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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class CF540D {
    BufferedReader br;
    PrintWriter out;
    StringTokenizer st;
    boolean eof;

    void solve() throws IOException {
        int r = nextInt();
        int s = nextInt();
        int p = nextInt();

        double[][][] dp = new double[1 + r][1 + s][1 + p];
        dp[r][s][p] = 1.0;
        for(int sum3 = r + s + p; sum3 >= 0; sum3--) {
            for(int sum2 = sum3; sum2 >= 0; sum2--) {
                int k = sum3 - sum2;
                for(int i = sum2; i >= 0; i--) {
                    int j = sum2 - i;
                    if(i >= 0 && i <= r && j >= 0 && j <= s && k >= 0 && k <= p) {
                        if(dp[i][j][k] == 0) {
                            continue;
                        }
                        int num = i * j + i * k + j * k;
                        if(num == 0) {
                            continue;
                        }
                        double d1 = 1.0 * i * j / (i * j + i * k + j * k);
                        double d2 = 1.0 * i * k / (i * j + i * k + j * k);
                        double d3 = 1.0 * j * k / (i * j + i * k + j * k);
                        if(i >= 1 && j >= 1) {
                            dp[i][j - 1][k] += dp[i][j][k] * d1;
                        }
                        if(i >= 1 && k >= 1) {
                            dp[i - 1][j][k] += dp[i][j][k] * d2;
                        }
                        if(k >= 1 && j >= 1) {
                            dp[i][j][k - 1] += dp[i][j][k] * d3;
                        }
                    }
                }
            }
        }
        double r1 = 0;
        double s1 = 0;
        double p1 = 0;
        for(int i = 1; i <= r; i++) {
            r1 += dp[i][0][0];
        }
        for(int j = 1; j <= s; j++) {
            s1 += dp[0][j][0];
        }
        for(int k = 1; k <= p; k++) {
            p1 += dp[0][0][k];
        }
        out(r1 + " ");
        out(s1 + " ");
        out(p1);
    }

    void shuffle(long[] a) {
        int n = a.length;
        for(int i = 0; i < n; i++) {
            int r = i + (int) (Math.random() * (n - i));
            long tmp = a[i];
            a[i] = a[r];
            a[r] = tmp;
        }
    }
    private void outln(Object o) {
        System.out.println(o);
    }
    private void out(Object o) {
        System.out.print(o);
    }
    public CF540D() throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        solve();
        out.close();
    }
    public static void main(String[] args) throws IOException {
        new CF540D();
    }

    public long[] nextLongArr(int n) throws IOException{
        long[] res = new long[n];
        for(int i = 0; i < n; i++)
            res[i] = nextLong();
        return res;
    }
    public int[] nextIntArr(int n) throws IOException {
        int[] res = new int[n];
        for(int i = 0; i < n; i++)
            res[i] = nextInt();
        return res;
    }
    public String nextToken() {
        while (st == null || !st.hasMoreTokens()) {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (Exception e) {
                eof = true;
                return null;
            }
        }
        return st.nextToken();
    }
    public String nextString() {
        try {
            return br.readLine();
        } catch (IOException e) {
            eof = true;
            return null;
        }
    }
    public int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }
    public long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }
    public double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }
}