// -*- coding:utf-8-unix -*- // #![feature(map_first_last)] #![allow(dead_code)] #![allow(unused_imports)] #![allow(unused_macros)] use std::collections::*; use std::convert::*; use std::convert::{From, Into}; use std::fmt::Debug; use std::fs::File; use std::io::prelude::*; use std::io::*; use std::marker::Copy; use std::mem::*; use std::ops::Bound::*; use std::ops::{Add, Mul, Neg, Sub}; use std::str; use std::vec; use std::{cmp, process::Output}; use std::{cmp::Ordering, env::consts::DLL_PREFIX}; use std::{cmp::Ordering::*, f32::consts::PI}; const INF: i64 = 1223372036854775807; const UINF: usize = INF as usize; const FINF: f64 = 122337203685.0; const INF128: i128 = 1223372036854775807000000000000; const LINF: i64 = 2147483647; // const MOD: i64 = 1000000007; const MOD: i64 = 998244353; const UMOD: usize = MOD as usize; use std::cmp::*; use std::collections::*; use std::io::stdin; use std::io::stdout; use std::io::Write; macro_rules! p { ($x:expr) => { println!("{}", $x); }; } macro_rules! d { ($x:expr) => { dbg!($x); }; } macro_rules! v { ($x:expr) => { if $x == 0 { vec![]; } else if $x == 1 { BTreeSet::new(); } else if $x == 2 { BTreeMap::new(); } }; } // use str::Chars; #[allow(dead_code)] fn read() -> T { let mut s = String::new(); std::io::stdin().read_line(&mut s).ok(); s.trim().parse().ok().unwrap() } #[allow(dead_code)] fn readi() -> (i64) { let mut str = String::new(); let _ = stdin().read_line(&mut str).unwrap(); let mut iter = str.split_whitespace(); iter.next().unwrap().parse::().unwrap() } #[allow(dead_code)] fn read_vec() -> Vec { read::() .split_whitespace() .map(|e| e.parse().ok().unwrap()) .collect() } #[allow(dead_code)] fn read_vec2(n: u32) -> Vec> { (0..n).map(|_| read_vec()).collect() } #[allow(dead_code)] fn readii() -> (i64, i64) { let mut str = String::new(); let _ = stdin().read_line(&mut str).unwrap(); let mut iter = str.split_whitespace(); ( iter.next().unwrap().parse::().unwrap(), iter.next().unwrap().parse::().unwrap(), ) } fn readff() -> (f64, f64) { let mut str = String::new(); let _ = stdin().read_line(&mut str).unwrap(); let mut iter = str.split_whitespace(); ( iter.next().unwrap().parse::().unwrap(), iter.next().unwrap().parse::().unwrap(), ) } #[allow(dead_code)] fn readiii() -> (i64, i64, i64) { let mut str = String::new(); let _ = stdin().read_line(&mut str).unwrap(); let mut iter = str.split_whitespace(); ( iter.next().unwrap().parse::().unwrap(), iter.next().unwrap().parse::().unwrap(), iter.next().unwrap().parse::().unwrap(), ) } #[allow(dead_code)] fn readuu() -> (usize, usize) { let mut str = String::new(); let _ = stdin().read_line(&mut str).unwrap(); let mut iter = str.split_whitespace(); ( iter.next().unwrap().parse::().unwrap(), iter.next().unwrap().parse::().unwrap(), ) } fn readcc() -> (char, char) { let mut str = String::new(); let _ = stdin().read_line(&mut str).unwrap(); let mut iter = str.split_whitespace(); ( iter.next().unwrap().parse::().unwrap(), iter.next().unwrap().parse::().unwrap(), ) } #[allow(dead_code)] fn readuuu() -> (usize, usize, usize) { let mut str = String::new(); let _ = stdin().read_line(&mut str).unwrap(); let mut iter = str.split_whitespace(); ( iter.next().unwrap().parse::().unwrap(), iter.next().unwrap().parse::().unwrap(), iter.next().unwrap().parse::().unwrap(), ) } #[allow(dead_code)] fn readuuuu() -> (usize, usize, usize, usize) { let mut str = String::new(); let _ = stdin().read_line(&mut str).unwrap(); let mut iter = str.split_whitespace(); ( iter.next().unwrap().parse::().unwrap(), iter.next().unwrap().parse::().unwrap(), iter.next().unwrap().parse::().unwrap(), iter.next().unwrap().parse::().unwrap(), ) } fn readiiii() -> (i64, i64, i64, i64) { let mut str = String::new(); let _ = stdin().read_line(&mut str).unwrap(); let mut iter = str.split_whitespace(); ( iter.next().unwrap().parse::().unwrap(), iter.next().unwrap().parse::().unwrap(), iter.next().unwrap().parse::().unwrap(), iter.next().unwrap().parse::().unwrap(), ) } macro_rules! M { (a :expr ) => { M::new({ a }) }; } #[derive(Copy, Clone)] pub struct M(i64); impl M { fn new(x: i64) -> Self { M(x.rem_euclid(MOD)) } fn pow(self, n: usize) -> Self { match n { 0 => M::new(1), _ => { let mut a = self.pow(n >> 1); a *= a; if n & 1 == 1 { a *= self; } a } } } fn inv(self) -> Self { self.pow((MOD - 2) as usize) } } impl std::ops::Neg for M { type Output = M; fn neg(self) -> Self::Output { Self::new(-self.0) } } impl std::ops::AddAssign for M { fn add_assign(&mut self, rhs: Self) { self.0 += rhs.0; self.0 %= MOD; } } impl std::ops::AddAssign for M { fn add_assign(&mut self, rhs: i64) { *self += M::new(rhs); } } impl std::ops::AddAssign for M { fn add_assign(&mut self, rhs: usize) { *self += M::new(rhs as i64); } } impl std::ops::Add for M where M: std::ops::AddAssign, { type Output = Self; fn add(self, other: T) -> Self { let mut res = self; res += other; res } } impl std::ops::SubAssign for M { fn sub_assign(&mut self, rhs: Self) { self.0 -= rhs.0; if self.0 < 0 { self.0 += MOD; } } } impl std::ops::SubAssign for M { fn sub_assign(&mut self, rhs: i64) { *self -= M::new(rhs); if (*self).0 < 0 { self.0 += MOD; } } } impl std::ops::SubAssign for M { fn sub_assign(&mut self, rhs: usize) { *self -= M::new(rhs as i64); if (*self).0 < 0 { self.0 += MOD; } } } impl std::ops::Sub for M where M: std::ops::SubAssign, { type Output = Self; fn sub(self, other: T) -> Self { let mut res = self; res -= other; res } } impl std::ops::MulAssign for M { fn mul_assign(&mut self, rhs: Self) { self.0 *= rhs.0; self.0 %= MOD; } } impl std::ops::MulAssign for M { fn mul_assign(&mut self, rhs: i64) { *self *= M::new(rhs); } } impl std::ops::MulAssign for M { fn mul_assign(&mut self, rhs: usize) { *self *= M::new(rhs as i64); } } impl std::ops::Mul for M where M: std::ops::MulAssign, { type Output = Self; fn mul(self, other: T) -> Self { let mut res = self; res *= other; res } } impl std::ops::DivAssign for M { fn div_assign(&mut self, rhs: Self) { *self *= rhs.inv(); } } impl std::ops::DivAssign for M { fn div_assign(&mut self, rhs: i64) { *self /= M::new(rhs); } } impl std::ops::DivAssign for M { fn div_assign(&mut self, rhs: usize) { *self /= M::new(rhs as i64); } } impl std::ops::Div for M where M: std::ops::DivAssign, { type Output = Self; fn div(self, other: T) -> Self { let mut res = self; res /= other; res } } impl std::fmt::Display for M { fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result { write!(f, "{}", self.0) } } impl std::ops::Deref for M { type Target = i64; fn deref(&self) -> &Self::Target { &self.0 } } impl std::ops::DerefMut for M { fn deref_mut(&mut self) -> &mut Self::Target { &mut self.0 } } #[allow(dead_code)] pub fn gcd(a: usize, b: usize) -> usize { if b == 0 { a } else { gcd(b, a % b) } } #[allow(dead_code)] pub fn lcm(a: usize, b: usize) -> usize { a / gcd(a, b) * b } #[allow(dead_code)] /// (gcd, x, y) pub fn extgcd(a: i64, b: i64) -> (i64, i64, i64) { if b == 0 { (a, 1, 0) } else { let (gcd, x, y) = extgcd(b, a % b); (gcd, y, x - (a / b) * y) } } #[allow(dead_code)] /// x ^ n % m pub fn mod_pow(x: usize, n: usize, m: usize) -> usize { let mut res = 1; let mut x = x % m; let mut n = n; while n > 0 { if n & 1 == 1 { res = (res * x) % m; } x = (x * x) % m; n >>= 1; } res } #[allow(dead_code)] pub fn mod_inverse(a: usize, m: usize) -> usize { let (_, x, _) = extgcd(a as i64, m as i64); ((m as i64 + x) as usize % m) % m } #[allow(dead_code)] pub fn fact_table(len: usize, m: usize) -> Vec { let mut res = vec![1; len + 1]; for i in 1..len + 1 { res[i] = (i as usize * res[i - 1]) % m; } res } #[allow(dead_code)] /// Factorial and Inverse factorial table pub fn fact_inv_table(size: usize, m: usize) -> (Vec, Vec) { let mut fact = vec![1; size]; let mut fact_inv = vec![1; size]; for i in 2..size { fact[i] = fact[i - 1] * i as usize % m; fact_inv[i] = m - ((m / i as usize) * fact_inv[(m % i as usize) as usize] % m); } for i in 1..size { fact_inv[i] = fact_inv[i - 1] * fact_inv[i] % m; } (fact, fact_inv) } #[allow(dead_code)] /// (a mod p, e when n! = a p\^e) pub fn mod_fact(n: usize, p: usize, fact: &[usize]) -> (usize, usize) { if n == 0 { (1, 0) } else { let (a, b) = mod_fact(n / p, p, fact); let pow = b + n / p; if n / p % 2 != 0 { (a * (p - fact[(n % p) as usize]) % p, pow) } else { (a * fact[(n % p) as usize] % p, pow) } } } #[allow(dead_code)] /// C(n, k) % p pub fn mcom(n: usize, k: usize, fact: &[usize]) -> usize { let p = MOD as usize; if k == 0 { return 1; } if n < k { 0 } else { let (a1, e1) = mod_fact(n, p, fact); let (a2, e2) = mod_fact(k, p, fact); let (a3, e3) = mod_fact(n - k, p, fact); if e1 > e2 + e3 { 0 } else { a1 * mod_inverse(a2 * a3 % p, p) % p } } } pub fn mperm(n: usize, k: usize, fact: &[usize]) -> usize { let p = MOD as usize; if k == 0 { return 1; } if n < k { 0 } else { let (a1, e1) = mod_fact(n, p, fact); let (a2, e2) = mod_fact(k, p, fact); let (a3, e3) = mod_fact(n - k, p, fact); if e1 > e2 + e3 { 0 } else { a1 * mod_inverse(a3 % p, p) % p } } } pub fn hcom(n: usize, k: usize, fact: &[usize]) -> usize { return mcom(n + k - 1, k, fact); } pub struct Combination { m: usize, f_table: Vec, } impl Combination { // 0 <= size <= 10^8 is constrained. pub fn new(mod_num: usize, table_size: usize) -> Self { Self { m: mod_num, f_table: vec![0; table_size], } } pub fn build(&mut self) { let size = self.f_table.len(); self.f_table = fact_table(size, self.m); } fn fact_table(len: usize, m: usize) -> Vec { let mut res = vec![1; len + 1]; for i in 1..len + 1 { res[i] = (i as usize * res[i - 1]) % m; } res } pub fn p(&mut self, n: usize, k: usize) -> usize { let p = MOD as usize; if k == 0 { return 1; } if n < k { 0 } else { let (a1, e1) = mod_fact(n, p, &self.f_table); let (a2, e2) = mod_fact(k, p, &self.f_table); let (a3, e3) = mod_fact(n - k, p, &self.f_table); if e1 > e2 + e3 { 0 } else { a1 * mod_inverse(a3 % p, p) % p } } } pub fn c(&mut self, n: usize, k: usize) -> usize { let p = MOD as usize; if n == 0 { return 0; } if k == 0 { return 1; } if n < k { 0 } else { let (a1, e1) = mod_fact(n, p, &self.f_table); let (a2, e2) = mod_fact(k, p, &self.f_table); let (a3, e3) = mod_fact(n - k, p, &self.f_table); if e1 > e2 + e3 { 0 } else { a1 * mod_inverse(a2 * a3 % p, p) % p } } } pub fn h(&mut self, n: usize, k: usize) -> usize { return mcom(n + k - 1, k, &self.f_table); } pub fn factorial(&mut self, n: usize) -> usize { return self.p(n, n); } fn extgcd(a: i64, b: i64) -> (i64, i64, i64) { if b == 0 { (a, 1, 0) } else { let (gcd, x, y) = extgcd(b, a % b); (gcd, y, x - (a / b) * y) } } pub fn mod_inverse(a: usize, m: usize) -> usize { let (_, x, _) = extgcd(a as i64, m as i64); ((m as i64 + x) as usize % m) % m } fn mod_fact(&mut self, n: usize, p: usize, fact: &[usize]) -> (usize, usize) { if n == 0 { (1, 0) } else { let (a, b) = mod_fact(n / p, p, fact); let pow = b + n / p; if n / p % 2 != 0 { (a * (p - fact[(n % p) as usize]) % p, pow) } else { (a * fact[(n % p) as usize] % p, pow) } } } } fn djikstra(graph: &Vec>, start: usize) -> Vec { let mut dist = vec![INF as usize; graph.len()]; let mut heap = BinaryHeap::new(); heap.push(Reverse((0 as usize, start))); dist[start] = 0; while let Some(Reverse(x)) = heap.pop() { let cost = x.0; let v = x.1; if cost > dist[v] { continue; } for edge in &graph[v] { let nc = cost + edge.1; let nv = edge.0; if nc < dist[nv] { heap.push(Reverse((nc, nv))); dist[nv] = nc; } } } return dist; } fn dfs(v: usize, graph: &Vec>, used: &mut Vec, data: &mut Vec) { used[v] = 1; let mut res = 0 as usize; for i in graph[v].iter() { let nv = (*i).0; if used[nv] == 1 { continue; } dfs(nv, &graph, used, data); res += data[nv]; } res += 1; data[v] = res; return; } fn solve() { let n: usize = read(); let mut graph = vec![vec![(0 as usize, 0 as usize); (0) as usize]; (n) as usize]; let mut data = vec![0; n]; if n == 2 { println!("{:?}", 0); return; } for i in 0..n - 1 { let (mut a, mut b) = readuu(); a -= 1; b -= 1; graph[a].push((b, 1)); graph[b].push((a, 1)); data[a] += 1; data[b] += 1; } let mut root = 0 as usize; for i in 0..n { if data[i] == 1 { root = i; } } // let mut d = djikstra(&graph, root); // d!(d.clone()); let mut used = vec![0; n]; let mut data = vec![0; n]; dfs(0, &graph, &mut used, &mut data); let mut res = M(1); res *= M(((n as i64) * (n as i64 - 1) / 2) as i64); res *= M(n as i64 - 1); // println!("{:?}", data.clone()); // println!("{:?}", res.0); for i in 1..n { let mut x = data[i] as i64; res -= M(n as i64 - x) * x; } // println!("{:?}", res.0); res /= M(((n as i64) * (n as i64 - 1) / 2) as i64); res /= M(n as i64 - 1); println!("{:?}", res.0); return; } fn main() { solve(); }