Long Recovery

题意翻译

平面上有一无穷大的坐标系，每个点 $(x,y)$ 和 $3$ 个点相邻 对于 $x$ 是奇数的情况相邻点的坐标是 $(x\pm1,y)(x-1,y+1)$，否则就是 $(x\pm 1,y)(x+1,y-1)$ 每个坐标可能是黑点或白点之一，每秒整个坐标系会发生如下两种操作之一 - 对于一个有两个相邻黑点的白点，白点变成黑点 - 对于一个有两个相邻白点的黑点，黑点变成白点 注意即使有多个点满足能改变颜色的条件，每秒也只会有一个点改变颜色 我们希望黑色点能尽快变成白点 给定 $n$ 个黑点的坐标，在最坏情况下是不是存在一种变色方案使得黑点会永远存在，如果是，输出 `SICK` 否则输出 `RECOVERED` 并求在**最坏情况下**将所有黑点变成白点需要用的最短时间

题目描述

A patient has been infected with an unknown disease. His body can be seen as an infinite grid of triangular cells which looks as follows: Two cells are neighboring if they share a side. Therefore, each cell ( $ x $ , $ y $ ) has exactly three neighbors: - ( $ x+1 $ , $ y $ ) - ( $ x-1 $ , $ y $ ) - ( $ x+1 $ , $ y-1 $ ) if $ x $ is even and ( $ x-1 $ , $ y+1 $ ) otherwise. Initially some cells are infected, all the others are healthy. The process of recovery begins. Each second, for exactly one cell (even though there might be multiple cells that could change its state) one of the following happens: - A healthy cell with at least $ 2 $ infected neighbors also becomes infected. - An infected cell with at least $ 2 $ healthy neighbors also becomes healthy. If no such cell exists, the process of recovery stops. Patient is considered recovered if the process of recovery has stopped and all the cells are healthy. We're interested in a worst-case scenario: is it possible that the patient never recovers, or if it's not possible, what is the maximum possible duration of the recovery process?

输入输出格式

输入格式

The first line contains one integer $ n $ $ (1 \leq n \leq 250000) $ — the number of infected cells. The $ i $ -th of the next $ n $ lines contains two space-separated integers $ x_i $ and $ y_i $ $ (0 \leq x_i, y_i < 500) $ , meaning that cell $ (x_i, y_i) $ is infected. All cells $ (x_i, y_i) $ are distinct, and all other cells are considered healthy.

输出格式

If it is possible that the organism never fully recovers from the disease, print SICK. Otherwise, you should print RECOVERED and in the next line an integer $ k $ — the longest possible recovery period, modulo $ 998244353 $ .

输入输出样例

输入样例 #1

4
0 0
1 0
2 0
0 1

输出样例 #1

RECOVERED
4

输入样例 #2

3
1 0
3 0
1 1

输出样例 #2

SICK

说明

For the first testcase, the following drawings describe the longest possible recovery process. It can be proven that there are no recovery periods of length $ 5 $ or longer, and the organism always recovers in this testcase.  $ \hspace{40pt} \downarrow $  $ \hspace{40pt} \downarrow $  $ \hspace{40pt} \downarrow $  $ \hspace{40pt} \downarrow $ $ \hspace{15pt} $ RECOVERED For the second testcase, it is possible for the cells $ (2, 0) $ , $ (2, 1) $ , $ (0, 1) $ to become infected. After that, no cell can change its state, so the answer is SICK, as not all of the cells are healthy.