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;
int main() {
  cin.sync_with_stdio(0);
  cin.tie(0);
  cin.exceptions(cin.failbit);
  int n, m;
  cin >> n >> m;
  vector<vector<int> > a(n, vector<int>(m));
  for (auto &v : a)
    for (auto &x : v) cin >> x;
  for (auto &v : a)
    for (auto &x : v) --x;
  vector<int> rm(n), cm(m);
  for (int i = (0); i < (n); ++i)
    for (int j = (0); j < (m); ++j) {
      rm[i] = max(rm[i], a[i][j]);
      cm[j] = max(cm[j], a[i][j]);
    }
  vector<int> rc(n * m);
  for (int i = (0); i < (n); ++i)
    for (int j = (0); j < (m); ++j) {
      if (a[i][j] == rm[i]) rc[a[i][j]] += 1;
      if (a[i][j] == cm[j]) rc[a[i][j]] += 2;
    }
  int diag = count((rc).begin(), (rc).end(), 3);
  int xlo = diag, ylo = diag, xhi = diag, yhi = diag;
  vector<vector<int> > ans(n, vector<int>(m));
  queue<pair<int, int> > ls;
  for (int t = (n * m); t-- > (0);) {
    int ix, jx;
    if (rc[t] == 0) {
      pair<int, int> p = ls.front();
      ls.pop();
      ix = p.first, jx = p.second;
    } else if (rc[t] == 3) {
      --xlo, --ylo;
      ix = xlo, jx = ylo;
      for (int y = (ylo + 1); y < (yhi); ++y) ls.push({xlo, y});
      for (int x = (xlo + 1); x < (xhi); ++x) ls.push({x, ylo});
    } else if (rc[t] == 1) {
      ++xhi;
      ix = xhi - 1, jx = yhi - 1;
      for (int y = (yhi - 1); y-- > (ylo);) ls.push({xhi - 1, y});
    } else {
      ++yhi;
      ix = xhi - 1, jx = yhi - 1;
      for (int x = (xhi - 1); x-- > (xlo);) ls.push({x, yhi - 1});
    }
    ans[ix][jx] = t;
  }
  for (auto &v : ans) {
    for (auto &x : v) cout << x + 1 << ' ';
    cout << endl;
  }
}