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.*;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
public class Hello {
  static int r,s,q;
  static double a[][][];

  static double dfs0(int r0, int s0, int q0)
  {
    if (a[r0][s0][q0] >= 0) return a[r0][s0][q0];
    if (r0 == 0) return 0.0;
    if (s0 == 0 && q0 > 0) return 0.0;
    if (q0 == 0 && s0 > 0) return 1.0;
    double down = (r0 + s0 + q0) * (r0 + s0 + q0 - 1) / 2;
    double up = (r0) * (r0-1) / 2 + (s0) * (s0-1) / 2 + (q0) * (q0-1) / 2;
    double d = (r0*s0*dfs0(r0,s0-1,q0) + q0*s0*dfs0(r0,s0,q0-1) + q0*r0*dfs0(r0-1,s0,q0)) / down;
    a[r0][s0][q0] = d / (1.0 - up / down);
    return a[r0][s0][q0];
  }
  static double dfs1(int r0, int s0, int q0)
  {
    if (a[r0][s0][q0] >= 0) return a[r0][s0][q0];
    if (s0 == 0) return 0.0;
    if (q0 == 0 && r0 > 0) return 0.0;
    if (r0 == 0 && q0 > 0) return 1.0;
    double down = (r0 + s0 + q0) * (r0 + s0 + q0 - 1) / 2;
    double up = (r0) * (r0-1) / 2 + (s0) * (s0-1) / 2 + (q0) * (q0-1) / 2;
    double d = (r0*s0*dfs1(r0,s0-1,q0) + q0*s0*dfs1(r0,s0,q0-1) + q0*r0*dfs1(r0-1,s0,q0)) / down;
    a[r0][s0][q0] = d / (1.0 - up / down);
    return a[r0][s0][q0];
  }
  public static void main(String[] args) {
    //try {
    //  FileInputStream fis = new FileInputStream("data.txt");
    //  System.setIn(fis);
      //Scanner in = new Scanner(System.in);
      FastReader in = new FastReader(System.in);
      
      
      r = in.nextInt();
      s = in.nextInt();
      q = in.nextInt();
      a = new double[r + 1][s + 1][q + 1];
      
      for (int i = 0;i <= r;++i) for (int j = 0;j <= s;++j) for (int k = 0;k <= q;++k) a[i][j][k] = -1.0;
      double ans0 = dfs0(r, s, q);

      for (int i = 0;i <= r;++i) for (int j = 0;j <= s;++j) for (int k = 0;k <= q;++k) a[i][j][k] = -1.0;
      double ans1 = dfs1(r, s, q);

      //for (int i = 0;i <= r;++i) for (int j = 0;j <= s;++j) for (int k = 0;k <= q;++k) a[i][j][k] = -1;
      double ans2 = 1.0 - ans0 - ans1;

      System.out.println(ans0 + " " + ans1 + " " + ans2);
      
    //} catch (FileNotFoundException e){
    //  System.out.println("error");
    //}
  }
}

class FastReader {
    private boolean finished = false;
 
    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;
    private SpaceCharFilter filter;
 
    public FastReader(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 nextInt() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        int res = 0;
        do {
            if (c == ',') {
                c = read();
            }
            if (c < '0' || c > '9') {
                throw new InputMismatchException();
            }
            res *= 10;
            res += c - '0';
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }
 
    public long nextLong() {
        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 nextString() {
        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 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 nextLine() {
        String s = readLine0();
        while (s.trim().length() == 0)
            s = readLine0();
        return s;
    }
 
    public String nextLine(boolean ignoreEmptyLines) {
        if (ignoreEmptyLines) {
            return nextLine();
        } else {
            return readLine0();
        }
    }
 
    public BigInteger nextBigInteger() {
        try {
            return new BigInteger(nextString());
        } catch (NumberFormatException e) {
            throw new InputMismatchException();
        }
    }
 
    public char nextCharacter() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        return (char) c;
    }
 
    public double nextDouble() {
        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, nextInt());
            }
            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, nextInt());
                }
                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 nextString();
    }
 
    public SpaceCharFilter getFilter() {
        return filter;
    }
 
    public void setFilter(SpaceCharFilter filter) {
        this.filter = filter;
    }
 
    public interface SpaceCharFilter {
        public boolean isSpaceChar(int ch);
    }
}