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

public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        Task solver = new Task();
        solver.solve(1, in, out);
        out.close();
    }
}

class Task {
	
	public void solve(int testNumber, InputReader in, OutputWriter out) {
    	int r=in.readInt(), s=in.readInt(), p=in.readInt();
    	double[][][] R=new double[r+1][s+1][p+1], S=new double[r+1][s+1][p+1], P=new double[r+1][s+1][p+1];
    	for (int i=0; i<=r; i++) for (int j=0; j<=s; j++) for (int k=0; k<=p; k++) {
    		if (i==0 && j==0 && k==0) R[i][j][k]=S[i][j][k]=P[i][j][k]=0;
    		else if (i==0 && j==0) {
    			P[i][j][k]=1;
    			R[i][j][k]=S[i][j][k]=0;
    		} else if (i==0 && k==0) {
    			S[i][j][k]=1;
    			R[i][j][k]=P[i][j][k]=0;
    		} else if (j==0 && k==0) {
    			R[i][j][k]=1;
    			S[i][j][k]=P[i][j][k]=0;
    		} else if (i==0) {
    			S[i][j][k]=1;
    			R[i][j][k]=P[i][j][k]=0;
    		} else if (j==0) {
    			P[i][j][k]=1;
    			R[i][j][k]=S[i][j][k]=0;
    		} else if (k==0) {
    			R[i][j][k]=1;
    			S[i][j][k]=P[i][j][k]=0;
    		} else {
    			int rs=i*j, rp=i*k, sp=j*k, t=rs+rp+sp;
    			R[i][j][k]=(R[i-1][j][k]*rp+R[i][j-1][k]*rs+R[i][j][k-1]*sp)/t;
    			S[i][j][k]=(S[i-1][j][k]*rp+S[i][j-1][k]*rs+S[i][j][k-1]*sp)/t;
    			P[i][j][k]=(P[i-1][j][k]*rp+P[i][j-1][k]*rs+P[i][j][k-1]*sp)/t;
    		}
    	}
    	out.printLine(R[r][s][p], S[r][s][p], P[r][s][p]);
    }
}

class InputReader {
    private boolean finished = false;

    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;
    private SpaceCharFilter filter;

    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 peek() {
            if (numChars == -1)
                    return -1;
            if (curChar >= numChars) {
                    curChar = 0;
                    try {
                            numChars = stream.read(buf);
                    } catch (IOException e) {
                            return -1;
                    }
                    if (numChars <= 0)
                            return -1;
            }
            return buf[curChar];
    }

    public int readInt() {
            int c = read();
            while (isSpaceChar(c))
                    c = read();
            int sgn = 1;
            if (c == '-') {
                    sgn = -1;
                    c = read();
            }
            int res = 0;
            do {
                    if (c < '0' || c > '9')
                            throw new InputMismatchException();
                    res *= 10;
                    res += c - '0';
                    c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
    }

    public long readLong() {
            int c = read();
            while (isSpaceChar(c))
                    c = read();
            int sgn = 1;
            if (c == '-') {
                    sgn = -1;
                    c = read();
            }
            long res = 0;
            do {
                    if (c < '0' || c > '9')
                            throw new InputMismatchException();
                    res *= 10;
                    res += c - '0';
                    c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
    }

    public String readString() {
            int c = read();
            while (isSpaceChar(c))
                    c = read();
            StringBuilder res = new StringBuilder();
            do {
                    if (Character.isValidCodePoint(c))
                            res.appendCodePoint(c);
                    c = read();
            } while (!isSpaceChar(c));
            return res.toString();
    }

    public boolean isSpaceChar(int c) {
            if (filter != null)
                    return filter.isSpaceChar(c);
            return isWhitespace(c);
    }

    public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

    private String readLine0() {
            StringBuilder buf = new StringBuilder();
            int c = read();
            while (c != '\n' && c != -1) {
                    if (c != '\r')
                            buf.appendCodePoint(c);
                    c = read();
            }
            return buf.toString();
    }

    public String readLine() {
            String s = readLine0();
            while (s.trim().length() == 0)
                    s = readLine0();
            return s;
    }

    public String readLine(boolean ignoreEmptyLines) {
            if (ignoreEmptyLines)
                    return readLine();
            else
                    return readLine0();
    }

    public BigInteger readBigInteger() {
            try {
                    return new BigInteger(readString());
            } catch (NumberFormatException e) {
                    throw new InputMismatchException();
            }
    }

    public char readCharacter() {
            int c = read();
            while (isSpaceChar(c))
                    c = read();
            return (char) c;
    }

    public double readDouble() {
            int c = read();
            while (isSpaceChar(c))
                    c = read();
            int sgn = 1;
            if (c == '-') {
                    sgn = -1;
                    c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                    if (c == 'e' || c == 'E')
                            return res * Math.pow(10, readInt());
                    if (c < '0' || c > '9')
                            throw new InputMismatchException();
                    res *= 10;
                    res += c - '0';
                    c = read();
            }
            if (c == '.') {
                    c = read();
                    double m = 1;
                    while (!isSpaceChar(c)) {
                            if (c == 'e' || c == 'E')
                                    return res * Math.pow(10, readInt());
                            if (c < '0' || c > '9')
                                    throw new InputMismatchException();
                            m /= 10;
                            res += (c - '0') * m;
                            c = read();
                    }
            }
            return res * sgn;
    }

    public boolean isExhausted() {
            int value;
            while (isSpaceChar(value = peek()) && value != -1)
                    read();
            return value == -1;
    }

    public String next() {
            return readString();
    }

    public SpaceCharFilter getFilter() {
            return filter;
    }

    public void setFilter(SpaceCharFilter filter) {
            this.filter = filter;
    }

    public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
    }
}

class OutputWriter {
    private final PrintWriter writer;

    public OutputWriter(OutputStream outputStream) {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
    }

    public OutputWriter(Writer writer) {
            this.writer = new PrintWriter(writer);
    }

    public void print(char[] array) {
            writer.print(array);
    }

    public void print(Object...objects) {
            for (int i = 0; i < objects.length; i++) {
                    if (i != 0)
                            writer.print(' ');
                    writer.print(objects[i]);
            }
    }

public void print(int[] array) {
    for (int i = 0; i < array.length; i++) {
        if (i != 0)
            writer.print(' ');
        writer.print(array[i]);
    }
}

public void print(long[] array) {
    for (int i = 0; i < array.length; i++) {
        if (i != 0)
            writer.print(' ');
        writer.print(array[i]);
    }
}

public void print(Collection<Integer> collection) {
            boolean first = true;
            for (int i: collection) {
                    if (first)
                            first = false;
                    else
                            writer.print(' ');
                    writer.print(i);
            }
    }

    public void printLine(int[] array) {
    print(array);
    writer.println();
}

public void printLine(long[] array) {
    print(array);
    writer.println();
}

public void printLine(Collection<Integer> collection) {
            print(collection);
            writer.println();
    }

    public void printLine() {
            writer.println();
    }

public void printLine(Object...objects) {
            print(objects);
            writer.println();
    }

    public void print(char i) {
            writer.print(i);
    }

    public void printLine(char i) {
            writer.println(i);
    }

    public void printLine(char[] array) {
            writer.println(array);
    }

    public void printFormat(String format, Object...objects) {
            writer.printf(format, objects);
    }

    public void close() {
            writer.close();
    }

    public void flush() {
            writer.flush();
    }

    public void print(long i) {
            writer.print(i);
    }

    public void printLine(long i) {
            writer.println(i);
    }

    public void print(int i) {
            writer.print(i);
    }

    public void printLine(int i) {
            writer.println(i);
    }
}