Codeforces Ratkwesh And Cheese Solution in Java

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.StringTokenizer;


public class Ratkweshandcheese {
 
 static double EPS = 1e-10;

 public static void main(String[] args) 
 {
  MyScannerrat sc=new MyScannerrat();
  double x=sc.nextDouble();
  double y=sc.nextDouble();
  double z=sc.nextDouble();
  boolean fmax=true;
  if((x<=1) && (y<=1) && (z<=1) )
  {
   fmax=false;
  }
  int count=0;
  int index=-1;
  double max=0;
  String types[]={"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"};
  for(int i=1;i<=12;i++)
  {
   double res;
   double base;
   double log;
   double other;
   count++;
   if(count==5)
    count=1;
   if(i<=4)
   { base=x;
   
   }
   else if(i<=8){
    base=y;
   }
   else{
    base=z;
   }
   if(base<=1 && fmax)
    continue;
   if(i==1 || i==3 ||i==10 || i==12)
    log=y;
   else if(i==2 || i==4 ||i==6 || i==8)
    log=z;
   else
    log=x;
   other=x+y+z-base-log;
   if(count==1 || count==2)
   { res=typea(base,log,other);
   }
   else{
    res=typeb(log,other,base);
   }
   
   
   if(fmax && res>(max+EPS) || index==-1)
   {
    max=res;
    index=i;
   }
   else if(!fmax && res<(max-EPS))
   {
    max=res;
    index=i;
   }
  }
  
  System.out.println(types[index-1]);
 }
 public static double typea(double base,double log,double other)
 {
  return other*Math.log(log)+lnln(base);
  
 }
 static double lnln(double v)
 {
  if(v<1)
   v=1/v;
  return Math.log(Math.log(v));
 }
 public static double typeb(double a,double b,double base)
 {
  return Math.log(a)+Math.log(b)+lnln(base);
 }
}
class MyScannerrat
{
 BufferedReader br;
 StringTokenizer st;
 MyScannerrat()
 {
  br=new BufferedReader(new InputStreamReader(System.in));
 }
 String next()
 {
  
  while(st==null || !st.hasMoreTokens())
  {
   try
   {
    st=new StringTokenizer(br.readLine());
   }
   catch(Exception e)
   {
    e.printStackTrace();
   }
  }
  return st.nextToken();
  
 }
 int nextInt()
 {
  return Integer.parseInt(next());
 }
 long nextLong()
 {
  return Long.parseLong(next());
 }
 double nextDouble()
 {
  return Double.parseDouble(next());
 }
 String nextLine()
 {
  String str="";
  try
  {
   str=br.readLine();
  }
  catch(Exception e)
  {
   e.printStackTrace();
  }
  return str;
  
 }
}