Rat Kwesh and Cheese

题意翻译

给三个实数 $x,y,z$。求出值最大的 $a_i$，输出 $i$ 对应的字符串。 $a_i$ 的表达式在上方已经列出。

题目描述

Wet Shark asked Rat Kwesh to generate three positive real numbers $ x $ , $ y $ and $ z $ , from $ 0.1 $ to $ 200.0 $ , inclusive. Wet Krash wants to impress Wet Shark, so all generated numbers will have exactly one digit after the decimal point. Wet Shark knows Rat Kwesh will want a lot of cheese. So he will give the Rat an opportunity to earn a lot of cheese. He will hand the three numbers $ x $ , $ y $ and $ z $ to Rat Kwesh, and Rat Kwesh will pick one of the these twelve options: 1. $a_1=x^{y^z}$； 2. $a_2=x^{z^y}$； 3. $a_3=(x^y)^z$； 4. $a_4=(x^z)^y$； 5. $a_5=y^{x^z}$； 6. $a_6=y^{z^x}$； 7. $a_7=(y^x)^z$； 8. $a_8=(y^z)^x$； 9. $a_9=z^{x^y}$； 10. $a_{10}=z^{y^x}$； 11. $a_{11}=(z^x)^y$； 12. $a_{12}=(z^y)^x$。 Let $ m $ be the maximum of all the $ a_{i} $ , and $ c $ be the smallest index (from $ 1 $ to $ 12 $ ) such that $ a_{c}=m $ . Rat's goal is to find that $ c $ , and he asks you to help him. Rat Kwesh wants to see how much cheese he gets, so he you will have to print the expression corresponding to that $ a_{c} $ .

输入输出格式

输入格式

The only line of the input contains three space-separated real numbers $ x $ , $ y $ and $ z $ ( $ 0.1<=x,y,z<=200.0 $ ). Each of $ x $ , $ y $ and $ z $ is given with exactly one digit after the decimal point.

输出格式

Find the maximum value of expression among $ x^{y^z} $ , $ x^{z^y} $ , $ (x^{y})^{z} $ , $ (x^{z})^{y} $ , $ y^{x^z} $ , $ y^{z^x} $ , $ (y^{x})^{z} $ , $ (y^{z})^{x} $ , $ z^{x^y} $ , $ z^{y^x} $ , $ (z^{x})^{y} $ , $ (z^{y})^{x} $ and print the corresponding expression. If there are many maximums, print the one that comes first in the list. $ x^{y^z} $ should be outputted as x^y^z (without brackets), and $ (x^{y})^{z} $ should be outputted as (x^y)^z (quotes for clarity).

输入输出样例

输入样例 #1

1.1 3.4 2.5

输出样例 #1

z^y^x

输入样例 #2

2.0 2.0 2.0

输出样例 #2

x^y^z

输入样例 #3

1.9 1.8 1.7

输出样例 #3

(x^y)^z