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.math.BigInteger;
import java.util.*;

public class Template implements Runnable {

    BufferedReader in;
    PrintWriter out;
    StringTokenizer tok = new StringTokenizer("");

    void init() throws FileNotFoundException {
        try {
            in = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter("output.txt");
        } catch (Exception e) {
            String filename = "";
            if (filename.isEmpty()) {
                in = new BufferedReader(new InputStreamReader(System.in));
                out = new PrintWriter(System.out);
            } else {
                in = new BufferedReader(new FileReader(filename + ".in"));
                out = new PrintWriter(filename + ".out");
            }
        }
    }

    String readString() throws IOException {
        while (!tok.hasMoreTokens()) {
            try {
                tok = new StringTokenizer(in.readLine(), " :");
            } catch (Exception e) {
                return null;
            }
        }
        return tok.nextToken();
    }

    int readInt() throws IOException {
        return Integer.parseInt(readString());
    }

    int[] readIntArray(int size) throws IOException {
        int[] res = new int[size];
        for (int i = 0; i < size; i++) {
            res[i] = readInt();
        }
        return res;
    }

    long readLong() throws IOException {
        return Long.parseLong(readString());
    }

    double readDouble() throws IOException {
        return Double.parseDouble(readString());
    }

    <T> List<T>[] createGraphList(int size) {
        List<T>[] list = new List[size];
        for (int i = 0; i < size; i++) {
            list[i] = new ArrayList<>();
        }
        return list;
    }

    public static void main(String[] args) {
        new Thread(null, new Template(), "", 1l * 200 * 1024 * 1024).start();
    }

    long timeBegin, timeEnd;

    void time() {
        timeEnd = System.currentTimeMillis();
        System.err.println("Time = " + (timeEnd - timeBegin));
    }

    long memoryTotal, memoryFree;

    void memory() {
        memoryFree = Runtime.getRuntime().freeMemory();
        System.err.println("Memory = " + ((memoryTotal - memoryFree) >> 10)
                + " KB");
    }

    public void run() {
        try {
            timeBegin = System.currentTimeMillis();
            memoryTotal = Runtime.getRuntime().freeMemory();
            init();
            solve();
            out.close();
            if (System.getProperty("ONLINE_JUDGE") == null) {
                time();
                memory();
            }
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(-1);
        }
    }

    boolean have2nz(int... v) {
        Arrays.sort(v);
        if (v[1] == 0) return false;
        return true;
    }

    double prob(int x, int y, int all) {
        return x * y * 1d / all;
    }

    void solve() throws IOException {
        int r = readInt();
        int s = readInt();
        int p = readInt();

        double[][][] dp = new double[r + 1][s + 1][p + 1];
        dp[r][s][p] = 1;
        for (int total = r + s + p; total > 1; total--) {
            for (int cr = 0; cr <= r; cr++) {
                for (int cs = 0; cs <= s; cs++) {
                    int cp = total - cr - cs;
                    if (cp < 0 || cp > p) continue;
                    if (!have2nz(cr, cs, cp)) continue;

                    int all = cr * cs + cr * cp + cs * cp;

                    if (cr > 0 && cs > 0) {
                        dp[cr][cs - 1][cp] += prob(cr, cs, all) * dp[cr][cs][cp];
                    }
                    if (cr > 0 && cp > 0) {
                        dp[cr - 1][cs][cp] += prob(cr, cp, all) * dp[cr][cs][cp];
                    }
                    if (cs > 0 && cp > 0) {
                        dp[cr][cs][cp - 1] += prob(cs, cp, all) * dp[cr][cs][cp];
                    }
                }
            }
        }

        double x = 0, y = 0, z = 0;
        for (int i = 1; i <= r; i++) {
            x += dp[i][0][0];
        }
        for (int i = 0; i <= s; i++) {
            y += dp[0][i][0];
        }
        for (int i = 0; i <= p; i++) {
            z += dp[0][0][i];
        }
        out.println(x + " " + y + " " + z);

    }

}