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:
/*
 *
 * @author Mukesh Singh
 *
 */

import java.io.*;
import java.util.*;
import java.text.DecimalFormat;
@SuppressWarnings("unchecked")
public class AB {	
	//solve test cases
	void solve() throws Exception {
		int r = in.nextInt();
		int s = in.nextInt();
		int p = in.nextInt();
		double[][][]dp = new double[r+2][s+2][p+2];
		int a , b, c ;
		double rp = 0 ;double sp = 0 ;double pp = 0 ;
		for(int i = r ; i >= 0 ; -- i ){
			for(int j = s ; j >= 0 ; --j ){
				for(int k = p ; k >= 0 ; --k ){
					if(i == r && j == s && p == k ){
						dp[i][j][k] = 1.0 ; 
						continue ;
					}
					double res = 0 ;
					a = i ; b = j+1 ; c = k ;
					if((a*b+a*c+b*c) > 0 )
						res += (a*b*dp[a][b][c])/(double)(a*b+a*c+b*c);
					a = i ; b = j ; c = k+1 ;
					if((a*b+a*c+b*c) > 0 )
						res += (b*c*dp[a][b][c])/(double)(a*b+a*c+b*c);
					a = i+1 ; b = j ; c = k ;
					if((a*b+a*c+b*c) > 0 )
						res += (a*c*dp[a][b][c])/(double)(a*b+a*c+b*c);
					dp[i][j][k] = res ;
					if((i > 0) && j == 0 && k == 0 ) rp+= dp[i][j][k] ;
					if(i == 0 && (j > 0) && k == 0 ) sp+= dp[i][j][k] ;
					if(i== 0 && j == 0 && (k > 0) ) pp+= dp[i][j][k] ;
				}
			}
		}
		/*for(int i = 0; i <= r ; ++i ){
			for(int j = 0 ;  j <= s ; ++j ){
				for(int k = 0 ; k <= p ; ++k){
					System.out.print(String.format("%2.6f ",dp[i][j][k]));
				}
				System.out.println();
			}
			System.out.println();
		}*/
		System.out.println(rp+" "+sp+" "+pp);
	}
	//@ main function
	public static void main(String[] args) throws Exception {
		new AB();
	}
	
	InputReader in;
	PrintStream out ;
	DecimalFormat df ;
	AB() {
		try {
			File defaultInput = new File("file.in");
			if (defaultInput.exists()) 
				in = new InputReader("file.in");
			else 
				in = new InputReader();
			defaultInput = new File("file.out");
			if (defaultInput.exists()) 
				out = new PrintStream(new FileOutputStream("file.out"));
			else
				out = new PrintStream(System.out);
			df = new DecimalFormat("######0.00");
			solve();
			out.close();
		} 
		catch (Exception e) {
			e.printStackTrace();
			System.exit(261);
		}
	}
	
	class InputReader {
		BufferedReader reader;
		StringTokenizer tokenizer;
		
		InputReader() {
			reader = new BufferedReader(new InputStreamReader(System.in));
		}
		
		InputReader(String fileName) throws FileNotFoundException {
			reader = new BufferedReader(new FileReader(new File(fileName)));
		}
		
		String readLine() throws IOException {
			return reader.readLine();
		}
		
		String nextToken() throws IOException {
			while (tokenizer == null || !tokenizer.hasMoreTokens())
				tokenizer = new StringTokenizer(readLine());
			return tokenizer.nextToken();
		}
		
		boolean hasMoreTokens() throws IOException {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				String s = readLine();
				if (s == null)
					return false;
				tokenizer = new StringTokenizer(s);
			}
			return true;
		}
		
		int nextInt() throws NumberFormatException, IOException {
			return Integer.parseInt(nextToken());
		}
		
		long nextLong() throws NumberFormatException, IOException {
			return Long.parseLong(nextToken());
		}
		
		double nextDouble() throws NumberFormatException, IOException {
			return Double.parseDouble(nextToken());
		}
	}
}