Solitaire

`New version` ### 题目描述 `Vasya`手里有一副54张扑克牌。为了消遣，`Vasya`开始玩纸牌游戏。 `Vasya`将$nm$张牌摆成一个$n\times m$的矩形。如果其中有大小王，`Vasya`会从剩下的$54-nm$张扑克牌中任意选牌将它们换下。`Vasya`在换牌时会尽量使得纸牌游戏能被解决。 `Vasya`认为：一轮纸牌游戏能被解决，当且仅当大小王被换下后，存在两个不重叠的$3\times 3$正方形，每个正方形中的扑克牌**花色一致**或**点数互不相同**。 请你求出给定的纸牌游戏能否被解决。如果有解，给出任意一组解即可。 ### 输入格式 第一行包含两个整数$n,m\ (3\leq n,m\leq 17,n\times m\leq 52)$，表示矩形的大小。其中$n$表示矩形的行数，$m$表示矩形的列数。 接下来$n$行，每行$m$个字符串。每个字符串包含两个字符。大小王表示为`J1`和`J2`。剩下的扑克牌中，第一个字符表示点数，第二个字符表示花色。点数包含：`2`,`3`,`4`,`5`,`6`,`7`,`8`,`9`,`T`,`J`,`Q`,`K`和`A`。花色包含：`C`,`D`,`H`和`S`。数据保证所有的牌互不相同。 ### 输出格式 如果无解，输出`No solution.` 否则输出共$4$行。 第一行输出`Solution exists.` 第二行输出大小王的替换情况，有三种可能： - 如果没有大小王，输出`There are no jokers.` - 如果有一张王牌，输出`Replace J`$x\ $`with`$\ y$`.`$x$为王牌的标号，$y$为换上的扑克牌。 - 如果有两张王牌，输出`Replace J1 with`$\ x\ $`and J2 with`$\ y\ $`.`$x$为换下`J1`的扑克牌，$y$为换下`J2`的扑克牌。 第三行输出第一个正方形的左上角$(x_{1},y_{1})$，格式为：`Put the first square to `$(x_{1},y_{1})$`.` 第四行输出第二个正方形的左上角$(x_{2},y_{2})$，格式为：`Put the second square to `$(x_{2},y_{2})$`.`

Vasya has a pack of $ 54 $ cards ( $ 52 $ standard cards and $ 2 $ distinct jokers). That is all he has at the moment. Not to die from boredom, Vasya plays Solitaire with them. Vasya lays out $ nm $ cards as a rectangle $ n×m $ . If there are jokers among them, then Vasya should change them with some of the rest of $ 54-nm $ cards (which are not layed out) so that there were no jokers left. Vasya can pick the cards to replace the jokers arbitrarily. Remember, that each card presents in pack exactly once (i. e. in a single copy). Vasya tries to perform the replacements so that the solitaire was solved. Vasya thinks that the solitaire is solved if after the jokers are replaced, there exist two non-overlapping squares $ 3×3 $ , inside each of which all the cards either have the same suit, or pairwise different ranks. Determine by the initial position whether the solitaire can be solved or not. If it can be solved, show the way in which it is possible.

The first line contains integers $ n $ and $ m $ ( $ 3<=n,m<=17 $ , $ n×m<=52 $ ). Next $ n $ lines contain $ m $ words each. Each word consists of two letters. The jokers are defined as "J1" and "J2" correspondingly. For the rest of the cards, the first letter stands for the rank and the second one — for the suit. The possible ranks are: "2", "3", "4", "5", "6", "7", "8", "9", "T", "J", "Q", "K" and "A". The possible suits are: "C", "D", "H" and "S". All the cards are different.

If the Solitaire can be solved, print on the first line "Solution exists." without the quotes. On the second line print in what way the jokers can be replaced. Three variants are possible: - "There are no jokers.", if there are no jokers in the input data. - "Replace J $ x $ with $ y $ .", if there is one joker. $ x $ is its number, and $ y $ is the card it should be replaced with. - "Replace J1 with $ x $ and J2 with $ y $ .", if both jokers are present in the input data. $ x $ and $ y $ here represent distinct cards with which one should replace the first and the second jokers correspondingly. On the third line print the coordinates of the upper left corner of the first square $ 3×3 $ in the format "Put the first square to ( $ r $ , $ c $ ).", where $ r $ and $ c $ are the row and the column correspondingly. In the same manner print on the fourth line the coordinates of the second square $ 3×3 $ in the format "Put the second square to ( $ r $ , $ c $ ).". If there are several solutions to that problem, print any of them. If there are no solutions, print of the single line "No solution." without the quotes. See the samples to understand the output format better.

4 6
2S 3S 4S 7S 8S AS
5H 6H 7H 5S TC AC
8H 9H TH 7C 8C 9C
2D 2C 3C 4C 5C 6C

No solution.

4 6
2S 3S 4S 7S 8S AS
5H 6H 7H J1 TC AC
8H 9H TH 7C 8C 9C
2D 2C 3C 4C 5C 6C

Solution exists.
Replace J1 with 2H.
Put the first square to (1, 1).
Put the second square to (2, 4).

4 6
2S 3S 4S 7S 8S AS
5H 6H 7H QC TC AC
8H 9H TH 7C 8C 9C
2D 2C 3C 4C 5C 6C

Solution exists.
There are no jokers.
Put the first square to (1, 1).
Put the second square to (2, 4).

The pretests cover all the possible output formats.