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.File;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;


public class Main {

	static class Task {
		
		int NN = 200005;
		int MOD = 1000000007;;
		int INF = 2000000000;
		long INFINITY = 2000000000000000000L;
		int r, s, p;
		public void solve(InputReader in, PrintWriter out) {
			r = in.nextInt();
			s = in.nextInt();
			p = in.nextInt();
			dp = 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)
						dp[i][j][k] = -1;
				}
			}
			double [] ans = new double [3];
			for(int i=1;i<=r;++i) {
				ans[0] += rec(i, 0, 0);
			}
			for(int i=1;i<=s;++i) {
				ans[1] += rec(0, i, 0);
			}
			for(int i=1;i<=p;++i) {
				ans[2] += rec(0, 0, i);
			}
			for(int i=0;i<3;++i) {
				out.print(ans[i] + " ");
			}
			out.println("");
		}
		
		double [][][] dp;
		
		double rec(int i, int j, int k) {			
			if(i > r || j > s || k > p)
				return 0;
			if(dp[i][j][k] != -1)
				return dp[i][j][k];
			double a = (i*(i - 1) + j*(j-1) + k*(k-1));
			double b = ((i+j+k)*(i+j+k-1));
			if(i == r && j == s && k == p)
				return dp[i][j][k] = b*1.0/(b-a);
			double ret = 0;
			double factor = (i+j+k+1)*(i+j+k);
			factor = 2.0 / factor;
			if(b > a)
				factor *= b*1.0/(b-a);
			if(k > 0)
				ret += rec(i + 1, j, k) * factor * (k*(i+1));
			if(i > 0)
				ret += rec(i, j + 1, k) * factor * (i*(j+1));
			if(j > 0)
				ret += rec(i, j, k + 1) * factor * (j*(k+1));
			return dp[i][j][k] = ret;
			
		}
		
	}
	
	static void prepareIO(boolean isFileIO) {
		//long t1 = System.currentTimeMillis();
		Task solver = new Task();
		// Standard IO
		if(!isFileIO) {
			InputStream inputStream = System.in;
	        OutputStream outputStream = System.out;
	        InputReader in = new InputReader(inputStream);
	        PrintWriter out = new PrintWriter(outputStream);
	        solver.solve(in, out);
	        //out.println("time(s): " + (1.0*(System.currentTimeMillis()-t1))/1000.0);
	        out.close();
		}
        // File IO
		else {
			String IPfilePath = System.getProperty("user.home") + "/Downloads/ip.in";
	        String OPfilePath = System.getProperty("user.home") + "/Downloads/op.out";
	        InputReader fin = new InputReader(IPfilePath);
	        PrintWriter fout = null;
	        try {
				fout = new PrintWriter(new File(OPfilePath));
			} catch (FileNotFoundException e) {
				e.printStackTrace();
			}
	        solver.solve(fin, fout);
	        //fout.println("time(s): " + (1.0*(System.currentTimeMillis()-t1))/1000.0);
	        fout.close();
		}
	}
	
	public static void main(String[] args) {
        prepareIO(false);
	}
	
	static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }
        
        public InputReader(String filePath) {
        	File file = new File(filePath);
            try {
				reader = new BufferedReader(new FileReader(file));
			} catch (FileNotFoundException e) {
				// TODO Auto-generated catch block
				e.printStackTrace();
			}
            tokenizer = null;
        }
        
        public String nextLine() {
        	String str = "";
        	try {
				str = reader.readLine();
			} catch (IOException e) {
				// TODO Auto-generated catch block
				e.printStackTrace();
			}
        	return str;
        }
        
        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public double nextDouble() {
        	return Double.parseDouble(next());
        }
        
    }

}