code_contests-1437/instruction.md

p02942 AtCoder Grand Contest 037 - Sorting a Grid

Problem Description

We have a grid with N rows and M columns of squares. Each integer from 1 to NM is written in this grid once. The number written in the square at the i-th row from the top and the j-th column from the left is A_{ij}.

You need to rearrange these numbers as follows:

1. First, for each of the N rows, rearrange the numbers written in it as you like.
2. Second, for each of the M columns, rearrange the numbers written in it as you like.
3. Finally, for each of the N rows, rearrange the numbers written in it as you like.

After rearranging the numbers, you want the number written in the square at the i-th row from the top and the j-th column from the left to be M\times (i-1)+j. Construct one such way to rearrange the numbers. The constraints guarantee that it is always possible to achieve the objective.

Constraints

• 1 \leq N,M \leq 100
• 1 \leq A_{ij} \leq NM
• A_{ij} are distinct.

Input

Input is given from Standard Input in the following format:

N M A_{11} A_{12} ... A_{1M} : A_{N1} A_{N2} ... A_{NM}

Output

Print one way to rearrange the numbers in the following format:

B_{11} B_{12} ... B_{1M} : B_{N1} B_{N2} ... B_{NM} C_{11} C_{12} ... C_{1M} : C_{N1} C_{N2} ... C_{NM}

Here B_{ij} is the number written in the square at the i-th row from the top and the j-th column from the left after Step 1, and C_{ij} is the number written in that square after Step 2.

Examples

Input

3 2 2 6 4 3 1 5

Output

2 6 4 3 5 1 2 1 4 3 5 6

Input

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

Output

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

Contest Information

• Contest ID: 0
• Problem Index:
• Points: 0.0
• Rating: 0
• Tags:
• Time Limit: {'seconds': 2, 'nanos': 0} seconds
• Memory Limit: 1073741824 bytes

Task

Solve this competitive programming problem. Provide a complete solution that handles all the given constraints and edge cases.