CF1646F 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.

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.