Playing Around the Table
Description
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.
Input
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 $i$.
Output
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.
Samples
2
2 1
1 2
1
2 1
3
1 1 1
2 2 2
3 3 3
6
1 2 3
3 1 2
2 3 1
1 2 3
3 1 2
2 3 1
Note
In the first test case, if the first player passes a card with number $2$ and the second player passes a card with number $1$, then the first player has two cards with number $1$ and the second player has two cards with number $2$. Then, after making this operation, both players are solid.
In the second test case, $0$ operations would be enough too. Note that you do not need to minimize the number of operations.