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.InputStream;
import java.io.InputStreamReader;
import java.io.IOException;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.Reader;
import java.util.StringTokenizer;

// Codeforces Round #301 (Div. 2)
// Bad Luck Island
public class Problem_540_D {
    

    public static void main(String[] args)
    {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        PrintWriter out = new PrintWriter(outputStream);
        Problem_540_D solver = new Problem_540_D();
        solver.solve(1, new InputStreamReader(inputStream), out);
        out.close();
    }

    public void solve(int test, Reader input, PrintWriter out)
    {
        MyScanner in = new MyScanner(input);
        
        int R = in.nextInt();
        int S = in.nextInt();
        int P = in.nextInt();
        
        int n = R + P + S;
        
        double[][][] dp = new double[R+1][S+1][P+1];
        
        dp[R][S][P] = 1.0;
        for(int sum = n; sum > 0; sum--) {
          for(int r = R; r >= 0; r--) {
            for(int s = S; s >= 0; s--) {
              int p = sum - r - s;
              if(p < 0 || p > P) continue;
              if(r == 0 && s == 0) continue;
              if(r == 0 && p == 0) continue;
              if(s == 0 && p == 0) continue;
              
              double cur = dp[r][s][p];
              
              int wr = r * s;
              int ws = s * p;
              int wp = p * r;
              
              double tw = wr + ws + wp;
              
              if(r > 0) dp[r-1][s][p] += (cur * wp) / tw;
              if(s > 0) dp[r][s-1][p] += (cur * wr) / tw;
              if(p > 0) dp[r][s][p-1] += (cur * ws) / tw;
            }
          }
        }
        
        double ar = 0.0;
        double as = 0.0;
        double ap = 0.0;
        for(int r = 1; r <= R; r++) ar += dp[r][0][0];
        for(int s = 1; s <= S; s++) as += dp[0][s][0];
        for(int p = 1; p <= P; p++) ap += dp[0][0][p];
        
        out.printf("%.12f %.12f %.12f\n", ar, as, ap);
    }

    //-----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner(Reader reader) {
            br = new BufferedReader(reader);
        }

        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());
        }
        
        int[] nextIntArray(int n)
        {
          int[] res = new int[n];
          for(int i = 0; i < n; i++)
            res[i] = nextInt();
          return res;
        }

        long[] nextLongArray(int n)
        {
          long[] res = new long[n];
          for(int i = 0; i < n; i++)
            res[i] = nextLong();
          return res;
        }
        
        double[] nextDoubleArray(int n)
        {
          double[] res = new double[n];
          for(int i = 0; i < n; i++)
            res[i] = nextDouble();
          return res;
        }
        
        String nextLine(){
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

    }
    //--------------------------------------------------------

}