103176: [Atcoder]ABC317 G - Rearranging

Problem Statement

There is a grid with $N$ rows and $M$ columns. The square at the $i$-th row from the top and the $j$-th column from the left contains the integer $A_{i,j}$.
Here, the squares contain $M$ occurrences of each of $1,\ldots,N$, for a total of $NM$ integers.

You perform the following operations to swap the numbers written on the squares.

• For $i=1,\ldots,N$ in this order, do the following.
  • Freely rearrange the numbers written in the $i$-th row. That is, freely choose a permutation $P=(P_{1},\ldots,P_{M})$ of $1,\ldots,M$, and replace $A_{i,1},\ldots,A_{i,M}$ with $A_{i,P_{1}},\ldots,A_{i,P_{M}}$ simultaneously.

Your goal is to perform the operations so that each column contains each of $1,\ldots,N$ once. Determine if this is possible, and if so, print such a resulting grid.

Constraints

• $1 \leq N,M \leq 100$
• $1 \leq A_{i,j} \leq M$
• All input values are integers.
• The $NM$ numbers $A_{1,1},\ldots,A_{N,M}$ contain exactly $M$ occurrences of each of $1,\ldots,N$.

Input

The Input is given from Standard Input in the following format:

$N$ $M$
$A_{1,1}$ $\ldots$ $A_{1,M}$
$\vdots$
$A_{N,1}$ $\ldots$ $A_{N,M}$

Output

If it is impossible to perform the operations so that each column contains each of $1,\ldots,N$ once, print No.
Otherwise, print Yes in the first line, and in the subsequent $N$ lines, print a resulting grid where each column contains each of $1,\ldots,N$ once, in the following format.
Let $B_{i,j}$ be the number written in the square at the $i$-th row from the top and $j$-th column from the left of the grid. For each $1\leq i \leq N$, the $(i+1)$-th line should contain $B_{i,1},\ldots,B_{i,M}$ in this order, with spaces in between.

If multiple solutions exist, any of them is accepted.

Sample Input 1

3 2
1 1
2 3
2 3

Sample Output 1

Yes
1 1
3 2
2 3

Also, the following output is accepted.

Yes
1 1
2 3
3 2

Sample Input 2

4 4
1 2 3 4
1 1 1 2
3 2 2 4
4 4 3 3

Sample Output 2

Yes
1 4 3 2
2 1 1 1
4 2 2 3
3 3 4 4