题目链接

题目翻译

给出一个大小为 $N \times M$ 的矩阵 $a$，矩阵内的元素 $\in [1 , N \times M]$，且两两不同

下面给出一些定义：

$R_i$ 为第 $i$ 行的元素集合，即$R_i=\{a_{i,1},a_{i,2},...,a_{i,m}\}$

$C_j$ 为第 $j$ 列的元素集合，即$C_j=\{a_{1,j},a_{2,j},...,a_{n,j}\}$

$X$ 为矩阵每一行的最大元素的集合，$Y$ 为矩阵每一列的最大元素的集合，即

$X = \{\max(R_1),\max(R_2),..,\max(R_n)\}$

$Y = \{\max(C_1),\max(C_2),..,\max(C_m)\}$

$S(a) = (X , Y)$

求构造一个新的 $N \times M$ 的矩阵 $a'$ 使其满足

• 矩阵内的元素 $\in [1 , N \times M]$，且两两不同
• $S(a') = S(a)$
• 对于任意的行或列，使其满足先上升后下降，即存在 $k$ 满足

行：$a_{i,1}<a_{i,2}<...<a_{i,k}>a_{i,k+1}>...>a_{i,M}$

列：$a_{1,j}<a_{2,j}<...<a_{k,j}>a_{k+1,j}>...>a_{N,j}$

如果存在多种合法构造，输出其中一种；若不存在，请输出 $-1$

Description

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.

Samples

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

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 $S(A') = (X, Y) = (\{ 9, 8, 6 \}, \{ 9, 8, 4 \})$