Koa the Koala has a matrix $A$ of $n$ rows and $m$ columns. Elements of this matrix are distinct integers from $1$ to $n \cdot m$ (each number from $1$ to $n \cdot m$ 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$R_i(M) = [ M_{i1}, M_{i2}, \ldots, M_{im} ]$for all$i$($1 \le i \le n$). - The
$j$-th column of$M$is defined as$C_j(M) = [ M_{1j}, M_{2j}, \ldots, M_{nj} ]$for all$j$($1 \le j \le m$).
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)), \ldots, \max(R_n(A)) \}$$Y = \{ \max(C_1(A)), \max(C_2(A)), \ldots, \max(C_m(A)) \}$
Koa asks you to find some matrix $A'$ of $n$ rows and $m$ columns, such that each number from $1$ to $n \cdot m$ appears exactly once in the matrix, and the following conditions hold:
$S(A') = S(A)$$R_i(A')$is bitonic for all$i$($1 \le i \le n$)$C_j(A')$is bitonic for all$j$($1 \le j \le m$)
An array $t$ ($t_1, t_2, \ldots, t_k$) is called bitonic if it first increases and then decreases.
More formally: $t$ is bitonic if there exists some position $p$ ($1 \le p \le k$) such that: $t_1 \lt t_2 \lt \ldots \lt t_p \gt t_{p+1} \gt \ldots \gt t_k$.
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 $m$ ($1 \le n, m \le 250$) — 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 $A_{ij}$ ($1 \le A_{ij} \le n \cdot m$) of matrix $A$. It is guaranteed that every number from $1$ to $n \cdot m$ 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 $n \cdot m$ 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.
Note
Let's analyze the first sample:
For matrix $A$ we have:
$X = \{ \max(R_1(A)), \max(R_2(A)), \max(R_3(A)) \} = \{ 6, 9, 8 \}$$Y = \{ \max(C_1(A)), \max(C_2(A)), \max(C_3(A)) \} = \{ 4, 8, 9 \}$- So
$S(A) = (X, Y) = (\{ 6, 9, 8 \}, \{ 4, 8, 9 \})$
For matrix $A'$ we have:
- Note that each of this arrays are bitonic.
$X = \{ \max(R_1(A')), \max(R_2(A')), \max(R_3(A')) \} = \{ 9, 8, 6 \}$$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 3
3 5 6
1 7 9
4 8 2
9 5 1
7 8 2
3 6 4
2 2
4 1
3 2
4 1
3 2
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
题面与样例版权归 Codeforces 及出题人所有;中文翻译由 AI 生成(CI 管线),如有出入请以原文为准。