Cheaterius's Problem

题意翻译

小A有一很多2X2的牌，四个块上都有写数字，他不能翻转这些牌而只能将它们旋转90、180、270度，所以一种牌可以显示出共4种状态。 给一堆牌，问总共有几种不同的牌（旋转后相同的算一种）。 输入:第一行一个整数n表示牌数，之后n张2x2的牌，每两张牌之间用"**"隔开。 输出:一个整数，表示有几种不同的牌。 1<=n<=1000 感谢@稀神探女 提供的翻译

题目描述

Cheaterius is a famous in all the Berland astrologist, magician and wizard, and he also is a liar and a cheater. One of his latest inventions is Cheaterius' amulets! They bring luck and wealth, but are rather expensive. Cheaterius makes them himself. The technology of their making is kept secret. But we know that throughout long nights Cheaterius glues together domino pairs with super glue to get squares $ 2×2 $ which are the Cheaterius' magic amulets! That's what one of Cheaterius's amulets looks likeAfter a hard night Cheaterius made $ n $ amulets. Everyone of them represents a square $ 2×2 $ , every quarter contains 1 to 6 dots. Now he wants sort them into piles, every pile must contain similar amulets. Two amulets are called similar if they can be rotated by 90, 180 or 270 degrees so that the following condition is met: the numbers of dots in the corresponding quarters should be the same. It is forbidden to turn over the amulets. Write a program that by the given amulets will find the number of piles on Cheaterius' desk.

输入输出格式

输入格式

The first line contains an integer $ n $ ( $ 1<=n<=1000 $ ), where $ n $ is the number of amulets. Then the amulet's descriptions are contained. Every description occupies two lines and contains two numbers (from 1 to 6) in each line. Between every pair of amulets the line "\*\*" is located.

输出格式

Print the required number of piles.

输入输出样例

输入样例 #1

4
31
23
**
31
23
**
13
32
**
32
13

输出样例 #1

1

输入样例 #2

4
51
26
**
54
35
**
25
61
**
45
53

输出样例 #2

2