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 Rust (1.15.1) (judge verdict: Accepted)

#![allow(non_snake_case, unused)]
use std::collections::*;

////////// missing functions in 1.15.1 //////////
macro_rules! eprint {
	($($t:tt)*) => {{
		use ::std::io::Write;
		let _ = write!(::std::io::stderr(), $($t)*);
	}};
}
macro_rules! eprintln {
	() => { eprintln!(""); };
	($($t:tt)*) => {{
		use ::std::io::Write;
		let _ = writeln!(::std::io::stderr(), $($t)*);
	}};
}
macro_rules! dbg {
	($v:expr) => {{
		let val = $v;
		eprintln!("[{}:{}] {} = {:?}", file!(), line!(), stringify!($v), val);
		val
	}}
}
/////////////////////////////////////////////////
pub trait SetMinMax {
	fn setmin(&mut self, v: Self) -> bool;
	fn setmax(&mut self, v: Self) -> bool;
}
impl<T> SetMinMax for T where T: PartialOrd {
	fn setmin(&mut self, v: T) -> bool {
		*self > v && { *self = v; true }
	}
	fn setmax(&mut self, v: T) -> bool {
		*self < v && { *self = v; true }
	}
}

macro_rules! mat {
	($($e:expr),*) => { Vec::from(vec![$($e),*]) };
	($($e:expr,)*) => { Vec::from(vec![$($e),*]) };
	($e:expr; $d:expr) => { Vec::from(vec![$e; $d]) };
	($e:expr; $d:expr $(; $ds:expr)+) => { Vec::from(vec![mat![$e $(; $ds)*]; $d]) };
}

macro_rules! ok {
	($a:ident$([$i:expr])*.$f:ident()$(@$t:ident)*) => {
		$a$([$i])*.$f($($t),*)
	};
	($a:ident$([$i:expr])*.$f:ident($e:expr$(,$es:expr)*)$(@$t:ident)*) => { {
		let t = $e;
		ok!($a$([$i])*.$f($($es),*)$(@$t)*@t)
	} };
}

pub fn readln() -> String {
	let mut line = String::new();
	::std::io::stdin().read_line(&mut line).unwrap_or_else(|e| panic!("{}", e));
	line
}

macro_rules! read {
	($($t:tt),*; $n:expr) => {{
		let stdin = ::std::io::stdin();
		let ret = ::std::io::BufRead::lines(stdin.lock()).take($n).map(|line| {
			let line = line.unwrap();
			let mut it = line.split_whitespace();
			_read!(it; $($t),*)
		}).collect::<Vec<_>>();
		ret
	}};
	($($t:tt),*) => {{
		let line = readln();
		let mut it = line.split_whitespace();
		_read!(it; $($t),*)
	}};
}

macro_rules! _read {
	($it:ident; [char]) => {
		_read!($it; String).chars().collect::<Vec<_>>()
	};
	($it:ident; [u8]) => {
		Vec::from(_read!($it; String).into_bytes())
	};
	($it:ident; usize1) => {
		$it.next().unwrap_or_else(|| panic!("input mismatch")).parse::<usize>().unwrap_or_else(|e| panic!("{}", e)) - 1
	};
	($it:ident; [usize1]) => {
		$it.map(|s| s.parse::<usize>().unwrap_or_else(|e| panic!("{}", e)) - 1).collect::<Vec<_>>()
	};
	($it:ident; [$t:ty]) => {
		$it.map(|s| s.parse::<$t>().unwrap_or_else(|e| panic!("{}", e))).collect::<Vec<_>>()
	};
	($it:ident; $t:ty) => {
		$it.next().unwrap_or_else(|| panic!("input mismatch")).parse::<$t>().unwrap_or_else(|e| panic!("{}", e))
	};
	($it:ident; $($t:tt),+) => {
		($(_read!($it; $t)),*)
	};
}

pub fn main() {
	let _ = ::std::thread::Builder::new().name("run".to_string()).stack_size(32 * 1024 * 1024).spawn(run).unwrap().join();
}

// dp[u] = h(f(e(dp[v1], w1), e(dp[v2], w2), ...), u)
// f must be associative.
// (rooted, subtree)
fn tree_dp<T: Clone + Default, W: Clone, E: Fn(T, W) -> T, F: Fn(T, T) -> T, H: Fn(T, usize) -> T>(g: &Vec<Vec<(usize, W)>>, e: E, f: F, h: H, zero: T) -> (Vec<T>, Vec<Vec<T>>) {
	let n = g.len();
	let mut parent = vec![!0; n];
	let mut parent_i = vec![!0; n];
	let mut order = vec![0];
	for i in 0..n {
		let u = order[i];
		for (j, &(v, _)) in g[u].iter().enumerate() {
			if v != parent[u] {
				parent[v] = u;
				order.push(v);
				parent_i[v] = j;
			}
		}
	}
	let mut cs = vec![zero.clone(); n];
	for &u in order.iter().rev() {
		for &(v, ref w) in &g[u] {
			if v != parent[u] {
				cs[u] = f(cs[u].clone(), e(cs[v].clone(), w.clone()));
			}
		}
		cs[u] = h(cs[u].clone(), u);
	}
	let mut rooted = vec![zero.clone(); n];
	let mut subtree = vec![vec![]; n];
	for &u in &order {
		subtree[u] = vec![zero.clone(); g[u].len()];
		let mut pre = vec![zero.clone(); g[u].len()];
		let mut a = zero.clone();
		for (j, &(v, ref w)) in g[u].iter().enumerate() {
			pre[j] = a.clone();
			if v == parent[u] {
				a = f(a, e(subtree[v][parent_i[u]].clone(), w.clone()));
			} else {
				a = f(a, e(cs[v].clone(), w.clone()));
			}
		}
		rooted[u] = h(a, u);
		a = zero.clone();
		for (j, &(v, ref w)) in g[u].iter().enumerate().rev() {
			subtree[u][j] = h(f(pre[j].clone(), a.clone()), u);
			if v == parent[u] {
				a = f(e(subtree[v][parent_i[u]].clone(), w.clone()), a);
			} else {
				a = f(e(cs[v].clone(), w.clone()), a);
			}
		}
	}
	(rooted, subtree)
}

fn run() {
	let N = read!(usize);
	let mut g = vec![vec![]; N];
	for (a, b) in read!(usize1, usize1; N - 1) {
		g[a].push((b, ()));
		g[b].push((a, ()));
	}
	let (rooted, _) = tree_dp(&g, |a, _| (a.0 + 1.0, 1.0), |a, b| (a.0 + b.0, a.1 + b.1), |a, _| (if a.1 == 0.0 { 0.0 } else { a.0 / a.1 }, a.1), (0.0, 0.0));
	for i in 0..N {
		println!("{}", rooted[i].0);
	}
}