A10230 | Rat Kwesh and Cheese

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 $a_{c}$ .

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.

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).