')), max(C_3(A')) \} = \{ 9, 8, 4 \} 
  * So S(A') = (X, Y) = (\{ 9, 8, 6 \}, \{ 9, 8, 4 \}) 

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int MAX = 255;
int a[MAX][MAX];
int ans[MAX][MAX];
int n, m;
int di[4] = {0, 0, 1, -1};
int dj[4] = {1, -1, 0, 0};
bool valid(int i, int j) {
  if (i < 0 || i >= n) return false;
  if (j < 0 || j >= m) return false;
  return true;
}
int num_neighbors(int i, int j) {
  int res = 0;
  for (int d = 0; d < 4; d++) {
    int ni = i + di[d];
    int nj = j + dj[d];
    if (valid(ni, nj) == false) continue;
    if (ans[ni][nj] != 0) res++;
  }
  return res;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cin >> n >> m;
  for (int i = 0; i < n; i++)
    for (int j = 0; j < m; j++) cin >> a[i][j];
  set<int> rows;
  for (int i = 0; i < n; i++) {
    int rowmax = 0;
    for (int j = 0; j < m; j++) {
      rowmax = max(rowmax, a[i][j]);
    }
    rows.insert(rowmax);
  }
  set<int> cols;
  for (int j = 0; j < m; j++) {
    int colmax = 0;
    for (int i = 0; i < n; i++) {
      colmax = max(colmax, a[i][j]);
    }
    cols.insert(colmax);
  }
  int ci = -1;
  int cj = -1;
  vector<int> bad;
  for (int i = n * m; i >= 1; i--) {
    if (rows.count(i) && cols.count(i)) {
      ci++;
      cj++;
      ans[ci][cj] = i;
    } else if (rows.count(i)) {
      ci++;
      ans[ci][cj] = i;
    } else if (cols.count(i)) {
      cj++;
      ans[ci][cj] = i;
    } else {
      bad.emplace_back(i);
    }
  }
  set<pair<int, int>> available;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) {
      if (ans[i][j] != 0) continue;
      if (num_neighbors(i, j) != 2) continue;
      available.insert(make_pair(i, j));
    }
  }
  for (int i : bad) {
    pair<int, int> pos = *available.begin();
    available.erase(pos);
    ans[pos.first][pos.second] = i;
    for (int d = 0; d < 4; d++) {
      int ni = pos.first + di[d];
      int nj = pos.second + dj[d];
      if (valid(ni, nj) == false) continue;
      if (ans[ni][nj] != 0) continue;
      if (num_neighbors(ni, nj) != 2) continue;
      available.insert(make_pair(ni, nj));
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < m; j++) {
      cout << ans[i][j] << " ";
    }
    cout << '\n';
  }
  return 0;
}