D. Rearrangetime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputKoa 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 < t_2 < \ldots < t_p > t_{p+1} > \ldots > t_k.Help Koa to find such matrix or to determine that it doesn't exist.InputThe 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.OutputIf 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.ExamplesInput
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
NoteLet'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 \}) 
3 3
3 5 6
1 7 9
4 8 2

9 5 1 7 8 2 3 6 4 
['brute force', 'constructive algorithms', 'graphs', 'greedy', 'sortings', '*2800']