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.util.*;
import java.lang.*;
import java.io.*;
import java.math.*;
import java.util.concurrent.*;

public class Main {
    //---------------------------------------------------------------------------

    static double[][][][] dp;
    static int M = 101;

    static double[] f(int r, int s, int p) {
        double[] ret = new double[3];
        if (dp[r][s][p][0] != -1) {
            return dp[r][s][p];
        }
        if (r == 0 && s == 0 && p == 0) {
            dp[r][s][p] = ret;
            return ret;
        }
        if (r == 0) {
            ret[1] = 1;
            dp[r][s][p] = ret;
            return ret;
        }
        if (s == 0) {
            ret[2] = 1;
            dp[r][s][p] = ret;
            return ret;
        }
        if (p == 0) {
            ret[0] = 1;
            dp[r][s][p] = ret;
            return ret;
        }
        ret[0] = (r * s / (double)(r * s + r * p + s * p)) * f(r, s - 1, p)[0]
                + (r * p / (double)(r * s + r * p + s * p)) * f(r - 1, s, p)[0]
                + (s * p / (double)(r * s + r * p + s * p)) * f(r, s, p - 1)[0];
        ret[1] = (r * s / (double)(r * s + r * p + s * p)) * f(r, s - 1, p)[1]
                + (r * p / (double)(r * s + r * p + s * p)) * f(r - 1, s, p)[1]
                + (s * p / (double)(r * s + r * p + s * p)) * f(r, s, p - 1)[1];
        ret[2] = (r * s / (double)(r * s + r * p + s * p)) * f(r, s - 1, p)[2]
                + (r * p / (double)(r * s + r * p + s * p)) * f(r - 1, s, p)[2]
                + (s * p / (double)(r * s + r * p + s * p)) * f(r, s, p - 1)[2];
        dp[r][s][p] = ret;
        return ret;
    }

    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);
        //-----------------------------------------------------------------------
        dp = new double[M][M][M][3];
        for (int i = 0; i < M; i++) {
            for (int j = 0; j < M; j++) {
                for (int k = 0; k < M; k++) {
                    Arrays.fill(dp[i][j][k], -1);
                }
            }
        }
        int r = in.nextInt();
        int s = in.nextInt();
        int p = in.nextInt();
        double[] res = f(r, s, p);
        for (int i = 0; i < 3; i++) {
            out.printf("%.15f ", res[i]);
        }
        out.println();
        //-----------------------------------------------------------------------
        out.close();
    }

    //---------------------------------------------------------------------------
    static void shuffleArray(int[] ar) {
        Random rnd = ThreadLocalRandom.current();
        for (int i = ar.length - 1; i > 0; i--) {
            int index = rnd.nextInt(i + 1);
            int a = ar[index];
            ar[index] = ar[i];
            ar[i] = a;
        }
    }

    static class Pair implements Comparator {

        int first, second;

        public Pair() {

        }

        public Pair(int f, int s) {
            this.first = f;
            this.second = s;
        }

        @Override
        public int compare(Object o1, Object o2) {
            Pair p1 = (Pair) o1;
            Pair p2 = (Pair) o2;
            int ret = Integer.compare(p1.first, p2.first);
            if (ret == 0) {
                ret = Integer.compare(p1.second, p2.second);
            }
            return ret;
        }
    }

    static class InputReader {

        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        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());
        }

        public char[] nextCharArray() {
            return next().toCharArray();
        }

        public boolean hasNext() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    String s = reader.readLine();
                    if (s == null) {
                        return false;
                    }
                    tokenizer = new StringTokenizer(s);
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return true;
        }

        public void skipLine() {
            try {
                tokenizer = null;
                reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
    }
}