// ---------- begin ModInt ---------- mod modint { #[allow(dead_code)] pub struct Mod; impl ConstantModulo for Mod { const MOD: u32 = 1_000_000_007; } #[allow(dead_code)] pub struct StaticMod; static mut STATIC_MOD: u32 = 0; impl Modulo for StaticMod { fn modulo() -> u32 { unsafe { STATIC_MOD } } } #[allow(dead_code)] impl StaticMod { pub fn set_modulo(p: u32) { unsafe { STATIC_MOD = p; } } } use std::marker::*; use std::ops::*; pub trait Modulo { fn modulo() -> u32; } pub trait ConstantModulo { const MOD: u32; } impl Modulo for T where T: ConstantModulo, { fn modulo() -> u32 { T::MOD } } pub struct ModInt(pub u32, PhantomData); impl Clone for ModInt { fn clone(&self) -> Self { ModInt::new_unchecked(self.0) } } impl Copy for ModInt {} impl Add for ModInt { type Output = ModInt; fn add(self, rhs: Self) -> Self::Output { let mut d = self.0 + rhs.0; if d >= T::modulo() { d -= T::modulo(); } ModInt::new_unchecked(d) } } impl AddAssign for ModInt { fn add_assign(&mut self, rhs: Self) { *self = *self + rhs; } } impl Sub for ModInt { type Output = ModInt; fn sub(self, rhs: Self) -> Self::Output { let mut d = T::modulo() + self.0 - rhs.0; if d >= T::modulo() { d -= T::modulo(); } ModInt::new_unchecked(d) } } impl SubAssign for ModInt { fn sub_assign(&mut self, rhs: Self) { *self = *self - rhs; } } impl Mul for ModInt { type Output = ModInt; fn mul(self, rhs: Self) -> Self::Output { let v = self.0 as u64 * rhs.0 as u64 % T::modulo() as u64; ModInt::new_unchecked(v as u32) } } impl MulAssign for ModInt { fn mul_assign(&mut self, rhs: Self) { *self = *self * rhs; } } impl Neg for ModInt { type Output = ModInt; fn neg(self) -> Self::Output { if self.0 == 0 { Self::zero() } else { Self::new_unchecked(T::modulo() - self.0) } } } impl std::fmt::Display for ModInt { fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result { write!(f, "{}", self.0) } } impl std::fmt::Debug for ModInt { fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result { write!(f, "{}", self.0) } } impl std::str::FromStr for ModInt { type Err = std::num::ParseIntError; fn from_str(s: &str) -> Result { let val = s.parse::()?; Ok(ModInt::new(val)) } } impl From for ModInt { fn from(val: usize) -> ModInt { ModInt::new_unchecked((val % T::modulo() as usize) as u32) } } impl From for ModInt { fn from(val: u64) -> ModInt { ModInt::new_unchecked((val % T::modulo() as u64) as u32) } } impl From for ModInt { fn from(val: i64) -> ModInt { let m = T::modulo() as i64; ModInt::new((val % m + m) as u32) } } #[allow(dead_code)] impl ModInt { pub fn new_unchecked(d: u32) -> Self { ModInt(d, PhantomData) } pub fn zero() -> Self { ModInt::new_unchecked(0) } pub fn one() -> Self { ModInt::new_unchecked(1) } pub fn is_zero(&self) -> bool { self.0 == 0 } } #[allow(dead_code)] impl ModInt { pub fn new(d: u32) -> Self { ModInt::new_unchecked(d % T::modulo()) } pub fn pow(&self, mut n: u64) -> Self { let mut t = Self::one(); let mut s = *self; while n > 0 { if n & 1 == 1 { t *= s; } s *= s; n >>= 1; } t } pub fn inv(&self) -> Self { assert!(self.0 != 0); self.pow(T::modulo() as u64 - 2) } } #[allow(dead_code)] pub fn mod_pow(r: u64, mut n: u64, m: u64) -> u64 { let mut t = 1 % m; let mut s = r % m; while n > 0 { if n & 1 == 1 { t = t * s % m; } s = s * s % m; n >>= 1; } t } } // ---------- end ModInt ---------- // ---------- begin Rerooting ---------- pub trait RerootingOperator { type Value: Clone; type Edge: Clone; fn init(&mut self, v: usize) -> Self::Value; fn merge(&mut self, p: &Self::Value, c: &Self::Value, e: &Self::Edge) -> Self::Value; } pub struct Rerooting { manager: R, size: usize, edge: Vec<(usize, usize, R::Edge, R::Edge)>, } impl Rerooting { pub fn new(size: usize, manager: R) -> Self { assert!(size > 0 && size < 10usize.pow(8)); Rerooting { manager: manager, size: size, edge: vec![], } } pub fn add_edge(&mut self, a: usize, b: usize, cost: R::Edge) { assert!(a < self.size && b < self.size && a != b); self.add_edge_bi(a, b, cost.clone(), cost); } pub fn add_edge_bi(&mut self, a: usize, b: usize, ab: R::Edge, ba: R::Edge) { assert!(a < self.size && b < self.size && a != b); self.edge.push((a, b, ab, ba)); } pub fn solve(&mut self) -> Vec { let size = self.size; let mut graph = vec![vec![]; size]; for e in self.edge.iter() { graph[e.0].push((e.1, e.2.clone())); graph[e.1].push((e.0, e.3.clone())); } let root = 0; let mut topo = vec![root]; let mut parent = vec![root; size]; let mut parent_edge: Vec> = (0..size).map(|_| None).collect(); for i in 0..size { let v = topo[i]; let child = std::mem::take(&mut graph[v]); for e in child.iter() { let k = graph[e.0].iter().position(|e| e.0 == v).unwrap(); let c = graph[e.0].remove(k).1; parent_edge[e.0] = Some(c); parent[e.0] = v; topo.push(e.0); } graph[v] = child; } let manager = &mut self.manager; let mut down: Vec<_> = (0..size).map(|v| manager.init(v)).collect(); for &v in topo.iter().rev() { for e in graph[v].iter() { down[v] = manager.merge(&down[v], &down[e.0], &e.1); } } let mut up: Vec<_> = (0..size).map(|v| manager.init(v)).collect(); let mut stack = vec![]; for &v in topo.iter() { if let Some(e) = parent_edge[v].take() { let ini = manager.init(v); up[v] = manager.merge(&ini, &up[v], &e); } if !graph[v].is_empty() { stack.push((graph[v].as_slice(), up[v].clone())); while let Some((g, val)) = stack.pop() { if g.len() == 1 { up[g[0].0] = val; } else { let m = g.len() / 2; let (a, b) = g.split_at(m); for a in [(a, b), (b, a)].iter() { let mut p = val.clone(); for a in a.0.iter() { p = manager.merge(&p, &down[a.0], &a.1); } stack.push((a.1, p)); } } } } for e in graph[v].iter() { up[v] = manager.merge(&up[v], &down[e.0], &e.1); } } up } } // ---------- end Rerooting ---------- // ---------- begin input macro ---------- // reference: https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 macro_rules! input { (source = $s:expr, $($r:tt)*) => { let mut iter = $s.split_whitespace(); input_inner!{iter, $($r)*} }; ($($r:tt)*) => { let s = { use std::io::Read; let mut s = String::new(); std::io::stdin().read_to_string(&mut s).unwrap(); s }; let mut iter = s.split_whitespace(); input_inner!{iter, $($r)*} }; } macro_rules! input_inner { ($iter:expr) => {}; ($iter:expr, ) => {}; ($iter:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($iter, $t); input_inner!{$iter $($r)*} }; } macro_rules! read_value { ($iter:expr, ( $($t:tt),* )) => { ( $(read_value!($iter, $t)),* ) }; ($iter:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($iter, $t)).collect::>() }; ($iter:expr, chars) => { read_value!($iter, String).chars().collect::>() }; ($iter:expr, bytes) => { read_value!($iter, String).bytes().collect::>() }; ($iter:expr, usize1) => { read_value!($iter, usize) - 1 }; ($iter:expr, $t:ty) => { $iter.next().unwrap().parse::<$t>().expect("Parse error") }; } // ---------- end input macro ---------- use std::io::Write; use modint::*; type M = ModInt; struct R; impl RerootingOperator for R { // sum d^2, sum d, cnt type Value = (M, M, M); type Edge = M; fn init(&mut self, _v: usize) -> Self::Value { (M::zero(), M::zero(), M::one()) } fn merge(&mut self, p: &Self::Value, c: &Self::Value, e: &Self::Edge) -> Self::Value { let w = *e; (p.0 + w * w * c.2 + M::new(2) * w * c.1 + c.0, p.1 + c.1 + w * c.2, p.2 + c.2) } } fn run() { input! { n: usize, e: [(usize1, usize1, M); n - 1], } let mut solver = Rerooting::new(n, R); for (a, b, w) in e { solver.add_edge(a, b, w); } let ans = solver.solve().into_iter().fold(M::zero(), |s, a| s + a.0) * M::new(2).inv(); println!("{}", ans); } fn main() { run(); }