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.BufferedWriter;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.ObjectInputStream.GetField;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.InputMismatchException;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Scanner;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;


	public class Q1 {
		
		static long MOD = 1000000007;
		static boolean b[], b1[];
		static ArrayList<Integer>[] amp, pa;
		static ArrayList<Graph>[] amp1;
		static int left[],s[],right[],sum[],dist[],cnt[],arr[],start[],color[],parent[],prime[],size[];
		static long ans = 0,k;
		static int p = 0;
		static FasterScanner sc = new FasterScanner(System.in);
		static Queue<Pair> queue = new LinkedList<>();
		static PriorityQueue<Integer> pq;
		static BufferedWriter log;
		static HashSet<Integer>[] hs;
		static HashMap<String,Integer> hm;
		static HashMap<Pair,Integer> hmp;
		static Stack<Integer> st;
		static Pair prr[];
		static long parent1[],parent2[],size1[],size2[],arr1[];
		public static void main(String[] args) throws Exception {
	    	new Thread(null, new Runnable() {
				public void run() {
					try {
						soln();
					} catch (Exception e) {
						System.out.println(e);
					}
				}
			}, "1", 1 << 26).start();
		}
		static double dp[][][];
		public static void soln() throws IOException {
			//FasterScanner in = new FasterScanner(new FileInputStream("C:\\Users\\Admin\\Desktop\\QCL.txt"));
			//PrintWriter out = new PrintWriter("C:\\Users\\Admin\\Desktop\\A1.txt");
			log = new BufferedWriter(new OutputStreamWriter(System.out));
			int n = sc.nextInt(), m = sc.nextInt(), k = sc.nextInt();
			dp = new double[n+1][m+1][k+1];
			
			dp[n][m][k] = 1;
			for(int i = n;i>=0;i--){
				for(int j = m; j>=0;j--){
					for(int c =k;c>=0;c--){
						double sum = i*j+j*c+c*i;
						if(c>0 && sum>0) dp[i][j][c-1] += (dp[i][j][c]*(j*c))/(sum);
					if(j>0 && sum>0) dp[i][j-1][c] += (dp[i][j][c]*(j*i))/(sum);
				if(i>0 && sum>0) dp[i-1][j][c] += (dp[i][j][c]*(c*i))/(sum);
					}
				}
			}
			//System.out.println(1);
			double r = 0, s = 0, p = 0;
			for(int i = 1; i<=n;i++){
				r+=dp[i][0][0];
			}
			for(int i = 1; i<=m;i++){
				s+=dp[0][i][0];
			}
			for(int i = 1; i<=k;i++){
				p+=dp[0][0][i];
			}
			System.out.println(r+" "+s+" "+p);
			log.close();
			//out.close();
		}
		static void dfs(int x){
			b[x] = true;
			for(Graph g:amp1[x]){
				if(!b[g.vertex]){
					int min = g.weight, max = min;
					ans+=2*min;
					for(Graph g1:amp1[g.vertex]){
						ans+=Math.max(max, prr[g1.vertex].v);
						ans+=Math.min(min, prr[g1.vertex].u);
					}
				}
			}
		}
		public static void buildWeightedGraph(int n){
			for(int i =0 ;i< n; i++){
				int x = sc.nextInt(), y = sc.nextInt(), w = sc.nextInt();
				amp1[--x].add(new Graph(--y,w));
				amp1[y].add(new Graph(x,w));
			}
		}
		
		public static void seive(int n){
			b = new boolean[(n+1)];
			Arrays.fill(b, true);
			b[1] = false;
			for(int i = 2;i*i<=n;i++){
				if(b[i]){
					for(int p = 2*i;p<=n;p+=i){
						b[p] = false;
						prime[p] = i;
					}
				}
			}
			for(int i = 2;i<=n;i++){
				if(b[i]) prime[i] = i;
			}
		}
		
		static class Graph{
			int vertex;
			int weight;
			Graph(int v, int w){
				vertex = v;
				weight = w;
			}
		}
		static class Pair implements Comparable<Pair> {
			int u;
			int v;
			public Pair(int u, int v) {
				this.u = u;
				this.v = v;
			}
			
			public int hashCode() {
				int hu = (int) (u ^ (u >>> 32));
				int hv = (int) (v ^ (v >>> 32));
				return 31*hu + hv;
			}
	 
			public boolean equals(Object o) {
				Pair other = (Pair) o;
				return ((u == other.u && v == other.v));
			}
	 
			public int compareTo(Pair other) {
				return Long.compare(u, other.u); //!= 0 ? (Long.compare(u, other.u))// : (Long.compare(v, other.v));
				//return Long.compare(w, other.w);
			}
			
			public String toString() {
				return "[u=" + u + ", v=" + v + "]";
			}
		}
		
		public static void buildGraph(int n){
			for(int i =0;i<n;i++){
				int x = sc.nextInt()-1, y = sc.nextInt()-1;
				amp[x].add(y);
			}
		}
		
		
		public static int getParent(long x){
			while(parent[(int) x]!=x){
				parent[ (int) x] = parent[(int) parent[ (int) x]];
				x = parent[ (int) x];
			}
			return (int) x;
		}
		static long min(long a, long b, long c){
			if(a<b && a<c) return a;
			if(b<c) return b;
			return c;
		}
		/*
		
		static class Pair3{
			int x, y ,z;
			Pair3(int x, int y, int z){
				this.x = x;
				this.y = y;
				this.z = z;
			}
		}*/
		static int sum(int n){
			String str = Integer.toString(n);
			int cnt = 0;
			for(int i = 0; i< str.length();i++){
				cnt+=(str.charAt(i)-'0');
			}
			return cnt;
		}
		 static void KMPSearch(String pat, String txt)
		    {
		        int M = pat.length();
		        int N = txt.length();
		 
		        // create lps[] that will hold the longest
		        // prefix suffix values for pattern
		        int lps[] = new int[M];
		        int j = 0;  // index for pat[]
		 
		        // Preprocess the pattern (calculate lps[]
		        // array)
		        computeLPSArray(pat,M,lps);
		 
		        int i = 0;  // index for txt[]
		        while (i < N)
		        {
		            if (pat.charAt(j) == txt.charAt(i))
		            {
		                j++;
		                i++;
		            }
		            if (j == M)
		            {
		               // parent.add((i-j));
		                j = lps[j-1];
		            }
		 
		            // mismatch after j matches
		            else if (i < N && pat.charAt(j) != txt.charAt(i))
		            {
		                // Do not match lps[0..lps[j-1]] characters,
		                // they will match anyway
		                if (j != 0)
		                    j = lps[j-1];
		                else
		                    i = i+1;
		            }
		        }
		    }
		 static void computeLPSArray(String pat, int M, int lps[])
		    {
		        // length of the previous longest prefix suffix
		        int len = 0;
		        int i = 1;
		        lps[0] = 0;  // lps[0] is always 0
		 
		        // the loop calculates lps[i] for i = 1 to M-1
		        while (i < M)
		        {
		            if (pat.charAt(i) == pat.charAt(len))
		            {
		                len++;
		                lps[i] = len;
		                i++;
		            }
		            else  // (pat[i] != pat[len])
		            {
		                // This is tricky. Consider the example.
		                // AAACAAAA and i = 7. The idea is similar 
		                // to search step.
		                if (len != 0)
		                {
		                    len = lps[len-1];
		 
		                    // Also, note that we do not increment
		                    // i here
		                }
		                else  // if (len == 0)
		                {
		                    lps[i] = len;
		                    i++;
		                }
		            }
		        }
		    }
		private static void permutation(String prefix, String str) {
		    int n = str.length();
		    if (n == 0); //hs.add(prefix);
		    else {
		        for (int i = 0; i < n; i++)
		            permutation(prefix + str.charAt(i), str.substring(0, i) + str.substring(i+1, n));
		    }
		}
		public static char give(char c1,char c2){
			if(c1!='a' && c2!='a') return 'a';
			if(c1!='b' && c2!='b') return 'b';
			return 'c';
		}
		
		public static void buildTree(int n){
			int arr[] = sc.nextIntArray(n);
			for(int i = 0;i<n;i++){
				int x = arr[i]-1;
				amp[i+1].add(x);
				amp[x].add(i+1);
			}
		}
		
		static class SegmentTree {
			long st[];
			//long lazy[];

			SegmentTree(int n) {
				int size = 4 * n;
				st = new long[size];
				//lazy = new long[size];
				//build(0, n - 1, 1);
			}
			
			/*long[] build(int ss, int se, int si) {
				if (ss == se) {
					st[si][0] = 1;
					st[si][1] = 1;
					st[si][2] = 1;
					return st[si];
				}
				int mid = (ss + se) / 2;
				long a1[] = build(ss, mid, si * 2), a2[] = build(mid + 1, se,
						si * 2 + 1);
				long ans[] = new long[3];
				if (arr[mid] < arr[mid + 1]) {
					ans[1] = Math.max(a2[1], Math.max(a1[1], a1[2] + a2[0]));
					if (a1[1] == (mid - ss + 1))
						ans[0] = ans[1];
					else
						ans[0] = a1[0];
					if (a2[2] == (se - mid))
						ans[2] = ans[1];
					else
						ans[2] = a2[2];
				} else {
					ans[1] = Math.max(a1[1], a2[1]);
					ans[0] = a1[0];
					ans[2] = a2[2];
				}
				st[si] = ans;
				return st[si];
			}*/

			void update(int si, int ss, int se, int idx, long x) {
				if (ss == se) {
					//arr[idx] += val;
					st[si]=x;
				} 
				else {
					int mid = (ss + se) / 2;
					if(ss <= idx && idx <= mid)
			        {
			             update(2*si, ss, mid, idx, x);
			        }
			        else
			        { update(2*si+1, mid+1, se, idx, x);
			        }
					st[si] = st[2*si]+st[2*si+1];
				}
			}
			long get(int qs, int qe, int ss, int se, int si){
				if(qs>se || qe<ss) return 0;
				if (qs <= ss && qe >= se) {
					return st[si];
				}
				int mid = (ss+se)/2;
				return get(qs, qe, ss, mid, si * 2)+get(qs, qe, mid + 1, se, si * 2 + 1);
			}
			/*void updateRange(int node, int start, int end, int l, int r, int val)
			{
			    if(lazy[node] != 0)
			    { 
			        // This node needs to be updated
			        st[node] += (end - start + 1) * lazy[node];    // Update it
			        if(start != end)
			        {
			            lazy[node*2] += lazy[node];                  // Mark child as lazy
			            lazy[node*2+1] += lazy[node];                // Mark child as lazy
			        }
			        lazy[node] = 0;                                  // Reset it
			    }
			    if(start > end || start > r || end < l)              // Current segment is not within range [l, r]
			        return;
			    if(start >= l && end <= r)
			    {
			        // Segment is fully within range
			        st[node] += (end - start + 1) * val;
			        if(start != end)
			        {
			            // Not leaf node
			            lazy[node*2] += val;
			            lazy[node*2+1] += val;
			        }
			        return;
			    }
			    int mid = (start + end) / 2;
			    updateRange(node*2, start, mid, l, r, val);        // Updating left child
			    updateRange(node*2 + 1, mid + 1, end, l, r, val);   // Updating right child
			    st[node] = st[node*2] + st[node*2+1];        // Updating root with max value 
			}

			int queryRange(int node, int start, int end, int l, int r)
			{
			    if(start > end || start > r || end < l)
			        return 0;         // Out of range
			    if(lazy[node] != 0)
			    {
			        // This node needs to be updated
			        st[node] += (end - start + 1) * lazy[node];            // Update it
			        if(start != end)
			        {
			            lazy[node*2] += lazy[node];         // Mark child as lazy
			            lazy[node*2+1] += lazy[node];    // Mark child as lazy
			        }
			        lazy[node] = 0;                 // Reset it
			    }
			    if(start >= l && end <= r)             // Current segment is totally within range [l, r]
			        return (int) st[node];
			    int mid = (start + end) / 2;
			    int p1 = queryRange(node*2, start, mid, l, r);         // Query left child
			    int p2 = queryRange(node*2 + 1, mid + 1, end, l, r); // Query right child
			    return (p1 + p2);
			}*/
			void print() {
				for (int i = 0; i < st.length; i++) {
					System.out.print(st[i]+" ");
				}
				System.out.println();
			}
		}
		static int convert(int x){
			int cnt = 0;
			String str = Integer.toBinaryString(x);
			//System.out.println(str);
			for(int i = 0;i<str.length();i++){
				if(str.charAt(i)=='1'){
					cnt++;
				}
			}
			int ans = (int) Math.pow(3, 6-cnt);
			return ans;
		}
		static class Node2{
			Node2 left = null;
			Node2 right = null;
			Node2 parent = null;
			int data;
		}
		static class BinarySearchTree{
			Node2 root = null;
			int height = 0;
			int max = 0;
			int cnt = 1;
			ArrayList<Integer> parent = new ArrayList<>();
			HashMap<Integer, Integer> hm = new HashMap<>();
			public void insert(int x){
				Node2 n = new Node2();
				n.data = x;
				if(root==null){
					root = n;
				}
				else{
					Node2 temp = root,temp2 = null;
					while(temp!=null){
						temp2 = temp;
						if(x>temp.data) temp = temp.right;
						else temp = temp.left;
					}
					if(x>temp2.data) temp2.right = n;
					else temp2.left = n;
					n.parent = temp2;
					parent.add(temp2.data);
				}
			}
			public Node2 getSomething(int x, int y, Node2 n){
				if(n.data==x || n.data==y) return n;
				else if(n.data>x && n.data<y) return n;
				else if(n.data<x && n.data<y) return getSomething(x,y,n.right);
				else return getSomething(x,y,n.left);
			}
			public Node2 search(int x,Node2 n){
				if(x==n.data){
					max = Math.max(max, n.data);
					return n;
				}
				if(x>n.data){
					max = Math.max(max, n.data);
					return search(x,n.right);
				}
				else{
					max = Math.max(max, n.data);
					return search(x,n.left);
				}
			}
			public int getHeight(Node2 n){
				if(n==null) return 0;
				height = 1+ Math.max(getHeight(n.left), getHeight(n.right));
				return height;
			}
		}
		static long findDiff(long[] arr, long[] brr, int m){
			int i = 0, j = 0;
			long fa = 1000000000000L;
			while(i<m && j<m){
				long x = arr[i]-brr[j];
				if(x>=0){
					if(x<fa) fa = x;
					j++;
				}
				else{
					if((-x)<fa) fa = -x;
					i++;
				}
			}
			return fa;
		}
		public static long max(long x, long y, long z){
			if(x>=y && x>=z) return x;
			if(y>=x && y>=z) return y;
			return z;
		}
		
		static long modInverse(long a, long mOD2){
		            return  power(a, mOD2-2, mOD2);
		}
		static long power(long x, long y, long m)
		{
		    if (y == 0)
		        return 1;
		    long p = power(x, y/2, m) % m;
		    p = (p * p) % m;
		 
		    return (y%2 == 0)? p : (x * p) % m;
		}
		static long power2(long x,BigInteger y,long m){
			long ans = 1;
			BigInteger two = new BigInteger("2");
			while(y.compareTo(BigInteger.ZERO)>0){
				if(y.getLowestSetBit()==y.bitCount()){
					x = (x*x)%MOD;
					y = y.divide(two);
				}
				else{
					ans = (ans*x)%MOD;
					y = y.subtract(BigInteger.ONE);
				}
			}
			return ans;
		}
		static BigInteger power2(BigInteger x, BigInteger y, BigInteger m){
			BigInteger ans = new BigInteger("1");
			BigInteger one  = new BigInteger("1");
			BigInteger two  = new BigInteger("2");
			BigInteger zero  = new BigInteger("0");
			while(y.compareTo(zero)>0){
				//System.out.println(y);
				if(y.mod(two).equals(one)){
					ans = ans.multiply(x).mod(m);
					y = y.subtract(one);
				}
				else{
					x = x.multiply(x).mod(m);
					y = y.divide(two);
				}
			}
			return ans;
		}
		static BigInteger power(BigInteger x, BigInteger y, BigInteger m)
		{
		    if (y.equals(0))
		        return (new BigInteger("1"));
		    BigInteger p = power(x, y.divide(new BigInteger("2")), m).mod(m);
		    p = (p.multiply(p)).mod(m);
		 
		    return (y.mod(new BigInteger("2")).equals(0))? p : (p.multiply(x)).mod(m);
		}
		static long d,x,y;
		public static void extendedEuclidian(long a, long b){
			if(b == 0) {
		        d = a;
		        x = 1;
		        y = 0;
		    }
		    else {
		        extendedEuclidian(b, a%b);
		        int temp = (int) x;
		        x = y;
		        y = temp - (a/b)*y;
		    }
		}
		
		public static long gcd(long n, long m){
			if(m!=0) return gcd(m,n%m);
			else return n;
		}
		
		static BufferedReader reader;
	    static StringTokenizer tokenizer;
	    static PrintWriter writer;
	
	
	   
	    static class FasterScanner {

			private final InputStream stream;
			private final byte[] buf = new byte[8192];
			private int curChar, snumChars;
			private SpaceCharFilter filter;

			public FasterScanner(InputStream stream) {
				this.stream = stream;
			}

			public int snext() {
				if (snumChars == -1)
					throw new InputMismatchException();
				if (curChar >= snumChars) {
					curChar = 0;
					try {
						snumChars = stream.read(buf);
					} catch (IOException e) {
						throw new InputMismatchException();
					}
					if (snumChars <= 0)
						return -1;
				}
				return buf[curChar++];
			}

			public int nextInt() {
				int c = snext();
				while (isSpaceChar(c)) {
					c = snext();
				}
				int sgn = 1;
				if (c == '-') {
					sgn = -1;
					c = snext();
				}
				int res = 0;
				do {
					if (c < '0' || c > '9')
						throw new InputMismatchException();
					res *= 10;
					res += c - '0';
					c = snext();
				} while (!isSpaceChar(c));
				return res * sgn;
			}

			public long nextLong() {
				int c = snext();
				while (isSpaceChar(c)) {
					c = snext();
				}
				int sgn = 1;
				if (c == '-') {
					sgn = -1;
					c = snext();
				}
				long res = 0;
				do {
					if (c < '0' || c > '9')
						throw new InputMismatchException();
					res *= 10;
					res += c - '0';
					c = snext();
				} while (!isSpaceChar(c));
				return res * sgn;
			}

			public int[] nextIntArray(int n) {
				int a[] = new int[n];
				for (int i = 0; i < n; i++) {
					a[i] = nextInt();
				}
				return a;
			}

			public long[] nextLongArray(int n) {
				long a[] = new long[n];
				for (int i = 0; i < n; i++) {
					a[i] = nextInt();
				}
				return a;
			}
	                
			public String readString() {
				int c = snext();
				while (isSpaceChar(c)) {
					c = snext();
				}
				StringBuilder res = new StringBuilder();
				do {
					res.appendCodePoint(c);
					c = snext();
				} while (!isSpaceChar(c));
				return res.toString();
			}

			public String nextLine() {
				int c = snext();
				while (isSpaceChar(c))
					c = snext();
				StringBuilder res = new StringBuilder();
				do {
					res.appendCodePoint(c);
					c = snext();
				} while (!isEndOfLine(c));
				return res.toString();
			}

			public boolean isSpaceChar(int c) {
				if (filter != null)
					return filter.isSpaceChar(c);
				return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
			}

			private boolean isEndOfLine(int c) {
				return c == '\n' || c == '\r' || c == -1;
			}

			public interface SpaceCharFilter {
				public boolean isSpaceChar(int ch);
			}
		}
	}