Problem: The Bad Luck Island is inhabited by three kinds of species: r rocks, s scissors and p papers. At some moments of time two random individuals meet (all pairs of individuals can meet equiprobably), and if they belong to different species, then one individual kills the other one: a rock kills scissors, scissors kill paper, and paper kills a rock. Your task is to determine for each species what is the probability that this species will be the only one to inhabit this island after a long enough period of time.

Input

The single line contains three integers r, s and p (1 ≤ r, s, p ≤ 100) — the original number of individuals in the species of rock, scissors and paper, respectively.

Output

Print three space-separated real numbers: the probabilities, at which the rocks, the scissors and the paper will be the only surviving species, respectively. The answer will be considered correct if the relative or absolute error of each number doesn't exceed 10 - 9.

Examples

Input

2 2 2


Output

0.333333333333 0.333333333333 0.333333333333


Input

2 1 2


Output

0.150000000000 0.300000000000 0.550000000000


Input

1 1 3


Output

0.057142857143 0.657142857143 0.285714285714

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.FileWriter;
import java.io.BufferedOutputStream;
import java.io.InputStreamReader;
import java.io.IOException;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.util.Arrays;
import java.util.Collections;
import java.util.*;
 
public class BadLuckIsland{
	
   public static void main(String[] args) throws IOException {
      MyScanner sc = new MyScanner();
      out = new PrintWriter(new BufferedOutputStream(System.out));
      
      int r = sc.nextInt();
      int s = sc.nextInt();
      int p = sc.nextInt();
      double [][][] dp1 = new double [r+1][s+1][p+1];
      double [][][] dp2 = new double [r+1][s+1][p+1];
      for (int i = 0; i <= r; i ++)
      {
    	  for (int j = 0; j <= s; j++)
    	  {
    		  for (int k = 0; k <= p; k++)
    		  {
    			  dp1[i][j][k] = -1;
    			  dp2[i][j][k] = -1;
    			  
    		  }
    	  }
      }
      
      for (int i = 0; i <= s; i ++)
      {
    	  for (int j = 0; j <= p; j++)
    	  {
    		  dp1[0][i][j] = 0;
    	  }
      }
      
      for (int i = 0; i <= r; i ++)
      {
    	  for (int j = 0; j <= p; j++)
    	  {
    		  dp2[i][0][j] = 0;
    	  }
      }
      
      for (int i = 1; i <= r; i++)
      {
    	  dp1[i][0][0] = 1;
      }
      
      for (int i = 1; i <= s; i++)
      {
    	  dp2[0][i][0] = 1;
      }
      
      for (int i = 1; i <= p; i++)
      {
    	  dp1[0][0][i] = 0;
    	  dp2[0][0][i] = 0;
      }
      
      

      double r_prob = rock(r, s , p, dp1);
      double s_prob = scissors(r, s, p, dp2);
      double p_prob = 1 - r_prob - s_prob;
      
      out.println(r_prob + " " + s_prob + " " + p_prob);
      out.close();
     
   }
   
     

   //-----------PrintWriter for faster output---------------------------------
   public static PrintWriter out;
      
   //-----------MyScanner class for faster input----------
   public static class MyScanner {
      BufferedReader br;
      StringTokenizer st;
 
      public MyScanner() {
         br = new BufferedReader(new InputStreamReader(System.in));
      }
 
      String next() {
          while (st == null || !st.hasMoreElements()) {
              try {
                  st = new StringTokenizer(br.readLine());
              } catch (IOException 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 (IOException e) {
	     e.printStackTrace();
	  }
	  return str;
      }
      
      

   }
   
   static double rock(int r, int s, int p, double [][][] dp)
   {
	   if (dp[r][s][p] == -1)
	   {
		   double total = combination(r + s + p, 2);
		   double prob = (double) ((combination(s, 2) + combination(r, 2) + combination(p, 2)) / (total));
		   double scalar = 1 / (1 - prob);
		   
		   if (r == 0)
		   {
			   return 0;
		   }
		   
		   else if (s == 0)
		   {
			   dp[r][s][p] = scalar * ((r * p)/(total) * rock(Math.max(r - 1, 0), s, p, dp));
			   return dp[r][s][p];
		   }
		   else if (p == 0)
		   {
			   
			   dp[r][s][p] = scalar * ((r * s)/(total) * rock(r, Math.max(s - 1, 0), p, dp));
			   return dp[r][s][p];
		   }
		   else
		   {
			   dp[r][s][p] = scalar * ((r * s)/(total) * rock(r, Math.max(s - 1, 0), p, dp) + (r * p)/(total) * rock(Math.max(r - 1, 0), s, p, dp) + (s * p)/(total) * rock(r, s , Math.max(p - 1, 0), dp));
			   return dp[r][s][p];
		   }
	   }
	   
	   return dp[r][s][p];
   }
   
   static double scissors (int r, int s, int p, double [][][] dp)
   {
	   if (dp[r][s][p] == -1)
	   {
		   double total = combination(r + s + p, 2);
		   double prob = (double) ((combination(s, 2) + combination(r, 2) + combination(p, 2)) / (total));
		   double scalar = 1 / (1 - prob);
		   if (r == 0)
		   {
			   dp[r][s][p] = scalar *  ((s * p)/(total) * scissors(r, s , Math.max(p - 1, 0), dp));
			   return dp[r][s][p];
		   }
		   
		   else if (s == 0)
		   {
			   return 0;
		   }
		   else if (p == 0)
		   {
			   dp[r][s][p] = scalar * ((r * s)/(total) * scissors(r, Math.max(s - 1, 0), p, dp));
			   return dp[r][s][p];
		   }
		   else
		   {
			   dp[r][s][p] = scalar * ((r * s)/(total) * scissors(r, Math.max(s - 1, 0), p, dp) + (r * p)/(total) * scissors(Math.max(r - 1, 0), s, p, dp) + (s * p)/(total) * scissors(r, s , Math.max(p - 1, 0), dp));
			   return dp[r][s][p];
		   }
	   }
	   
	   return dp[r][s][p];
   }
   

   
   static double combination (int n, int k)
   {
	   if (n < k)
	   {
		   return 0;
	   }
	   return (n * (n - 1)) / 2;
   }
   
 
}