Rearrange

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 })

inputFormat

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.

outputFormat

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 })

样例

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

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

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