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.BufferedWriter;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.math.BigDecimal;
import java.math.MathContext;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Objects;
import java.util.StringTokenizer;

/*
 * To change this license header, choose License Headers in Project Properties.
 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */
/**
 *
 * @author Gerasimov
 */
public class Main {

    /**
     * @param args the command line arguments
     */
    static double[][][][] mas;
    static int r;
    static int s;
    static int p;

    public static void main(String[] args) throws FileNotFoundException, IOException {
        BufferedReader inp = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer input = new StringTokenizer(inp.readLine());
        PrintWriter output = new PrintWriter(
                new BufferedWriter(new OutputStreamWriter(
                                System.out)));
        r = Integer.parseInt(input.nextToken());
        s = Integer.parseInt(input.nextToken());
        p = Integer.parseInt(input.nextToken());
        mas = new double[r + 2][s + 2][p + 2][1];
        mas[r][s][p][0] = 1;
        double ver = mas[r][s][p][0];
        while (ver > 0.000000000000000001) {

            ver = ver * (r * (r - 1) + s * (s - 1) + p * (p - 1)) / (r + s + p) / (r + s + p - 1);
            mas[r][s][p][0] += ver;
        }
        double[] res = new double[3];

        for (int i = r; i > 0; i--) {
            res[0] += Rasch2(i, 0, 0);
        }
        for (int i = s; i > 0; i--) {
            res[1] += Rasch2(0, i, 0);
        }
        for (int i = p; i > 0; i--) {
            res[2] += Rasch2(0, 0, i);
        }

        /* for (int i = r; i >= 0; i--) {
         for (int j = s; j >= 0; j--) {
         for (int k = p; k >= 0; k--) {
         if (i == 0 && j == 0 && k == 0) {
         } else {
         mas[i][j][k][0] += mas[i + 1][j][k][0] * (i + 1) * k / (i + j + k + 1) / (i + j + k) * 2
         + mas[i][j + 1][k][0] * (j + 1) * i / (i + j + k + 1) / (i + j + k) * 2
         + mas[i][j][k + 1][0] * (k + 1) * j / (i + j + k + 1) / (i + j + k) * 2;
         if (i == 0 && j == 0) {
         res[2] += mas[i][j][k][0];
         }
         if (p == 0 && i == 0) {
         res[1] += mas[i][j][k][0];
         }
         if (p == 0 && j == 0) {
         res[0] += mas[i][j][k][0];
         }
         }
         }
         }

         }*/
        output.printf("%.10f", res[0]);
        output.print(" ");
        output.printf("%.10f", res[1]);
        output.print(" ");
        output.printf("%.10f", res[2]);

        output.close();
    }

    public static double Rasch2(int i, int j, int k) {
        if (i > r || j > s || k > p) {
            return 0;
        } else {
            if (mas[i][j][k][0] == 0) {
                mas[i][j][k][0] += Rasch2(i + 1, j, k) * (i + 1) * k / (i + j + k + 1) / (i + j + k) * 2
                        + Rasch2(i, j + 1, k) * (j + 1) * i / (i + j + k + 1) / (i + j + k) * 2
                        + Rasch2(i, j, k + 1) * (k + 1) * j / (i + j + k + 1) / (i + j + k) * 2;

                if ((i > 0 && j > 0) || (k > 0 && j > 0) || (i > 0 && k > 0)) {
                    double ver = mas[i][j][k][0];
                    while (ver > 0.00000000000000001) {

                        ver = ver * (i * (i - 1) + j * (j - 1) + k * (k - 1)) / (i + j + k) / (i + j + k - 1);
                        mas[i][j][k][0] += ver;
                    }

                }

            }

            return mas[i][j][k][0];
        }
    }

    public static double[] Rasch(int r, int s, int p, double ver) {
        double[] res = new double[3];
        if (r == 0 && s == 0) {
            res[2] = ver;
            return res;
        }
        if (r == 0 && p == 0) {
            res[1] = ver;
            return res;
        }
        if (s == 0 && p == 0) {
            res[0] = ver;
            return res;
        }
        double[] r1 = new double[3];
        double[] r2 = new double[3];
        double[] r3 = new double[3];
        double[] r4 = new double[3];
        if (r != 0) {
            r1 = Rasch(r - 1, s, p, ver * r * p / (r + p + s) / (r + p + s - 1) * 2);
        }
        if (s != 0) {
            r2 = Rasch(r, s - 1, p, ver * s * r / (r + p + s) / (r + p + s - 1) * 2);
        }
        if (p != 0) {
            r3 = Rasch(r, s, p - 1, ver * p * s / (r + p + s) / (r + p + s - 1) * 2);
        }
        if (ver > 0.0000000000001) {
            r4 = Rasch(r, s, p, ver * (r * (r - 1) + s * (s - 1) + p * (p - 1)) / (r + p + s) / (r + p + s - 1));
        }
        res[0] = r1[0] + r2[0] + r3[0] + r4[0];
        res[1] = r1[1] + r2[1] + r3[1] + r4[1];
        res[2] = r1[2] + r2[2] + r3[2] + r4[2];
        return res;
    }

}