// https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 macro_rules! input { ($($r:tt)*) => { let stdin = std::io::stdin(); let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock())); let mut next = move || -> String{ bytes.by_ref().map(|r|r.unwrap() as char) .skip_while(|c|c.is_whitespace()) .take_while(|c|!c.is_whitespace()) .collect() }; input_inner!{next, $($r)*} }; } macro_rules! input_inner { ($next:expr) => {}; ($next:expr,) => {}; ($next:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($next, $t); input_inner!{$next $($r)*} }; } macro_rules! read_value { ($next:expr, ( $($t:tt),* )) => { ($(read_value!($next, $t)),*) }; ($next:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($next, $t)).collect::>() }; ($next:expr, chars) => { read_value!($next, String).chars().collect::>() }; ($next:expr, usize1) => (read_value!($next, usize) - 1); ($next:expr, $t:ty) => ($next().parse::<$t>().expect("Parse error")); } /// Verified by https://atcoder.jp/contests/abc198/submissions/21774342 mod mod_int { use std::ops::*; pub trait Mod: Copy { fn m() -> i64; } #[derive(Copy, Clone, Hash, PartialEq, Eq, PartialOrd, Ord)] pub struct ModInt { pub x: i64, phantom: ::std::marker::PhantomData } impl ModInt { // x >= 0 pub fn new(x: i64) -> Self { ModInt::new_internal(x % M::m()) } fn new_internal(x: i64) -> Self { ModInt { x: x, phantom: ::std::marker::PhantomData } } pub fn pow(self, mut e: i64) -> Self { debug_assert!(e >= 0); let mut sum = ModInt::new_internal(1); let mut cur = self; while e > 0 { if e % 2 != 0 { sum *= cur; } cur *= cur; e /= 2; } sum } #[allow(dead_code)] pub fn inv(self) -> Self { self.pow(M::m() - 2) } } impl Default for ModInt { fn default() -> Self { Self::new_internal(0) } } impl>> Add for ModInt { type Output = Self; fn add(self, other: T) -> Self { let other = other.into(); let mut sum = self.x + other.x; if sum >= M::m() { sum -= M::m(); } ModInt::new_internal(sum) } } impl>> Sub for ModInt { type Output = Self; fn sub(self, other: T) -> Self { let other = other.into(); let mut sum = self.x - other.x; if sum < 0 { sum += M::m(); } ModInt::new_internal(sum) } } impl>> Mul for ModInt { type Output = Self; fn mul(self, other: T) -> Self { ModInt::new(self.x * other.into().x % M::m()) } } impl>> AddAssign for ModInt { fn add_assign(&mut self, other: T) { *self = *self + other; } } impl>> SubAssign for ModInt { fn sub_assign(&mut self, other: T) { *self = *self - other; } } impl>> MulAssign for ModInt { fn mul_assign(&mut self, other: T) { *self = *self * other; } } impl Neg for ModInt { type Output = Self; fn neg(self) -> Self { ModInt::new(0) - self } } impl ::std::fmt::Display for ModInt { fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result { self.x.fmt(f) } } impl From for ModInt { fn from(x: i64) -> Self { Self::new(x) } } } // mod mod_int macro_rules! define_mod { ($struct_name: ident, $modulo: expr) => { #[derive(Copy, Clone, PartialEq, Eq, PartialOrd, Ord, Hash)] struct $struct_name {} impl mod_int::Mod for $struct_name { fn m() -> i64 { $modulo } } } } const MOD: i64 = 998_244_353; define_mod!(P, MOD); type MInt = mod_int::ModInt

; // Verified by: https://yukicoder.me/submissions/717057 trait LeaveOne: Default + Clone { type T: Default + Clone; type Me: Clone; type App; fn build(me: Self::Me, vals: &[Self::T], app: &Self::App) -> Self; fn leave_one(&self, excl: Self::T) -> Self::T; fn exchange_one(&self, excl: Self::T, incl: Self::T) -> Self::T; fn add_one(&self, incl: Self::T) -> Self::T; fn as_is(&self) -> Self::T; } struct Reroot { #[allow(unused)] pub dp1: Vec, #[allow(unused)] pub dp2: Vec>, #[allow(unused)] pub dp_loo: Vec, } impl Reroot { pub fn new(g: &[Vec], me: &[LOO::Me], app: &LOO::App) -> Self { let n = g.len(); let mut dp1 = vec![LOO::T::default(); n]; let mut dp2 = vec![vec![]; n]; let mut dp_loo = vec![LOO::default(); n]; Self::dfs1(0, n, &g, &mut dp_loo, &mut dp2, me, app); Self::dfs2(0, n, &g, &mut dp1, &dp_loo, &mut dp2, &app, LOO::T::default()); Reroot { dp1: dp1, dp2: dp2, dp_loo: dp_loo, } } fn dfs1( v: usize, par: usize, g: &[Vec], dp_loo: &mut [LOO], dp2: &mut [Vec], me: &[LOO::Me], app: &LOO::App, ) { let mut mydp2 = vec![LOO::T::default(); g[v].len()]; let mut chval = vec![]; for i in 0..g[v].len() { let w = g[v][i]; if w == par { continue; } Self::dfs1(w, v, g, dp_loo, dp2, me, app); mydp2[i] = dp_loo[w].as_is(); chval.push(mydp2[i].clone()); } dp_loo[v] = LOO::build(me[v].clone(), &chval, app); dp2[v] = mydp2; } fn dfs2( v: usize, par: usize, g: &[Vec], dp1: &mut [LOO::T], dp_loo: &[LOO], dp2: &mut [Vec], app: &LOO::App, passed: LOO::T, ) { for i in 0..g[v].len() { let w = g[v][i]; if w == par { dp2[v][i] = passed.clone(); continue; } let inherited = if par >= g.len() { dp_loo[v].leave_one(dp2[v][i].clone()) } else { dp_loo[v].exchange_one(dp2[v][i].clone(), passed.clone()) }; Self::dfs2(w, v, g, dp1, dp_loo, dp2, app, inherited); } dp1[v] = if par >= g.len() { dp_loo[v].as_is() } else { dp_loo[v].add_one(passed) }; } } // Depends on: tree/Reroot.rs #[derive(Default, Clone)] struct NumeralConcatenation { // the multiplier that would be multiplied by the value of the parent node mul: MInt, // the sum in the current rooted tree add: MInt, // the info of the root node me: (MInt, MInt), } impl LeaveOne for NumeralConcatenation { type T = (MInt, MInt); type Me = (MInt, MInt); type App = (); fn build(me: Self::Me, vals: &[Self::T], &(): &Self::App) -> Self { let mut mul = MInt::new(0); let mut add = MInt::new(0); for &(b, d) in vals { mul += b; add += d; } NumeralConcatenation { mul: (mul + 1) * me.0, add: add + me.1 * (mul + 1), me: me, } } fn leave_one(&self, (b, d): Self::T) -> Self::T { (self.mul - self.me.0 * b, self.add - self.me.1 * b - d) } fn exchange_one(&self, (b1, d1): Self::T, (b2, d2): Self::T) -> Self::T { (self.mul - (b1 - b2) * self.me.0, self.add - (b1 - b2) * self.me.1 - d1 + d2) } fn add_one(&self, (b, d): Self::T) -> Self::T { (self.mul + self.me.0 * b, self.add + self.me.1 * b + d) } fn as_is(&self) -> Self::T { (self.mul, self.add) } } fn main() { // In order to avoid potential stack overflow, spawn a new thread. let stack_size = 104_857_600; // 100 MB let thd = std::thread::Builder::new().stack_size(stack_size); thd.spawn(|| solve()).unwrap().join().unwrap(); } // https://yukicoder.me/problems/no/2360 (3) // 全方位木 DP。 fn solve() { input! { n: usize, a: [chars; n], uv: [(usize1, usize1); n - 1], } let mut t = vec![]; for i in 0..n { let mut mul = MInt::new(1); let mut add = MInt::new(0); for &c in &a[i] { mul *= 10; add = add * 10 + (c as u8 - b'0') as i64; } t.push((mul, add)); } let mut g = vec![vec![]; n]; for &(a, b) in &uv { g[a].push(b); g[b].push(a); } let reroot = Reroot::::new(&g, &t, &()); let mut ans = MInt::new(0); for i in 0..n { let (_mul, add) = reroot.dp1[i]; ans += add; } println!("{}", ans); }