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;
using ll = long long;
using ull = unsigned long long;
using pll = pair<ll, ll>;
using pii = pair<int, int>;
const int MN = 255;
int R, C, mat[MN][MN], ans[MN][MN];
int rowMx[MN], colMx[MN];
bitset<MN * MN> isMx;
map<int, pii> loc;
vector<int> allMx;
int main() {
  cin.tie(0), cout.tie(0), ios::sync_with_stdio(0);
  cin >> R >> C;
  for (int i = 1; i <= R; i++) {
    for (int j = 1; j <= C; j++) {
      cin >> mat[i][j];
    }
  }
  for (int i = 1; i <= R; i++) {
    int mx = 0;
    for (int j = 1; j <= C; j++) mx = max(mx, mat[i][j]);
    rowMx[i] = (mx);
    isMx[mx] = 1;
    allMx.push_back(mx);
  }
  for (int j = 1; j <= C; j++) {
    int mx = 0;
    for (int i = 1; i <= R; i++) mx = max(mx, mat[i][j]);
    colMx[j] = (mx);
    isMx[mx] = 1;
    allMx.push_back(mx);
  }
  sort(rowMx + 1, rowMx + R + 1, greater<int>());
  sort(colMx + 1, colMx + C + 1, greater<int>());
  sort(allMx.begin(), allMx.end());
  allMx.erase(unique(allMx.begin(), allMx.end()), allMx.end());
  int rowCur = 1, colCur = 1, small = min(R, C);
  while (rowCur <= R && colCur <= C) {
    if (rowMx[rowCur] == colMx[colCur]) {
      ans[rowCur][colCur] = rowMx[rowCur];
      loc[rowMx[rowCur]] = {rowCur, colCur};
      rowCur++, colCur++;
    } else {
      if (rowMx[rowCur] > colMx[colCur]) {
        ans[rowCur][colCur - 1] = rowMx[rowCur];
        loc[rowMx[rowCur]] = {rowCur, colCur - 1};
        rowCur++;
      } else {
        ans[rowCur - 1][colCur] = colMx[colCur];
        loc[colMx[colCur]] = {rowCur, colCur};
        colCur++;
      }
    }
  }
  while (rowCur <= R) {
    ans[rowCur][colCur - 1] = rowMx[rowCur];
    loc[rowMx[rowCur]] = {rowCur, colCur - 1};
    rowCur++;
  }
  while (colCur <= C) {
    ans[rowCur - 1][colCur] = colMx[colCur];
    loc[colMx[colCur]] = {rowCur - 1, colCur};
    colCur++;
  }
  int cur = 1;
  for (int mx : allMx) {
    auto [row, col] = loc[mx];
    for (int i = R; i > row; i--) {
      if (ans[i][col]) continue;
      while (isMx[cur]) cur++;
      ans[i][col] = cur++;
    }
    for (int i = 1; i < row; i++) {
      if (ans[i][col]) continue;
      while (isMx[cur]) cur++;
      ans[i][col] = cur++;
    }
    for (int i = C; i > col; i--) {
      if (ans[row][i]) continue;
      while (isMx[cur]) cur++;
      ans[row][i] = cur++;
    }
    for (int i = 1; i < col; i++) {
      if (ans[row][i]) continue;
      while (isMx[cur]) cur++;
      ans[row][i] = cur++;
    }
  }
  for (int i = 1; i <= R; i++) {
    for (int j = 1; j <= C; j++) cout << ans[i][j] << " \n"[j == C];
  }
}