#[allow(unused_imports)] use std::cmp::*; #[allow(unused_imports)] use std::collections::*; // 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, [ $t:tt ]) => {{ let len = read_value!($next, usize); read_value!($next, [$t; len]) }}; ($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>> 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 ::std::fmt::Debug for ModInt { fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result { let (mut a, mut b, _) = red(self.x, M::m()); if b < 0 { a = -a; b = -b; } write!(f, "{}/{}", a, b) } } impl From for ModInt { fn from(x: i64) -> Self { Self::new(x) } } // Finds the simplest fraction x/y congruent to r mod p. // The return value (x, y, z) satisfies x = y * r + z * p. fn red(r: i64, p: i64) -> (i64, i64, i64) { if r.abs() <= 10000 { return (r, 1, 0); } let mut nxt_r = p % r; let mut q = p / r; if 2 * nxt_r >= r { nxt_r -= r; q += 1; } if 2 * nxt_r <= -r { nxt_r += r; q -= 1; } let (x, z, y) = red(nxt_r, r); (x, y - q * z, z) } } // 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

; /** * Lazy Segment Tree. This data structure is useful for fast folding and updating on intervals of an array * whose elements are elements of monoid T. Note that constructing this tree requires the identity * element of T and the operation of T. This is monomorphised, because of efficiency. T := i64, biop = max, upop = (+) * Reference: http://d.hatena.ne.jp/kyuridenamida/20121114/1352835261 * Verified by https://codeforces.com/contest/1114/submission/49759034 */ pub trait ActionRing { type T: Clone + Copy; // data type U: Clone + Copy + PartialEq + Eq; // action fn biop(x: Self::T, y: Self::T) -> Self::T; fn update(x: Self::T, a: Self::U, height: usize) -> Self::T; fn upop(fst: Self::U, snd: Self::U) -> Self::U; fn e() -> Self::T; fn upe() -> Self::U; // identity for upop } pub struct LazySegTree { n: usize, dep: usize, dat: Vec, lazy: Vec, } impl LazySegTree { #[allow(unused)] pub fn new(n_: usize) -> Self { let mut n = 1; let mut dep = 0; while n < n_ { n *= 2; dep += 1; } // n is a power of 2 LazySegTree { n: n, dep: dep, dat: vec![R::e(); 2 * n - 1], lazy: vec![R::upe(); 2 * n - 1] } } #[allow(unused)] pub fn with(a: &[R::T]) -> Self { let n_ = a.len(); let mut n = 1; let mut dep = 0; while n < n_ { n *= 2; dep += 1; } // n is a power of 2 let mut dat = vec![R::e(); 2 * n - 1]; for i in 0..n_ { dat[n - 1 + i] = a[i]; } for i in (0..n - 1).rev() { dat[i] = R::biop(dat[2 * i + 1], dat[2 * i + 2]); } LazySegTree { n: n, dep: dep, dat: dat, lazy: vec![R::upe(); 2 * n - 1], } } #[inline] fn lazy_evaluate_node(&mut self, k: usize, height: usize) { if self.lazy[k] == R::upe() { return; } self.dat[k] = R::update(self.dat[k], self.lazy[k], height); if k < self.n - 1 { self.lazy[2 * k + 1] = R::upop(self.lazy[2 * k + 1], self.lazy[k]); self.lazy[2 * k + 2] = R::upop(self.lazy[2 * k + 2], self.lazy[k]); } self.lazy[k] = R::upe(); // identity for upop } #[inline] fn update_node(&mut self, k: usize) { self.dat[k] = R::biop(self.dat[2 * k + 1], self.dat[2 * k + 2]); } fn update_sub(&mut self, a: usize, b: usize, v: R::U, k: usize, height: usize, l: usize, r: usize) { self.lazy_evaluate_node(k, height); // [a,b) and [l,r) intersects? if r <= a || b <= l {return;} if a <= l && r <= b { self.lazy[k] = R::upop(self.lazy[k], v); self.lazy_evaluate_node(k, height); return; } self.update_sub(a, b, v, 2 * k + 1, height - 1, l, (l + r) / 2); self.update_sub(a, b, v, 2 * k + 2, height - 1, (l + r) / 2, r); self.update_node(k); } /* ary[i] = upop(ary[i], v) for i in [a, b) (half-inclusive) */ #[inline] pub fn update(&mut self, a: usize, b: usize, v: R::U) { let n = self.n; let dep = self.dep; self.update_sub(a, b, v, 0, dep, 0, n); } /* l,r are for simplicity */ fn query_sub(&mut self, a: usize, b: usize, k: usize, height: usize, l: usize, r: usize) -> R::T { self.lazy_evaluate_node(k, height); // [a,b) and [l,r) intersect? if r <= a || b <= l {return R::e();} if a <= l && r <= b {return self.dat[k];} let vl = self.query_sub(a, b, 2 * k + 1, height - 1, l, (l + r) / 2); let vr = self.query_sub(a, b, 2 * k + 2, height - 1, (l + r) / 2, r); self.update_node(k); R::biop(vl, vr) } /* [a, b) (note: half-inclusive) */ #[inline] pub fn query(&mut self, a: usize, b: usize) -> R::T { let n = self.n; let dep = self.dep; self.query_sub(a, b, 0, dep, 0, n) } } enum Affine {} impl ActionRing for Affine { type T = MInt; // data type U = (MInt, MInt); // action, (a, b) |-> x |-> ax + b fn biop(x: Self::T, y: Self::T) -> Self::T { x + y } fn update(x: Self::T, (a, b): Self::U, height: usize) -> Self::T { x * a + b * MInt::new(1 << height) } fn upop(fst: Self::U, snd: Self::U) -> Self::U { let (a, b) = fst; let (c, d) = snd; (a * c, b * c + d) } fn e() -> Self::T { 0.into() } fn upe() -> Self::U { // identity for upop (1.into(), 0.into()) } } trait Change { fn chmax(&mut self, x: Self); fn chmin(&mut self, x: Self); } impl Change for T { fn chmax(&mut self, x: T) { if *self < x { *self = x; } } fn chmin(&mut self, x: T) { if *self > x { *self = x; } } } 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(); } fn find_coef(a: &[i64], eq: bool) -> Vec { let n = a.len(); let mut b = vec![]; for i in 0..n { b.push((a[i], i)); } if eq { b.sort(); } else { b.sort_by_key(|&(a, b)| (a, n - b)); } let mut st = LazySegTree::::new(n); st.update(0, n, (0.into(), 1.into())); let mut ans = vec![MInt::new(1); n]; for (_, idx) in b { let p = st.query(0, idx + 1); let q = st.query(idx, idx + 1); ans[idx] = p * q.inv(); st.update(0, idx + 1, (2.into(), 0.into())); } ans } fn solve() { input! { n: usize, a: [i64; n], } let p = find_coef(&a, true); let mut a = a; a.reverse(); let mut q = find_coef(&a, false); q.reverse(); a.reverse(); let mut tot = MInt::new(0); for i in 0..n { tot += p[i] * q[i] * a[i]; } println!("{}", tot); // eprintln!("p = {:?}", p); // eprintln!("q = {:?}", q); }