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:
//package codeforces;


import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.Closeable;
import java.io.FileReader;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Comparator;
import java.util.List;
import java.util.Locale;
import java.util.Random;
import java.util.StringTokenizer;

public class A implements Closeable {
    BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
    PrintWriter writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));

    A() throws IOException {
//        reader = new BufferedReader(new FileReader("input.txt"));
//        writer = new PrintWriter(new FileWriter("output.txt"));
    }

    StringTokenizer stringTokenizer;

    String next() throws IOException {
        while (stringTokenizer == null || !stringTokenizer.hasMoreTokens()) {
            stringTokenizer = new StringTokenizer(reader.readLine());
        }
        return stringTokenizer.nextToken();
    }

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

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

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

    private int MOD = 1000 * 1000 * 1000 + 7;

    int sum(int a, int b) {
        a += b;
        return a >= MOD ? a - MOD : a;
    }

    int product(int a, int b) {
        return (int) (1l * a * b % MOD);
    }

    int pow(int x, int k) {
        int result = 1;
        while (k > 0) {
            if (k % 2 == 1) {
                result = product(result, x);
            }
            x = product(x, x);
            k /= 2;
        }
        return result;
    }

    int inv(int x) {
        return pow(x, MOD - 2);
    }

    void solve() throws IOException {
        final int r = nextInt(), s = nextInt(), p = nextInt();
        class Triple {
            final double rProb, sProb;

            public Triple(double rProb, double sProb) {
                this.rProb = rProb;
                this.sProb = sProb;
            }

            Triple combineWith(Triple that, double beta) {
                return new Triple(this.rProb + beta * that.rProb,
                        this.sProb + beta * that.sProb);
            }

            @Override
            public String toString() {
                return String.format(Locale.US, "%.10f %.10f %.10f", rProb, sProb, 1.0 - rProb - sProb);
            }
        }
        class Utils {
            Triple calculateProbabilities(int rocks, int scissors, int papers) {
                if(rocks == 0) {
                    return new Triple(0, 1);
                }
                if(scissors == 0) {
                    return new Triple(0, 0);
                }
                if(papers == 0) {
                    return new Triple(1, 0);
                }
                int denominator = rocks + scissors + papers;
                denominator *= denominator - 1;
                denominator /= 2;
                int foo = (rocks * (rocks - 1) + scissors * (scissors - 1) + papers * (papers -1)) / 2;
                //x = S + (foo/denom)*x
                //x * (1 - foo/denom) = S
                //x = S / (1 - foo/denom) = S / ((denom - foo)/denom) = (S * denom) / (denom - foo)
                Triple result = new Triple(0, 0);
                result = result.combineWith(calculateProbabilities(rocks - 1, scissors, papers), papers * rocks);
                result = result.combineWith(calculateProbabilities(rocks, scissors - 1, papers), rocks * scissors);
                result = result.combineWith(calculateProbabilities(rocks, scissors, papers - 1), scissors * papers);
                return new Triple(result.rProb / (denominator - foo), result.sProb / (denominator - foo));
            }
        }
        class CachedUtils extends Utils {
            Triple[][][] cache = new Triple[r + 1][s + 1][p + 1];

            @Override
            Triple calculateProbabilities(int rocks, int scissors, int papers) {
                if(cache[rocks][scissors][papers] == null) {
                    cache[rocks][scissors][papers] = super.calculateProbabilities(rocks, scissors, papers);
                }
                return cache[rocks][scissors][papers];
            }
        }
        writer.println(new CachedUtils().calculateProbabilities(r, s, p));

    }

    public static void main(String[] args) throws IOException {
        try (A a = new A()) {
            a.solve();
        }
    }

    @Override
    public void close() throws IOException {
        reader.close();
        writer.close();
    }
}