#![allow(unused_imports, unused_macros)] use kyoproio::*; use std::{ collections::*, io::{self, prelude::*}, iter, mem, }; fn run(mut kin: I, mut out: O) { let n: usize = kin.input(); let mut g = AdjListBuilder::new(n + 1); g.extend_bi_edges(kin.iter().take(n - 1)); let g = g.build(); let mut size = vec![0i64; n + 1]; let ans = (n * n * n) as i64 - f(&g, &mut size, 1, 0); outln!(out, "{}", ans); } fn f(g: &AdjList, size: &mut [i64], u: usize, p: usize) -> i64 { let n = g.len() - 1; size[u] = 1; let mut res = 0; for &v in &g[u] { if v == p { continue; } res += f(g, size, v, u); res += size[v] * size[v]; size[u] += size[v]; } let p = n as i64 - size[u]; res += p * p; res } use std::{ fmt, // iter, ops::{Index, IndexMut}, }; pub struct AdjList(JaggedArray); impl AdjList { pub fn len(&self) -> usize { self.0.len() } pub fn iter(&self) -> AdjListIter { AdjListIter(self.0.iter()) } } impl Index for AdjList { type Output = [usize]; fn index(&self, i: usize) -> &[usize] { &self.0[i] } } impl IndexMut for AdjList { fn index_mut(&mut self, i: usize) -> &mut [usize] { &mut self.0[i] } } impl fmt::Debug for AdjList { fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> fmt::Result { f.debug_map().entries(self.iter().enumerate()).finish() } } pub struct AdjListIter<'a>(Iter<'a, usize>); impl<'a> Iterator for AdjListIter<'a> { type Item = &'a [usize]; fn next(&mut self) -> Option { self.0.next() } } pub struct AdjListBuilder(Builder); impl AdjListBuilder { pub fn new(n: usize) -> Self { Self(Builder::new(n)) } pub fn with_capacity(n: usize, cap: usize) -> Self { Self(Builder::with_capacity(n, cap)) } pub fn edge(&mut self, u: usize, v: usize) { self.0.push(u, v); } pub fn bi_edge(&mut self, u: usize, v: usize) { self.edge(u, v); self.edge(v, u); } pub fn extend_bi_edges>(&mut self, it: I) { self.0.extend( it.into_iter() .flat_map(|(u, v)| iter::once((u, v)).chain(iter::once((v, u)))), ); } pub fn build(self) -> AdjList { AdjList(self.0.build()) } } impl Extend<(usize, usize)> for AdjListBuilder { fn extend>(&mut self, iter: T) { self.0.extend(iter) } } pub struct JaggedArray { heads: Box<[usize]>, buf: Box<[T]>, } impl JaggedArray { pub fn len(&self) -> usize { self.heads.len() - 1 } pub fn is_empty(&self) -> bool { self.heads.is_empty() } pub fn iter<'a>(&'a self) -> Iter<'a, T> { Iter { a: self, i: 0 } } } impl Index for JaggedArray { type Output = [T]; fn index(&self, i: usize) -> &[T] { if let Some([l, r, ..]) = self.heads.get(i..) { unsafe { self.buf.get_unchecked(*l..*r) } } else { &[] } } } impl IndexMut for JaggedArray { fn index_mut(&mut self, i: usize) -> &mut [T] { if let Some([l, r, ..]) = self.heads.get(i..) { unsafe { self.buf.get_unchecked_mut(*l..*r) } } else { &mut [] } } } impl<'a, T> IntoIterator for &'a JaggedArray { type Item = &'a [T]; type IntoIter = Iter<'a, T>; fn into_iter(self) -> Self::IntoIter { self.iter() } } pub struct Iter<'a, T> { a: &'a JaggedArray, i: usize, } impl<'a, T> Iterator for Iter<'a, T> { type Item = &'a [T]; fn next(&mut self) -> Option { if self.i < self.a.len() { let res = &self.a[self.i]; self.i += 1; Some(res) } else { None } } fn size_hint(&self) -> (usize, Option) { let rest = self.a.len() - self.i; (rest, Some(rest)) } } pub struct Builder { heads: Vec, nodes: Vec<(T, usize)>, } impl Builder { pub fn new(n: usize) -> Self { Self::with_capacity(n, 0) } pub fn with_capacity(n: usize, cap: usize) -> Self { Self { heads: vec![!0; n + 1], nodes: Vec::with_capacity(cap), } } pub fn push(&mut self, i: usize, x: T) { self.nodes.push((x, self.heads[i])); self.heads[i] = self.nodes.len() - 1; } pub fn build(mut self) -> JaggedArray { let mut buf_i = self.nodes.len(); let mut buf = Vec::::with_capacity(buf_i); let buf_p = buf.as_mut_ptr(); *self.heads.last_mut().unwrap() = buf_i; unsafe { for h in self.heads.iter_mut().rev().skip(1) { let mut nodes_i = *h; while let Some((x, next)) = self.nodes.get(nodes_i) { buf_i -= 1; buf_p.add(buf_i).copy_from_nonoverlapping(x, 1); nodes_i = *next; } *h = buf_i; } self.nodes.set_len(0); buf.set_len(buf.capacity()); } JaggedArray { heads: self.heads.into(), buf: buf.into(), } } } impl Extend<(usize, T)> for Builder { fn extend>(&mut self, iter: I) { for (i, x) in iter { self.push(i, x); } } } // ----------------------------------------------------------------------------- fn main() -> io::Result<()> { std::thread::Builder::new() .stack_size(1 << 26) .spawn(|| { run( KInput::new(io::stdin().lock()), io::BufWriter::new(io::stdout().lock()), ) })? .join() .unwrap(); Ok(()) } #[macro_export] macro_rules! out { ($($arg:tt)*) => { write!($($arg)*).unwrap(); } } #[macro_export] macro_rules! outln { ($dst:expr $(, $($arg:tt)*)?) => {{ writeln!($dst $(, $($arg)*)?).unwrap(); if cfg!(debug_assertions) { $dst.flush().unwrap(); } }} } #[macro_export] macro_rules! d { ($h:expr, $($t:expr),* $(,)?) => { #[cfg(debug_assertions)] { eprint!("[{}:{}] {} = {:?}", file!(), line!(), stringify!($h), $h); $(eprint!(", {} = {:?}", stringify!($t), $t);)* eprintln!(); } }; ($h:expr) => { d!($h,) }; () => { eprintln!("[{}:{}]", file!(), line!()) } } pub mod kyoproio { use std::{ io::prelude::*, iter::FromIterator, marker::PhantomData, mem::{self, MaybeUninit}, str, }; pub trait Input { fn bytes(&mut self) -> &[u8]; fn str(&mut self) -> &str { str::from_utf8(self.bytes()).unwrap() } fn input(&mut self) -> T { T::input(self) } fn iter(&mut self) -> Iter { Iter(self, PhantomData) } fn collect>(&mut self, n: usize) -> B { self.iter().take(n).collect() } fn map U, B: FromIterator>( &mut self, n: usize, f: F, ) -> B { self.iter().take(n).map(f).collect() } } impl Input for &mut I { fn bytes(&mut self) -> &[u8] { (**self).bytes() } } pub struct KInput { src: R, buf: Vec, pos: usize, len: usize, } impl KInput { pub fn new(src: R) -> Self { Self { src, buf: vec![0; 1 << 16], pos: 0, len: 0, } } fn read(&mut self) -> usize { if self.pos > 0 { self.buf.copy_within(self.pos..self.len, 0); self.len -= self.pos; self.pos = 0; } else if self.len >= self.buf.len() { self.buf.resize(2 * self.buf.len(), 0); } let n = self.src.read(&mut self.buf[self.len..]).unwrap(); self.len += n; n } } impl Input for KInput { fn bytes(&mut self) -> &[u8] { loop { while let Some(d) = self.buf[self.pos..self.len] .iter() .position(u8::is_ascii_whitespace) { let p = self.pos; self.pos += d + 1; if d > 0 { return &self.buf[p..p + d]; } } if self.read() == 0 { return &self.buf[mem::replace(&mut self.pos, self.len)..self.len]; } } } } pub struct Iter<'a, T, I: ?Sized>(&'a mut I, PhantomData<*const T>); impl<'a, T: InputItem, I: Input + ?Sized> Iterator for Iter<'a, T, I> { type Item = T; fn next(&mut self) -> Option { Some(self.0.input()) } fn size_hint(&self) -> (usize, Option) { (!0, None) } } pub trait InputItem: Sized { fn input(src: &mut I) -> Self; } impl InputItem for Vec { fn input(src: &mut I) -> Self { src.bytes().to_owned() } } macro_rules! from_str { ($($T:ty)*) => {$( impl InputItem for $T { fn input(src: &mut I) -> Self { src.str().parse::<$T>().unwrap() } } )*} } from_str!(String char bool f32 f64); macro_rules! parse_int { ($($I:ty: $U:ty)*) => {$( impl InputItem for $I { fn input(src: &mut I) -> Self { let f = |s: &[u8]| s.iter().fold(0, |x, b| 10 * x + (b & 0xf) as $I); let s = src.bytes(); if let Some((&b'-', t)) = s.split_first() { -f(t) } else { f(s) } } } impl InputItem for $U { fn input(src: &mut I) -> Self { src.bytes().iter().fold(0, |x, b| 10 * x + (b & 0xf) as $U) } } )*} } parse_int!(isize:usize i8:u8 i16:u16 i32:u32 i64:u64 i128:u128); macro_rules! tuple { ($H:ident $($T:ident)*) => { impl<$H: InputItem, $($T: InputItem),*> InputItem for ($H, $($T),*) { fn input(src: &mut I) -> Self { ($H::input(src), $($T::input(src)),*) } } tuple!($($T)*); }; () => {} } tuple!(A B C D E F G); macro_rules! array { ($($N:literal)*) => {$( impl InputItem for [T; $N] { fn input(src: &mut I) -> Self { unsafe { let mut arr: [MaybeUninit; $N] = MaybeUninit::uninit().assume_init(); for elem in &mut arr { *elem = MaybeUninit::new(src.input()); } mem::transmute_copy(&arr) } } } )*} } array!(1 2 3 4 5 6 7 8); }