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.BigInteger;
import java.util.Map.Entry;

import static java.lang.Math.*;

public class D extends PrintWriter {

	void run() {
		int n = 101;
		// r s p
		double[][][][] dp = new double[3][n][n][n];

		for (int i = 1; i < n; i++) {
			dp[0][i][0][0] = 1.0;
			dp[1][0][i][0] = 1.0;
			dp[2][0][0][i] = 1.0;
		}

		for (int i = 1; i < n; i++) {
			for (int j = 0; j < n; j++) {
				dp[0][i][j][0] = 1.0;
				dp[1][0][i][j] = 1.0;
				dp[2][j][0][i] = 1.0;
			}
		}

		for (int i = 1; i < n; i++) {
			for (int j = 1; j < n; j++) {
				for (int k = 1; k < n; k++) {
					double m = i + j + k;
					if (m <= 1.5) {
						continue;
					}

					double z = i * j + j * k + k * i;

					double ki = i * k / z;
					double ij = i * j / z;
					double jk = k * j / z;

					for (int q = 0; q < 3; q++) {
						dp[q][i][j][k] += dp[q][i - 1][j][k] * ki;
						dp[q][i][j][k] += dp[q][i][j - 1][k] * ij;
						dp[q][i][j][k] += dp[q][i][j][k - 1] * jk;
					}
				}
			}
		}

		int r = nextInt(), s = nextInt(), p = nextInt();

		print(dp[0][r][s][p]);
		print(' ');
		print(dp[1][r][s][p]);
		print(' ');
		print(dp[2][r][s][p]);
		println();
	}

	int[][] nextMatrix(int n, int m) {
		int[][] matrix = new int[n][m];
		for (int i = 0; i < n; i++)
			for (int j = 0; j < m; j++)
				matrix[i][j] = nextInt();
		return matrix;
	}

	String next() {
		while (!tokenizer.hasMoreTokens())
			tokenizer = new StringTokenizer(nextLine());
		return tokenizer.nextToken();
	}

	boolean hasNext() {
		while (!tokenizer.hasMoreTokens()) {
			String line = nextLine();
			if (line == null) {
				return false;
			}
			tokenizer = new StringTokenizer(line);
		}
		return true;
	}

	int[] nextArray(int n) {
		int[] array = new int[n];
		for (int i = 0; i < n; i++) {
			array[i] = nextInt();
		}
		return array;
	}

	int nextInt() {
		return Integer.parseInt(next());
	}

	long nextLong() {
		return Long.parseLong(next());
	}

	double nextDouble() {
		return Double.parseDouble(next());
	}

	String nextLine() {
		try {
			return reader.readLine();
		} catch (IOException err) {
			return null;
		}
	}

	public D(OutputStream outputStream) {
		super(outputStream);
	}

	static BufferedReader reader;
	static StringTokenizer tokenizer = new StringTokenizer("");
	static Random rnd = new Random();
	static boolean OJ;

	public static void main(String[] args) throws IOException {
		OJ = System.getProperty("ONLINE_JUDGE") != null;
		D solution = new D(System.out);
		if (OJ) {
			reader = new BufferedReader(new InputStreamReader(System.in));
			solution.run();
		} else {
			reader = new BufferedReader(new FileReader(new File(D.class.getName() + ".txt")));
			long timeout = System.currentTimeMillis();
			while (solution.hasNext()) {
				solution.run();
				solution.println();
				solution.println("----------------------------------");
			}
			solution.println("time: " + (System.currentTimeMillis() - timeout));
		}
		solution.close();
		reader.close();
	}
}