F. Playing Around the Tabletime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputThere 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.InputThe 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.OutputIn 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.ExamplesInput
2
2 1
1 2
Output
1
2 1 
Input
3
1 1 1
2 2 2
3 3 3
Output
6
1 2 3
3 1 2
2 3 1
1 2 3
3 1 2
2 3 1
NoteIn 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. 
2
2 1
1 2

1 2 1  
['constructive algorithms', 'greedy', 'implementation', '*2900']