Sorting a Grid

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

inputFormat

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}

outputFormat

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

样例

3 2
2 6
4 3
1 5

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

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