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:

//package practice;
import java.util.*;
import java.io.*;


public class Practice {
    

   
    public static void main(String args[])
    { 
      InputReader in=new InputReader(System.in);
      int r=in.nextInt();
      int s=in.nextInt();
      int p=in.nextInt();
      double arr[][][]=new double[r+1][s+1][p+1];
      arr[r][s][p]=1;
      
      for(int i=r;i>=0;i--)
          for(int j=s;j>=0;j--)
              for(int k=p;k>=0;k--)
              {
                  double total=i*j+j*k+i*k;
                  if(total==0)
                      continue;
                  if(i>0)
                    arr[i-1][j][k]+=arr[i][j][k]*i*k/total;
                  if(j>0)
                   arr[i][j-1][k]+=arr[i][j][k]*i*j/total;
                  if(k>0)
                  arr[i][j][k-1]+=arr[i][j][k]*j*k/total;
                  
                  
              }
      double p1=0,p2=0,p3=0;
      for(int i=0;i<=r;i++)
          p1+=arr[i][0][0];
      for(int i=0;i<=s;i++)
          p2+=arr[0][i][0];
      for(int i=0;i<=p;i++)
          p3+=arr[0][0][i];
      
      System.out.println(p1+" "+p2+" "+p3);
    }
    
    
    
    
 static 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() {
            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 & 15;
 
                c = read();
            } while (!isSpaceChar(c));
 
            return res * sgn;
        }
 
        public int[] nextIntArray(int arraySize) {
            int array[] = new int[arraySize];
 
            for (int i = 0; i < arraySize; i++)
                array[i] = nextInt();
 
            return array;
        }
 
        public long nextLong() {
            int c = read();
 
            while (isSpaceChar(c))
                c = read();
 
            int sign = 1;
 
            if (c == '-') {
                sign = -1;
 
                c = read();
            }
 
            long result = 0;
 
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
 
                result *= 10;
                result += c & 15;
 
                c = read();
            } while (!isSpaceChar(c));
 
            return result * sign;
        }
 
        public long[] nextLongArray(int arraySize) {
            long array[] = new long[arraySize];
 
            for (int i = 0; i < arraySize; i++)
                array[i] = nextLong();
 
            return array;
        }
 
        public float nextFloat() // problematic
        {
            float result, div;
            byte c;
 
            result = 0;
            div = 1;
            c = (byte) read();
 
            while (c <= ' ')
                c = (byte) read();
 
            boolean isNegative = (c == '-');
 
            if (isNegative)
                c = (byte) read();
 
            do {
                result = result * 10 + c - '0';
            } while ((c = (byte) read()) >= '0' && c <= '9');
 
            if (c == '.')
                while ((c = (byte) read()) >= '0' && c <= '9')
                    result += (c - '0') / (div *= 10);
 
            if (isNegative)
                return -result;
 
            return result;
        }
 
        public double nextDouble() // not completely accurate
        {
            double ret = 0, div = 1;
            byte c = (byte) read();
 
            while (c <= ' ')
                c = (byte) read();
 
            boolean neg = (c == '-');
 
            if (neg)
                c = (byte) read();
 
            do {
                ret = ret * 10 + c - '0';
            } while ((c = (byte) read()) >= '0' && c <= '9');
 
            if (c == '.')
                while ((c = (byte) read()) >= '0' && c <= '9')
                    ret += (c - '0') / (div *= 10);
 
            if (neg)
                return -ret;
 
            return ret;
        }
 
        public String next() {
            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) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
 
        public String nextLine() {
            int c = read();
 
            StringBuilder result = new StringBuilder();
 
            do {
                result.appendCodePoint(c);
 
                c = read();
            } while (!isNewLine(c));
 
            return result.toString();
        }
 
        public boolean isNewLine(int c) {
            return c == '\n';
        }
 
        public void close() {
            try {
                stream.close();
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
 
    }
    
}