#![allow(unused_imports, non_snake_case)] #![allow(dead_code)] use crate::arraylist::List; use crate::scanner::Scanner; use std::cmp::min; fn main() { let mut scan = Scanner::new(); let n = scan.read::(); let mut g = list ! ( list ! ( ) ; n ); let mut edges = list!(); for _ in 0..n - 1 { let u = scan.read::() - 1; let v = scan.read::() - 1; let w = scan.read::(); g[u].push((v, w)); g[v].push((u, w)); edges.push((u, v, w)); } let mut env = Env { s: list ! ( 0 ; n ), g, }; env.count(-1, 0); let mut ret = 0; for &(u, v, w) in &edges { let a = min(env.s[u], env.s[v]) as i64; let b = n as i64 - a; ret += 2 * w * a * b; } println!("{}", ret); } struct Env { s: List, g: List>, } impl Env { fn count(&mut self, prev: i32, cur: i32) -> i32 { let mut ret = 0; for (next, _) in self.g[cur].clone() { if prev != next { ret += self.count(cur, next); } } ret += 1; self.s[cur] = ret; ret } } pub mod ext { pub mod range { use crate::independent::integer::Int; use std::cmp::{max, min}; use std::ops::{Bound, Range, RangeBounds}; pub trait IntRangeBounds: RangeBounds { fn lbopt(&self) -> Option { match self.start_bound() { Bound::Included(x) => Some(*x), Bound::Excluded(x) => Some(*x + U::one()), Bound::Unbounded => None, } } fn ubopt(&self) -> Option { match self.end_bound() { Bound::Included(x) => Some(*x + U::one()), Bound::Excluded(x) => Some(*x), Bound::Unbounded => None, } } #[doc = " inclusive"] fn lower_bound(&self, limit: U) -> U { self.lbopt().map_or(limit, |x| max(limit, x)) } #[doc = " exclusive"] fn upper_bound(&self, limit: U) -> U { self.ubopt().map_or(limit, |x| min(limit, x)) } fn to_harfopen(&self, lb: U, ub: U) -> Range { self.lower_bound(lb)..self.upper_bound(ub) } fn width(&self) -> U { if self.empty() { U::zero() } else { self.ubopt().unwrap() - self.lbopt().unwrap() } } fn empty(&self) -> bool { self.lbopt().is_none() || self.ubopt().is_none() || !(self.lbopt().unwrap() < self.ubopt().unwrap()) } fn contain_range(&self, inner: &Self) -> bool { (match (self.lbopt(), inner.lbopt()) { (Some(a), Some(b)) => a <= b, (None, _) => true, (Some(_), None) => false, }) && (match (inner.ubopt(), self.ubopt()) { (Some(a), Some(b)) => a <= b, (_, None) => true, (None, Some(_)) => false, }) } fn separate_range(&self, other: &Self) -> bool { if let (Some(a), Some(b)) = (self.ubopt(), other.lbopt()) { a <= b } else if let (Some(a), Some(b)) = (other.ubopt(), self.lbopt()) { a <= b } else { false } } fn overlap(&self, other: &Self) -> Range { let left = if let (Some(a), Some(b)) = (self.lbopt(), other.lbopt()) { max(a, b) } else { self.lbopt().or(other.lbopt()).unwrap() }; let right = if let (Some(a), Some(b)) = (self.ubopt(), other.ubopt()) { min(a, b) } else { self.ubopt().or(other.ubopt()).unwrap() }; left..right } } impl IntRangeBounds for T where T: RangeBounds {} } } pub mod scanner { use crate::arraylist::List; use std::io::{stdin, BufReader, Bytes, Read, Stdin}; use std::str::FromStr; macro_rules ! impl_readxn { ( $ name : ident , $ ( $ tpe : ident ) ,+ ) => { pub fn $ name <$ ( $ tpe : FromStr ) ,+> ( & mut self , n : i32 ) -> List < ( $ ( $ tpe ) ,+ ) > { ( 0 .. n ) . map ( | _ | ( $ ( self . read ::<$ tpe > ( ) ) ,+ ) ) . collect ( ) } } ; } pub struct Scanner { buf: Bytes>, } impl Scanner { pub fn new() -> Scanner { Scanner { buf: BufReader::new(stdin()).bytes(), } } pub fn read_next(&mut self) -> Option { let token = self .buf .by_ref() .map(|c| c.unwrap() as char) .skip_while(|c| c.is_whitespace()) .take_while(|c| !c.is_whitespace()) .collect::(); token.parse::().ok() } pub fn read(&mut self) -> T { self.read_next().unwrap() } pub fn readn(&mut self, n: i32) -> List { (0..n).map(|_| self.read::()).collect() } pub fn chars(&mut self) -> List { self.read::().chars().collect() } impl_readxn!(read2n, P, Q); impl_readxn!(read3n, P, Q, R); impl_readxn!(read4n, P, Q, R, S); impl_readxn!(read5n, P, Q, R, S, T); } } pub mod independent { pub mod integer { pub trait Int: std::ops::Add + std::ops::Sub + std::ops::Mul + std::ops::Div + std::ops::Rem + std::ops::AddAssign + std::ops::SubAssign + std::ops::MulAssign + std::ops::DivAssign + std::hash::Hash + PartialEq + Eq + PartialOrd + Ord + Copy { fn to_u8(&self) -> u8; fn to_u16(&self) -> u16; fn to_u32(&self) -> u32; fn to_u64(&self) -> u64; fn to_u128(&self) -> u128; fn to_i8(&self) -> i8; fn to_i16(&self) -> i16; fn to_i32(&self) -> i32; fn to_i64(&self) -> i64; fn to_i128(&self) -> i128; fn to_usize(&self) -> usize; fn to_isize(&self) -> isize; fn from_u8(x: u8) -> Self; fn from_u16(x: u16) -> Self; fn from_u32(x: u32) -> Self; fn from_u64(x: u64) -> Self; fn from_u128(x: u128) -> Self; fn from_i8(x: i8) -> Self; fn from_i16(x: i16) -> Self; fn from_i32(x: i32) -> Self; fn from_i64(x: i64) -> Self; fn from_i128(x: i128) -> Self; fn from_usize(x: usize) -> Self; fn from_isize(x: isize) -> Self; fn zero() -> Self; fn one() -> Self; fn next(&self) -> Self { *self + Self::one() } } macro_rules ! impl_integer_functions { ( $ selftpe : ident , $ ( $ tofn : ident , $ fromfn : ident , $ tpe : ident ) ,* ) => { $ ( fn $ tofn ( & self ) -> $ tpe { * self as $ tpe } fn $ fromfn ( x : $ tpe ) -> Self { x as $ selftpe } ) * } ; } macro_rules ! impl_integer { ( $ ( $ tpe : ident ) ,* ) => { $ ( impl Int for $ tpe { impl_integer_functions ! ( $ tpe , to_u8 , from_u8 , u8 , to_u16 , from_u16 , u16 , to_u32 , from_u32 , u32 , to_u64 , from_u64 , u64 , to_u128 , from_u128 , u128 , to_i8 , from_i8 , i8 , to_i16 , from_i16 , i16 , to_i32 , from_i32 , i32 , to_i64 , from_i64 , i64 , to_i128 , from_i128 , i128 , to_usize , from_usize , usize , to_isize , from_isize , isize ) ; fn zero ( ) -> Self { 0 } fn one ( ) -> Self { 1 } } ) * } ; } impl_integer!(u8, u16, u32, u64, u128, i8, i16, i32, i64, i128, usize, isize); } } pub mod arraylist { use crate::{ext::range::IntRangeBounds, independent::integer::Int}; use std::fmt::Formatter; use std::iter::FromIterator; use std::ops::{Index, IndexMut, RangeBounds}; use std::slice::Iter; #[derive(Clone, PartialEq, Eq)] pub struct List { pub vec: Vec, } impl List { #[inline] pub fn new() -> List { List { vec: vec![] } } #[inline] pub fn init(init: T, n: i32) -> List where T: Clone, { List { vec: vec![init; n as usize], } } #[inline] pub fn from_vec(vec: Vec) -> List { List { vec } } #[inline] pub fn acc<'a, S>(n: i32, mut f: S) -> List where S: FnMut(i32) -> T + 'a, { (0..n).map(|i| f(i)).collect() } #[inline] pub fn ilen(&self) -> i32 { self.vec.len() as i32 } #[inline] pub fn iter(&self) -> Iter<'_, T> { self.vec.iter() } #[inline] pub fn push(&mut self, item: T) { self.vec.push(item); } #[inline] pub fn sort(&mut self) where T: Ord, { self.vec.sort(); } #[inline] pub fn reverse(&mut self) { self.vec.reverse(); } #[inline] pub fn sort_by(&mut self, compare: F) where F: FnMut(&T, &T) -> std::cmp::Ordering, { self.vec.sort_by(compare) } #[inline] pub fn sort_by_key(&mut self, compare: F) where F: FnMut(&T) -> K, K: Ord, { self.vec.sort_by_key(compare) } #[inline] pub fn first(&self) -> Option<&T> { self.vec.first() } #[inline] pub fn last(&self) -> Option<&T> { self.vec.last() } #[inline] pub fn pop(&mut self) -> Option { self.vec.pop() } #[inline] pub fn swap(&mut self, i: i32, j: i32) { self.vec.swap(i as usize, j as usize); } #[inline] pub fn append(&mut self, mut other: Self) { self.vec.append(&mut other.vec); } #[inline] pub fn extend(&mut self, other: impl Iterator) { self.vec.extend(other); } #[inline] pub fn mirror(&self) -> std::iter::Cloned> where T: Clone, { self.iter().cloned() } #[inline] pub fn join(&self, sep: &str) -> String where T: std::fmt::Display, { self.iter() .map(|x| format!("{}", x)) .collect::>() .join(sep) } #[inline] pub fn map(&self, f: F) -> List where T: Clone, F: FnMut(T) -> B, { self.mirror().map(f).collect() } #[inline] pub fn filter

(&self, predicate: P) -> List where T: Clone, P: FnMut(&T) -> bool, { self.mirror().filter(predicate).collect() } #[inline] pub fn filter_map(&self, f: F) -> List where T: Clone, F: FnMut(T) -> Option, { self.mirror().filter_map(f).collect() } #[doc = " |acc, x| -> acc"] #[inline] pub fn fold(&self, init: B, f: F) -> B where T: Clone, F: FnMut(B, T) -> B, { self.mirror().fold(init, f) } #[inline] pub fn any

(&self, predicate: P) -> bool where P: FnMut(&T) -> bool, { self.iter().any(predicate) } #[inline] pub fn all

(&self, predicate: P) -> bool where P: FnMut(&T) -> bool, { self.iter().all(predicate) } #[inline] pub fn sum(&self) -> T where T: Int, { self.iter().cloned().fold(T::zero(), |acc, x| acc + x) } #[inline] pub fn enumerate(&self) -> List<(i32, T)> where T: Clone, { self.mirror() .enumerate() .map(|p| (p.0 as i32, p.1)) .collect() } #[inline] pub fn find

(&self, mut predicate: P) -> Option<&T> where P: FnMut(&T) -> bool, { self.iter().find(|x| predicate(*x)) } #[inline] pub fn index_of

(&self, mut predicate: P) -> Option where P: FnMut(&T) -> bool, { self.iter() .enumerate() .find(|&(_i, x)| predicate(x)) .map(|p| p.0 as i32) } #[inline] pub fn to>(&self) -> B where T: Clone, { self.mirror().collect() } #[inline] pub fn min(&self) -> Option<&T> where T: Ord, { self.iter().min() } #[inline] pub fn max(&self) -> Option<&T> where T: Ord, { self.iter().max() } #[inline] pub fn argmin(&self) -> Option where T: Ord, { let item = self.iter().min()?; self.iter() .enumerate() .find(|p| p.1 == item) .map(|p| p.0 as i32) } #[inline] pub fn argmax(&self) -> Option where T: Ord, { let item = self.iter().max()?; self.iter() .enumerate() .find(|p| p.1 == item) .map(|p| p.0 as i32) } #[inline] pub fn part(&self, range: U) -> List where T: Clone, U: RangeBounds, { List::from_vec( self.vec[range.lower_bound(0) as usize..range.upper_bound(self.ilen()) as usize] .to_vec(), ) } #[inline] pub fn first_exn(&self) -> &T { self.first().unwrap() } #[inline] pub fn last_exn(&self) -> &T { self.last().unwrap() } #[inline] pub fn pop_exn(&mut self) -> T { self.pop().unwrap() } #[inline] pub fn min_exn(&self) -> &T where T: Ord, { self.min().unwrap() } #[inline] pub fn max_exn(&self) -> &T where T: Ord, { self.max().unwrap() } #[inline] pub fn argmin_exn(&self) -> i32 where T: Ord, { self.argmin().unwrap() } #[inline] pub fn argmax_exn(&self) -> i32 where T: Ord, { self.argmax().unwrap() } #[inline] pub fn find_exn

(&self, predicate: P) -> &T where P: FnMut(&T) -> bool, { self.find(predicate).unwrap() } #[inline] pub fn index_of_exn

(&self, predicate: P) -> i32 where P: FnMut(&T) -> bool, { self.index_of(predicate).unwrap() } } impl std::ops::BitXorAssign for List { #[inline] fn bitxor_assign(&mut self, rhs: T) { self.push(rhs); } } impl Index for List { type Output = T; #[inline] fn index(&self, index: i32) -> &Self::Output { if cfg!(debug_assertions) { self.vec.index(index as usize) } else { unsafe { self.vec.get_unchecked(index as usize) } } } } impl IndexMut for List { #[inline] fn index_mut(&mut self, index: i32) -> &mut Self::Output { if cfg!(debug_assertions) { self.vec.index_mut(index as usize) } else { unsafe { self.vec.get_unchecked_mut(index as usize) } } } } impl FromIterator for List { fn from_iter>(iter: U) -> Self { List { vec: iter.into_iter().collect(), } } } impl IntoIterator for List { type Item = T; type IntoIter = std::vec::IntoIter; fn into_iter(self) -> std::vec::IntoIter { self.vec.into_iter() } } impl<'a, T> IntoIterator for &'a List { type Item = &'a T; type IntoIter = Iter<'a, T>; fn into_iter(self) -> Iter<'a, T> { self.vec.iter() } } impl std::fmt::Display for List { fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result { write!( f, "{}", self.iter() .map(|x| format!("{}", x)) .collect::>() .join(" ") ) } } impl std::fmt::Debug for List { fn fmt(&self, f: &mut Formatter<'_>) -> std::fmt::Result { write!( f, "[{}]", self.iter() .map(|x| format!("{:?}", x)) .collect::>() .join(", ") ) } } impl From> for List { fn from(vec: Vec) -> Self { Self::from_vec(vec) } } impl From<&[T]> for List { fn from(slice: &[T]) -> Self { slice.iter().cloned().collect() } } #[macro_export] macro_rules ! list { ( ) => { $ crate :: arraylist :: List :: new ( ) } ; ( $ ( $ v : expr ) ,+ $ ( , ) ? ) => { $ crate :: arraylist :: List :: from_vec ( [ $ ( $ v ) ,+ ] . to_vec ( ) ) } ; ( $ v : expr ; $ a : expr ) => { $ crate :: arraylist :: List :: init ( $ v , $ a ) } ; ( $ v : expr ; $ a : expr ; $ ( $ rest : expr ) ;+ ) => { $ crate :: arraylist :: List :: init ( list ! ( $ v ; $ ( $ rest ) ;+ ) , $ a ) } ; } }