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

public class Main {

    PrintWriter out = new PrintWriter(System.out);
    InputReader ir = new InputReader(System.in);
    final long kmod = 993960000099397l;
    double mem[][][][];

    void solve() throws IOException{
       int r = ir.readInt();
       int s = ir.readInt();
       int p = ir.readInt();
       mem = new double[r + 1][s + 1][p + 1][3];
       for(int i = 0; i <= r; i++) {
            for(int j = 0; j <= s; j++) {
                for(int k = 0; k <= p; k++)
                    Arrays.fill(mem[i][j][k], -1.0);
            }
       }
       for(int i = 0; i < 3; i++) {
            if(i == 0)
            mem[r][s][p][i] = rec0(r, s, p, i);
            if(i == 1)
            mem[r][s][p][i] = rec1(r, s, p, i);
            if(i == 2)
            mem[r][s][p][i] = rec2(r, s, p, i);
            out.printf("%.9f ", mem[r][s][p][i]);
       }
       out.println();
    }
    double rec1(int r, int s, int p, int id) {
        if(s == 0)
            return 0.0;
        if(p == 0 && r == 0)
            return 1.0;
        if(mem[r][s][p][id] != -1)
            return mem[r][s][p][id];
        double tot = r + s + p;
        double pro = 0;
        if(r != 0 && s != 0)
            pro = (r*s*1.0)/(r*s + p*r + s*p) * rec1(r, s- 1, p, id);
        if(s != 0 && p != 0)
            pro += (p*s*1.0)/(r*s + p*r + s*p) * rec1(r, s, p - 1, id);
        if(r != 0 && p != 0)
            pro += (r*p*1.0)/(r*s + p*r + s*p)* rec1(r - 1, s, p, id);
        return mem[r][s][p][id] = pro;
    }
    double rec2(int r, int s, int p, int id) {
        if(p == 0)
            return 0.0;
        if(s == 0 && r == 0)
            return 1.0;
        if(mem[r][s][p][id] != -1)
            return mem[r][s][p][id];
        double tot = r + s + p;
        double pro = 0;
        if(r != 0 && s != 0)
            pro = (r*s*1.0)/(r*s + p*r + s*p) * rec2(r, s- 1, p, id);
        if(s != 0 && p != 0)
            pro += (p*s*1.0)/(r*s + p*r + s*p) * rec2(r, s, p - 1, id);
        if(r != 0 && p != 0)
            pro += (r*p*1.0)/(r*s + p*r + s*p)* rec2(r - 1, s, p, id);
        return mem[r][s][p][id] = pro;
    }
    double rec0(int r, int s, int p, int id) {
        if(r == 0)
            return 0.0;
        if(p == 0 && s == 0)
            return 1.0;

        if(mem[r][s][p][id] != -1)
            return mem[r][s][p][id];
        double tot = r + s + p;
        double pro = 0;
        if(r != 0 && s != 0)
            pro = (r*s*1.0)/(r*s + p*r + s*p) * rec0(r, s- 1, p, id);
        if(s != 0 && p != 0)
            pro += (p*s*1.0)/(r*s + p*r + s*p) * rec0(r, s, p - 1, id);
        if(r != 0 && p != 0)
            pro += (r*p*1.0)/(r*s + p*r + s*p)* rec0(r - 1, s, p, id);
        return mem[r][s][p][id] = pro;
    }
    void run() throws IOException{
        solve();
        out.close();
    }
    public static void main(String args[]) throws IOException{
        new Main().run();
    }
}
class InputReader {
 
    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 final 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 {
            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 double readDouble() {
        return Double.parseDouble(readString());
    }
 
    public static boolean isWhitespace(int c) {
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }
 
    public String next() {
        return readString();
    }
 
    public interface SpaceCharFilter {
        public boolean isSpaceChar(int ch);
    }
}