CF65D Harry Potter and the Sorting Hat

如你们所知，霍格沃茨有四个学院：格兰芬多，赫奇帕奇，拉文克劳和斯莱特林。新生的分院由分院帽来完成。学生们按照字母表的顺序一个个被叫到众人面前，每一个都需要戴上分院帽，在思虑过后，分院帽会正式宣布学生们应当进入的学院。 分院帽将根据学生们的个性进行分院：勇敢无畏并因此而高尚者属于格兰芬多；正直忠诚、坚忍诚实者进入赫奇帕奇；睿智博学、聪明敏锐者投身拉文克劳；头脑精明但狡诈阴险之人也许会进斯莱特林。无论如何，一年级的新生赫敏·格兰杰非常关心即将到来的分院。她研究了所有有关于分院帽的著作，并得到了一个简单得多的结论。如果学生们有亲戚此前在霍格沃茨学习过，分院帽会把他们分入与亲戚相同的学院。而在其他情况下，比如有些学生的亲戚曾就读于不同的学院，或亲戚都是赫敏父母一样的麻瓜，分院帽将把学生分给那一刻拥有新生最少的学院。 赫敏已经询问过名单上在她前面的学生的亲戚情况。现在她和她的新朋友哈利波特以及罗恩韦斯莱希望知道分院帽将把赫敏分入哪个学院。

第一行输入一个整数n（1

输出赫敏可能被分进的所有学院，若多于一个则一行输出一个。 注：应输出学院英文名称。例：Gryffindor、Ravenclaw、Slytherin、Hufflepuff。

Consider the second example. There are only two students before Hermione. The first student is sent to Hufflepuff. The second disciple is given the choice between the houses where the least number of students has been sent, i.e. Gryffindor, Slytherin and Ravenclaw. If he chooses Gryffindor, Hermione is forced to choose between Ravenclaw and Slytherin, if he chooses Ravenclaw, Hermione will choose between Gryffindor and Slytherin, if he chooses Slytherin, Hermione will choose between Gryffindor and Ravenclaw. In the end, the following situation is possible (it depends on the choice of the second student and Hermione). Hermione will end up 1) in Gryffindor, 2) in Ravenclaw, 3) in Slytherin. Note that, despite the fact that in neither case Hermione will be given a choice between all the three options, they are all possible and they should all be printed in the answer. Hermione will not, under any circumstances, end up in Hufflepuff.