Help Greg the Dwarf

题意翻译

一个很不寻常的市民住在一个遥远的国度——他是矮人格库拉。然而，他不寻常的名字不是最奇怪的事情（而且，过去的每个人都习惯了只是叫他矮人格雷格），还有一些关于矮人格雷格的一些特殊的事实——他已经活了两百多年，而且，他住在一个废弃墓地的墓穴中，没人见他在白天出来过。此外，也没人见过他给自己买食物。这就是为什么在恶龙悲剧地死亡、牛持续从田野中消失后没人感到特别惊讶。邻里的人们非常确信无害的龙对消失的牛没有责任（考虑到恶龙一直对他的素食主义观点很诚挚）。但是甚至那也不是整个故事的最坏的部分。 最坏的部分是仅仅几分钟前，矮人格雷格用某些难以理解的方式进入了你的房子，并且让你帮他解决一个问题。关键是在很短的一段时间以前，格雷格决定订一口新的棺材（知道他怪异的性格，你一点也不会感到奇怪）。但问题是：一段非常长的双向的L形走廊通向格雷格的墓穴，无法拖着任何一口棺材通过那个走廊，这就是为什么他来寻求你的帮助。 你已经将任务抽象化到了一个这样的平面上：让走廊在转弯前和转弯后的宽度为 $a$ 和 $b$ （如图）。两端走廊相交成一个直角，棺材是一个边长分别为 $l$ 和 $w$ $(l\ge w)$ 的矩形。矮人格雷格已经决定了棺材的长$(l)$，这取决于他的身高；你的任务是决定棺材的最大可能的宽$(w)$，以这样的长和宽棺材可以被带到墓穴里。而且，由于棺材的质量很大（纯大理石！），棺材配备了轮子，因此它不能被抬离地面，但是可以在平面内平移和旋转。在进入走廊之前，你可以任意旋转棺材。 格雷格保证如果你帮助他，他就会奖励你永生（我想知道怎么实现？）。而且如果你不帮助他，嗯……相信我，你不想知道会发生什么的。 一句话题意：给出一个有直角拐角的L形走廊和一个长确定、宽不确定（宽不大于长）的矩形，矩形可以任意平移、旋转，要求求出能够通过拐角的矩形的最大的宽。 #### 输入格式 第一行包含三个以空格分隔的整数 $a,b,l$ （见题面陈述）$(1\le a,b,l\le10^4)$ #### 输出格式 输出棺材最大可能的宽度，绝对或相对误差不超过 $10^{-7}$。如果不存在具有给定长度和正宽度的棺材（可以满足问题陈述要求的棺材），输出"My poor head =("（不含引号）。 数据保证如果答案为正，不会小于 $10^{-7}$。 #### 说明/提示 在第一个样例里答案被棺材的长度限制（请记住——棺材的宽不能大于长） 在第二个样例里，棺材由于用于旋转的轮子可以被运送通过走廊：首先，从一端拖着棺材，直到有墙阻止继续前进，然后垂直于初始移动方向将其向前移到相邻的一侧。（请记住——棺材可以任意平移、旋转）

题目描述

A very unusual citizen lives in a far away kingdom — Dwarf Gracula. However, his unusual name is not the weirdest thing (besides, everyone long ago got used to calling him simply Dwarf Greg). What is special about Dwarf Greg — he's been living for over 200 years; besides, he lives in a crypt on an abandoned cemetery and nobody has ever seen him out in daytime. Moreover, nobody has ever seen Greg buy himself any food. That's why nobody got particularly surprised when after the infernal dragon's tragic death cattle continued to disappear from fields. The people in the neighborhood were long sure that the harmless dragon was never responsible for disappearing cattle (considering that the dragon used to be sincere about his vegetarian views). But even that's not the worst part of the whole story. The worst part is that merely several minutes ago Dwarf Greg in some unintelligible way got inside your house and asked you to help him solve a problem. The point is that a short time ago Greg decided to order a new coffin (knowing his peculiar character, you are not surprised at all). But the problem is: a very long in both directions L-shaped corridor leads to Greg's crypt, and you can't drag just any coffin through that corridor. That's why he asked you to help. You've formalized the task on a plane like this: let the corridor's width before and after the turn be equal to $ a $ and $ b $ correspondingly (see the picture). The corridor turns directly at a right angle, the coffin is a rectangle whose length and width are equal to $ l $ and $ w $ ( $ l>=w $ ) correspondingly. Dwarf Greg has already determined the coffin's length ( $ l $ ), which is based on his height; your task is to determine the coffin's maximally possible width ( $ w $ ), at which it can be brought to the crypt. Besides, due to its large mass (pure marble!) the coffin is equipped with rotating wheels; therefore it is impossible to lift it off the ground, however, arbitrary moves and rotations of the coffin in the plane become possible. The coffin may be rotated arbitrarily just before you drag it into crypt and move through the corridor. Greg promised that if you help him, he will grant you immortality (I wonder how?). And if you don't, well... trust me, you don't want to know what happens if you don't help him...

输入输出格式

输入格式

The first line contains three space-separated integers $ a $ , $ b $ and $ l $ from the problem's statement ( $ 1<=a,b,l<=10^{4} $ ).

输出格式

Print the maximally possible width of a coffin with absolute or relative error no more than $ 10^{-7} $ . If a coffin with the given length and positive width (the coffin that would meet the conditions from the problem's statement) does not exist, print "My poor head =(" (without quotes). It is guaranteed that if the answer is positive, it will be not less than $ 10^{-7} $ . All the hacks will also be checked to meet that condition.

输入输出样例

输入样例 #1

2 2 1

输出样例 #1

1.0000000

输入样例 #2

2 2 2

输出样例 #2

2.0000000

输入样例 #3

2 2 3

输出样例 #3

1.3284271

输入样例 #4

2 2 6

输出样例 #4

My poor head =(

说明

In the first example the answer is restricted by the coffin's length (remember — coffin's widths should not be larger than it's length). In the second example it is possible to drag the coffin through the corridor thanks to rotating wheels: firstly, drag it forward by one side while it will not be hampered by the wall, then move it forward by adjacent side perpendicularly to the initial movement direction (remember — arbitrary moves and rotations of the coffin are possible).