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 N = 255;
const int W = N * N;
int n, m, a[N][N], b[N], c[N], d[N][N], e[W], f[W];
vector<int> v[W];
queue<int> q;
set<int> S;
set<int>::iterator it;
int id(int x, int y) { return x * N + y; }
void adde(int x, int y, int z) {
  if (z) swap(x, y);
  v[x].push_back(y);
  e[y]++;
}
int main() {
  int i, j, x, y;
  scanf("%d%d", &n, &m);
  for (i = 1; i <= n; i = i + 1)
    for (j = 1; j <= m; j = j + 1)
      scanf("%d", &a[i][j]), b[i] = max(b[i], a[i][j]),
                             c[j] = max(c[j], a[i][j]);
  sort(b + 1, b + n + 1), sort(c + 1, c + m + 1);
  reverse(b + 1, b + n + 1), reverse(c + 1, c + m + 1);
  for (i = 0, j = 0; i < n || j < m;) {
    if (b[i + 1] == c[j + 1]) {
      i++, j++;
      d[i][j] = b[i];
    } else {
      if (b[i + 1] > c[j + 1])
        i++, d[i][j] = b[i];
      else
        j++, d[i][j] = c[j];
    }
  }
  for (i = 1; i <= n * m; i = i + 1) S.insert(i);
  for (i = 1; i <= n; i = i + 1)
    for (j = 1; j <= m; j = j + 1) f[id(i, j)] = W;
  for (i = 1; i <= n; i = i + 1)
    for (j = 1; j <= m; j = j + 1)
      if (d[i][j]) f[id(i, j)] = d[i][j];
  for (i = 1; i <= n; i = i + 1) {
    x = 0;
    for (j = 1; j < m; j = j + 1) {
      if (d[i][j] && d[i][j + 1]) continue;
      if (d[i][j]) x = 1;
      adde(id(i, j + 1), id(i, j), x);
    }
  }
  for (j = 1; j <= m; j = j + 1) {
    x = 0;
    for (i = 1; i < n; i = i + 1) {
      if (d[i][j] && d[i + 1][j]) continue;
      if (d[i][j]) x = 1;
      adde(id(i + 1, j), id(i, j), x);
    }
  }
  for (i = 1; i <= n; i = i + 1)
    for (j = 1; j <= m; j = j + 1)
      if (!e[id(i, j)]) q.push(id(i, j));
  while (!q.empty()) {
    x = q.front();
    q.pop();
    it = S.upper_bound(f[x]);
    it--;
    f[x] = (*it);
    S.erase(it);
    for (i = v[x].size(); i--;) {
      y = v[x][i];
      f[y] = min(f[y], f[x] - 1);
      e[y]--;
      if (!e[y]) q.push(y);
    }
  }
  for (i = 1; i <= n; i = i + 1) {
    for (j = 1; j <= m; j = j + 1) printf("%d ", f[id(i, j)]);
    printf("\n");
  }
  return 0;
}