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;
long long power(long long x, long long y);
long long mpower(long long x, long long y, long long p);
long long modInv(long long a, long long m);
long long gcdExtended(long long a, long long b, long long *x, long long *y);
bool isPrime(long long n);
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long t, i, j, k, l, h, p, q, r, x, y, z, a, b, c, d, f, n, m,
      M = 1000000007;
  char ch, ch2, ch3;
  string s, s1, s2, s3;
  t = 1;
  while (t--) {
    vector<pair<long long, long long> > v, w;
    unordered_map<long long, long long> N;
    set<pair<long long, long long> > S, SS;
    cin >> n >> m;
    long long A[n][m], B[n], C[m], X[n][m];
    for (i = 0; i < n; i++) {
      for (j = 0; j < m; j++) {
        cin >> A[i][j];
      }
    }
    for (i = 0; i < n; i++) {
      B[i] = 0;
      for (j = 0; j < m; j++) {
        B[i] = max(B[i], A[i][j]);
      }
    }
    for (j = 0; j < m; j++) {
      C[j] = 0;
      for (i = 0; i < n; i++) {
        C[j] = max(C[j], A[i][j]);
      }
    }
    sort(B, B + n, greater<long long>());
    sort(C, C + m, greater<long long>());
    p = n * m;
    long long Z[p + 1];
    for (i = 0; i <= p; i++) {
      Z[i] = 0;
    }
    Z[0] = 1;
    Z[p] = 1;
    for (i = 0; i < n; i++) {
      for (j = 0; j < m; j++) {
        X[i][j] = -1;
      }
    }
    X[0][0] = p;
    b = 1;
    c = 1;
    for (i = p - 1; i >= 0; i--) {
      if (b < n && B[b] == i && c < m && C[c] == i) {
        Z[i] = 1;
        X[b][c] = i;
        for (j = c - 1; j >= 0; j--) {
          v.push_back(make_pair(b, j));
        }
        for (j = b - 1; j >= 0; j--) {
          v.push_back(make_pair(j, c));
        }
        b++;
        c++;
      } else if (b < n && B[b] == i) {
        Z[i] = 1;
        X[b][c - 1] = i;
        for (j = c - 2; j >= 0; j--) {
          v.push_back(make_pair(b, j));
        }
        b++;
      } else if (c < m && C[c] == i) {
        Z[i] = 1;
        X[b - 1][c] = i;
        for (j = b - 2; j >= 0; j--) {
          v.push_back(make_pair(j, c));
        }
        c++;
      }
    }
    j = 0;
    for (i = p; i > 0; i--) {
      if (!Z[i]) {
        Z[i] = 1;
        X[v[j].first][v[j].second] = i;
        j++;
      }
    }
    for (i = 0; i < n; i++) {
      for (j = 0; j < m; j++) {
        cout << X[i][j] << " ";
      }
      cout << "\n";
    }
  }
  return 0;
}
long long modInv(long long a, long long m) {
  long long x, y;
  long long g = gcdExtended(a, m, &x, &y);
  long long res = (x % m + m) % m;
  return res;
}
long long gcdExtended(long long a, long long b, long long *x, long long *y) {
  if (a == 0) {
    *x = 0, *y = 1;
    return b;
  }
  long long x1, y1;
  long long gcd = gcdExtended(b % a, a, &x1, &y1);
  *x = y1 - (b / a) * x1;
  *y = x1;
  return gcd;
}
long long mpower(long long x, long long y, long long p) {
  long long res = 1;
  x = x % p;
  while (y > 0) {
    if (y & 1) res = (res * x) % p;
    y = y >> 1;
    x = (x * x) % p;
  }
  return res;
}
long long power(long long x, long long y) {
  long long res = 1;
  while (y > 0) {
    if (y & 1) res = res * x;
    y = y >> 1;
    x = x * x;
  }
  return res;
}
bool isPrime(long long n) {
  if (n <= 1) return false;
  if (n <= 3) return true;
  if (n % 2 == 0 || n % 3 == 0) return false;
  long long p = sqrt(n);
  for (int i = 5; i <= p; i = i + 6)
    if (n % i == 0 || n % (i + 2) == 0) return false;
  return true;
}