A14933 | Playing Around the Table

There are $n$ players, numbered from $1$ to $n$ sitting around a round table. The $(i+1)$ -th player sits to the right of the $i$ -th player for $1 \le i < n$ , and the $1$ -st player sits to the right of the $n$ -th player.

There are $n^2$ cards, each of which has an integer between $1$ and $n$ written on it. For each integer from $1$ to $n$ , there are exactly $n$ cards having this number.

Initially, all these cards are distributed among all the players, in such a way that each of them has exactly $n$ cards. In one operation, each player chooses one of his cards and passes it to the player to his right. All these actions are performed simultaneously.

Player $i$ is called solid if all his cards have the integer $i$ written on them. Their objective is to reach a configuration in which everyone is solid. Find a way to do it using at most $(n^2-n)$ operations. You do not need to minimize the number of operations.

The first line contains a single integer $n$ ( $2\le n\le 100$ ).

Then $n$ lines follow. The $i$ -th of them contains $n$ integers $c_1, c_2, \ldots, c_n$ ( $1\le c_j\le n$ ) — the initial cards of the $i$ -th player.

It is guaranteed that for each integer $i$ from $1$ to $n$ , there are exactly $n$ cards having the number $i$ .

In the first line print an integer $k$ ( $0\le k\le (n^2-n)$ ) — the numbers of operations you want to make.

Then $k$ lines should follow. In the $i$ -th of them print $n$ integers $d_1, d_2, \ldots, d_n$ ( $1\le d_j\le n$ ) where $d_j$ is the number written on the card which $j$ -th player passes to the player to his right in the $i$ -th operation.

We can show that an answer always exists under the given constraints. If there are multiple answers, print any.