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.OutputStream;
import java.io.PrintWriter;
import java.util.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author George Marcus
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskD solver = new TaskD();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskD {
    public void solve(int testNumber, InputReader in, PrintWriter out) {
        int R = in.nextInt();
        int S = in.nextInt();
        int P = in.nextInt();
        double[][][] dp = new double[R + 1][S + 1][P + 1];
        dp[R][S][P] = 1.0;
        for (int r = R; r >= 0; r--) {
            for (int s = S; s >= 0; s--) {
                for (int p = P; p >= 0; p--) {
                    int cnt = 0;
                    if (r > 0) cnt++;
                    if (s > 0) cnt++;
                    if (p > 0) cnt++;
                    if (cnt <= 1) {
                        continue;
                    }

                    {
                        int all = r + s + p;
                        int some = r * (r - 1) + s * (s - 1) + p * (p - 1);
                        double prob = (double) some / all / (all - 1);
                        dp[r][s][p] /= 1.0 - prob;
                    }
                    if (r > 0 && s > 0) {
                        // r -> s
                        int all = r + s + p;
                        double prob = 2.0 * r * s / all / (all - 1);
                        dp[r][s - 1][p] += dp[r][s][p] * prob;
                    }
                    if (s > 0 && p > 0) {
                        // s -> p
                        int all = r + s + p;
                        double prob = 2.0 * s * p / all / (all - 1);
                        dp[r][s][p - 1] += dp[r][s][p] * prob;
                    }
                    if (p > 0 && r > 0) {
                        // p -> r
                        int all = r + s + p;
                        double prob = 2.0 * p * r / all / (all - 1);
                        dp[r - 1][s][p] += dp[r][s][p] * prob;
                    }
                }
            }
        }

        double ansr = 0;
        for (int r = 0; r <= R; r++) {
            ansr += dp[r][0][0];
        }

        double anss = 0;
        for (int s = 0; s <= S; s++) {
            anss += dp[0][s][0];
        }

        double ansp = 0;
        for (int p = 0; p <= P; p++) {
            ansp += dp[0][0][p];
        }

        out.format("%.12f %.12f %.12f\n", ansr, anss, ansp);
    }
}

class InputReader {
    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;

    public InputReader(InputStream stream) {
        this.stream = stream;
    }

    public int read() {
        if (numChars == -1)
            throw new InputMismatchException();
        if (curChar >= numChars) {
            curChar = 0;
            try {
                numChars = stream.read(buf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (numChars <= 0)
                return -1;
        }
        return buf[curChar++];
    }

    public int nextInt() {
        return Integer.parseInt(nextString());
    }

    public String nextString() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        StringBuffer res = new StringBuffer();
        do {
            res.appendCodePoint(c);
            c = read();
        } while (!isSpaceChar(c));

        return res.toString();
    }

    private boolean isSpaceChar(int c) {
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

}