Problem:
Max Score: $800$ Points

Problem Statement

There is an undirected connected graph with $N$ vertices and $N-1$ edges. The i-th edge connects u_i and v_i.

E869120 the coder moves in the graph as follows:

He move to adjacent vertex, but he can't a visit vertex two or more times.

He ends move when there is no way to move.

Otherwise, he moves randomly. (equal probability) If he has $p$ way to move this turn, he choose each vertex with $1/p$ probability.

Calculate the expected value of the number of turns, when E869120 starts from vertex i, for all i (1 ≤ i ≤ N).

Input

The input is given from standard input in the following format.

N
u_1 v_1
u_2 v_2
:
u_{N-1} v_{N-1}

Output

In i-th (1 ≤ i ≤ N) line, print the expected vaule of the number of turns E869120 moves.

The relative error or absolute error of output should be within 10^{-6}.

Constraints

$1 \le N \le 150,000$

The graph is connected.

Subtasks

Subtask 1 [ $190$ points ]

There is no vertex which degree is more than 2.

This means the graph looks like a list.

Subtask 2 [ $220$ points ]

1 ≤ N ≤ 1000.

Subtask 3 [ $390$ points ]

There are no additional constraints.

Sample Input 1

4
1 2
2 3
2 4

Sample Output 1

2.0
1.0
2.0
2.0

Sample Input 2

4
1 2
2 4
4 3

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)


import java.io.*;
import java.math.*;
import java.util.*;

import static java.util.Arrays.*;

public class Main {
	private static final int mod = (int)1e9+7;

	final Random random = new Random(0);
	final IOFast io = new IOFast();

	/// MAIN CODE
	public void run() throws IOException {
//		int TEST_CASE = Integer.parseInt(new String(io.nextLine()).trim());
		int TEST_CASE = 1;
		while(TEST_CASE-- != 0) {
			int n = io.nextInt();
//			int n = 150000;
			
			g = new List[n];
			for (int i = 0; i < n; i++) {
				g[i] = new ArrayList<>();
			}
			
			for (int i = 0; i < n - 1; i++) {
				int s = io.nextInt() - 1;
				int t = io.nextInt() - 1;
//				int s = random.nextInt(i + 1);
//				int t = i + 1;
				g[s].add(t);
				g[t].add(s);
			}
			
			es = new int[n][];
			memo = new double[n][];
			for (int i = 0; i < n; i++) {
				es[i] = new int[g[i].size() + 1];
				memo[i] = new double[g[i].size() + 1];
				es[i][g[i].size()] = -1;
				for (int j = 0; j < g[i].size(); j++) {
					es[i][j] = g[i].get(j);
				}
				Arrays.sort(es[i]);
				Arrays.fill(memo[i], -1);
			}
			
			es2 = new int[n][][];
			for (int i = 0; i < n; i++) {
				es2[i] = new int[g[i].size()][2];
				for (int j = 0; j < g[i].size(); j++) {
					es2[i][j][0] = g[i].get(j);
					es2[i][j][1] = Arrays.binarySearch(es[g[i].get(j)], i);
				}
			}
			
			for (int i = 0; i < n; i++) {
//				io.out.printf("%.10f\n", rec(i, -1));
				print(rec(i, -1, 0));
			}
			io.out.println(res);
		}
	}
	
	int[][][] es2;
	double[][] memo;
	int[][] es;
	List<Integer>[] g;
	double rec(int v, int p, int idx) {
		if (memo[v][idx] >= 0) { return memo[v][idx]; }
		int childs = p == -1 ? g[v].size() : g[v].size() - 1;
		double ans = 0;
		for (int[] t : es2[v]) if (t[0] != -1 && t[0] != p) {
			ans += (rec(t[0], v, t[1]) + 1) / childs;
		}
		memo[v][idx] = ans;
		return ans;
	}

	StringBuilder res = new StringBuilder();
	StringBuilder sb = new StringBuilder();
	void print(double x) {
//		x += 5e-11;
		sb.setLength(0);
		sb.append((int)x);
		sb.append('.');
		for (int i = 0; i < 7; i++) {
			x -= (int)x;
			x *= 10;
			sb.append((char)((int)x + '0'));
		}
//		io.out.println(sb);
		sb.append("\n");
		res.append(sb);
	}
	
	/// TEMPLATE
	static int gcd(int n, int r) { return r == 0 ? n : gcd(r, n%r); }
	static long gcd(long n, long r) { return r == 0 ? n : gcd(r, n%r); }
	
	static <T> void swap(T[] x, int i, int j) { T t = x[i]; x[i] = x[j]; x[j] = t; }
	static void swap(int[] x, int i, int j) { int t = x[i]; x[i] = x[j]; x[j] = t; }

	void printArrayLn(int[] xs) { for(int i = 0; i < xs.length; i++) io.out.print(xs[i] + (i==xs.length-1?"\n":" ")); }
	void printArrayLn(long[] xs) { for(int i = 0; i < xs.length; i++) io.out.print(xs[i] + (i==xs.length-1?"\n":" ")); }
	
	static void dump(Object... o) { System.err.println(Arrays.deepToString(o)); } 
	
	void main() throws IOException {
		//		IOFast.setFileIO("rle-size.in", "rle-size.out");
		try { run(); }
		catch (EndOfFileRuntimeException e) { }
		io.out.flush();
	}
	public static void main(String[] args) throws IOException { new Main().main(); }
	
	static class EndOfFileRuntimeException extends RuntimeException {
		private static final long serialVersionUID = -8565341110209207657L; }

	static
	public class IOFast {
		private BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		private PrintWriter out = new PrintWriter(System.out);

		void setFileIn(String ins) throws IOException { in.close(); in = new BufferedReader(new FileReader(ins)); }
		void setFileOut(String outs) throws IOException { out.flush(); out.close(); out = new PrintWriter(new FileWriter(outs)); }
		void setFileIO(String ins, String outs) throws IOException { setFileIn(ins); setFileOut(outs); }

		private static int pos, readLen;
		private static final char[] buffer = new char[1024 * 8];
		private static char[] str = new char[500*8*2];
		private static boolean[] isDigit = new boolean[256];
		private static boolean[] isSpace = new boolean[256];
		private static boolean[] isLineSep = new boolean[256];

		static { for(int i = 0; i < 10; i++) { isDigit['0' + i] = true; } isDigit['-'] = true; isSpace[' '] = isSpace['\r'] = isSpace['\n'] = isSpace['\t'] = true; isLineSep['\r'] = isLineSep['\n'] = true; }
		public int read() throws IOException { if(pos >= readLen) { pos = 0; readLen = in.read(buffer); if(readLen <= 0) { throw new EndOfFileRuntimeException(); } } return buffer[pos++]; }
		public int nextInt() throws IOException { int len = 0; str[len++] = nextChar(); len = reads(len, isSpace); int i = 0; int ret = 0; if(str[0] == '-') { i = 1; } for(; i < len; i++) ret = ret * 10 + str[i] - '0'; if(str[0] == '-') { ret = -ret; } return ret; }
		public long nextLong() throws IOException { int len = 0; str[len++] = nextChar(); len = reads(len, isSpace); int i = 0; long ret = 0; if(str[0] == '-') { i = 1; } for(; i < len; i++) ret = ret * 10 + str[i] - '0'; if(str[0] == '-') { ret = -ret; } return ret; }
		public char nextChar() throws IOException { while(true) { final int c = read(); if(!isSpace[c]) { return (char)c; } } }
		int reads(int len, boolean[] accept) throws IOException { try { while(true) { final int c = read(); if(accept[c]) { break; } if(str.length == len) { char[] rep = new char[str.length * 3 / 2]; System.arraycopy(str, 0, rep, 0, str.length); str = rep; } str[len++] = (char)c; } } catch(EndOfFileRuntimeException e) { ; } return len; }
		int reads(char[] cs, int len, boolean[] accept) throws IOException { try { while(true) { final int c = read(); if(accept[c]) { break; } cs[len++] = (char)c; } } catch(EndOfFileRuntimeException e) { ; } return len; }
		public char[] nextLine() throws IOException { int len = 0; str[len++] = nextChar(); len = reads(len, isLineSep); try { if(str[len-1] == '\r') { len--; read(); } } catch(EndOfFileRuntimeException e) { ; } return Arrays.copyOf(str, len); }
		public String nextString() throws IOException { return new String(next()); }
		public char[] next() throws IOException { int len = 0; str[len++] = nextChar(); len = reads(len, isSpace); return Arrays.copyOf(str, len); }
//		public int next(char[] cs) throws IOException { int len = 0; cs[len++] = nextChar(); len = reads(cs, len, isSpace); return len; }
		public double nextDouble() throws IOException { return Double.parseDouble(nextString()); }
		public long[] nextLongArray(final int n) throws IOException { final long[] res = new long[n]; for(int i = 0; i < n; i++) { res[i] = nextLong(); } return res; }
		public int[] nextIntArray(final int n) throws IOException { final int[] res = new int[n]; for(int i = 0; i < n; i++) { res[i] = nextInt(); } return res; }
		public int[][] nextIntArray2D(final int n, final int k) throws IOException { final int[][] res = new int[n][]; for(int i = 0; i < n; i++) { res[i] = nextIntArray(k); } return res; }
		public int[][] nextIntArray2DWithIndex(final int n, final int k) throws IOException { final int[][] res = new int[n][k+1]; for(int i = 0; i < n; i++) { for(int j = 0; j < k; j++) { res[i][j] = nextInt(); } res[i][k] = i; } return res; }
		public double[] nextDoubleArray(final int n) throws IOException { final double[] res = new double[n]; for(int i = 0; i < n; i++) { res[i] = nextDouble(); } return res; }
	}
}