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.*;
import java.util.*;

public class Solution{
	InputStream is;
	static PrintWriter out;
	String INPUT = "";
	static long mod = (long)1e9+7L;
	
	double[][][] dp;
	int R, S, P;
	public void solve(){
		R = ni(); S = ni(); P = ni();
		dp = new double[R+1][S+1][P+1];
		for(int i = 0; i <= R; i++)for(int j = 0; j <= S; j++)Arrays.fill(dp[i][j], -1);

		double a = 0, b = 0, c = 0;
		for(int i = 1; i <= R; i++) a += f(i, 0, 0);
		for(int i = 1; i <= S; i++) b += f(0, i, 0);
		for(int i = 1; i <= P; i++) c += f(0, 0, i);
		out.println(a+" "+b+" "+c);
	}
	double f(int r, int s, int p){
		if(r > R || s > S || p > P)return 0;
		if(dp[r][s][p] != -1)return dp[r][s][p];
		if(r == R && s == S && p == P)return dp[r][s][p] = 1;

		dp[r][s][p] = 0;

		//probability when reach here by killing rock.
		if(p > 0){
			dp[r][s][p] += (f(r+1, s, p) * (r+1.0)*p/((r+1.0)*s + s*p + p*(r+1.0)));
		}

		//probability when reach here by killing scissor.
		if(r > 0){
			dp[r][s][p] += (f(r, s+1, p) * (s+1.0)*r/(r*(s+1.0) + (s+1.0)*p + p*r));
		}

		//probability when reach here by killing paper.
		if(s > 0){
			dp[r][s][p] += (f(r, s, p+1) * (p+1.0)*s/(r*s + s*(p+1.0) + (p+1.0)*r));
		}
		return dp[r][s][p];
	}

	void run(){
		is = new DataInputStream(System.in);
		out = new PrintWriter(System.out);
		int t=1;while(t-->0)solve();
		out.flush();
	}
	public static void main(String[] args)throws Exception{new Solution().run();}
	long mod(long v, long m){if(v<0){long q=(Math.abs(v)+m-1L)/m;v=v+q*m;}return v%m;}
    long mod(long v){if(v<0){long q=(Math.abs(v)+mod-1L)/mod;v=v+q*mod;}return v%mod;}
	//Fast I/O code is copied from uwi code.
	private byte[] inbuf = new byte[1024];
	public int lenbuf = 0, ptrbuf = 0;
	private int readByte(){
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	private double nd() { return Double.parseDouble(ns()); }
	private char nc() { return (char)skip(); }
	private String ns(){
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	private char[] ns(int n){
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	private char[][] nm(int n, int m){
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	private int[] na(int n){
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	private int ni(){
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	private long nl(){
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	static  int i(long x){return (int)Math.round(x);}
	static class Pair implements Comparable<Pair>{
		long fs,sc;
		Pair(long a,long b){
			fs=a;sc=b;
		}
		public int compareTo(Pair p){
			if(this.fs>p.fs)return 1;
			else if(this.fs<p.fs)return -1;
			else{
				return i(this.sc-p.sc);
			}
			//return i(this.sc-p.sc);
		}
		public String toString(){
			return "("+fs+","+sc+")";
		}	
	}
	
}