fn main() { type Fp = F998244353; let mut io = IO::new(); let n = io.scan(); let a: Vec = io.scan_vec(n); let (m, _, _, res) = compress(&a); let mut bitfv = FenwickTree::::new(m); let mut bitbv = FenwickTree::::new(m); let mut bitf = FenwickTree::::new(m); let mut bitb = FenwickTree::::new(m); let a = a.into_iter().map(Fp::new).collect::>(); for (&x, &y) in res.iter().zip(a.iter()) { bitb.add(x, 1); bitbv.add(x, y); } let mut ans = Fp::zero(); for i in 0..n { bitb.add(res[i], -1); bitbv.add(res[i], -a[i]); let bkc = Fp::new(bitb.sum(..res[i])); let frc = Fp::new(bitf.sum(res[i]+1..)); let bkv = bitbv.sum(..res[i]); let frv = bitfv.sum(res[i]+1..); ans += a[i] * bkc * frc + bkc * frv + frc * bkv; bitf.add(res[i], 1); bitfv.add(res[i], a[i]); } io.println(ans); } // ------------ traits start ------------ impl Scan for Fp { fn scan(s: &mut IO) -> Self { Self::new(i64::scan(s)) } } impl Print for Fp { fn print(w: &mut IO, x: Self) { w.print(x.into_inner()); } } // ------------ traits end ------------ // ------------ libraries start ------------ use std::collections::HashMap; pub fn compress(l: &[T])-> (usize, HashMap, Vec, Vec) { let mut f = l.to_owned(); f.sort(); f.dedup(); let dict: HashMap = f.iter().cloned().zip(0..f.len()).collect(); let res: Vec = l.iter().map(|x| *dict.get(x).unwrap()).collect(); (f.len(), dict, f, res) } // ------------ FenwickTree with generics start ------------ #[derive(Clone, Debug)] pub struct FenwickTree(Vec); impl FenwickTree { #[inline] fn lsb(x: usize) -> usize { x & x.wrapping_neg() } pub fn new(n: usize) -> Self { Self(vec![T::zero(); n+1]) } pub fn prefix_sum(&self, i: usize) -> T { std::iter::successors(Some(i), |&i| Some(i - Self::lsb(i))) .take_while(|&i| i != 0) .map(|i| self.0[i].clone()) .fold(T::zero(), |sum, x| sum + x) } pub fn add(&mut self, i: usize, x: T) { let n = self.0.len(); std::iter::successors(Some(i + 1), |&i| Some(i + Self::lsb(i))) .take_while(|&i| i < n) .for_each(|i| self.0[i] = self.0[i].clone() + x.clone()); } pub fn partition(&self, pred: impl Fn(usize, &T) -> bool) -> (usize, T) { assert!(pred(0, &self.0[0]), "need to be pred(0, 0)"); let mut j = 0; let mut current = self.0[0].clone(); let n = self.0.len(); for d in std::iter::successors(Some(n.next_power_of_two() >> 1), |&d| { Some(d >> 1)}) .take_while(|&d| d != 0) { if j + d < n { let next = current.clone() + self.0[j + d].clone(); if pred(j + d, &next) { current = next; j += d; } } } (j, current) } } impl From> for FenwickTree { fn from(src: Vec) -> Self { let mut table = std::iter::once(T::zero()) .chain(src.into_iter()) .collect::>(); let n = table.len(); (1..n) .map(|i| (i, i + Self::lsb(i))) .filter(|&(_, j)| j < n) .for_each(|(i, j)| { table[j] = table[j].clone() + table[i].clone(); }); Self(table) } } impl FenwickTree { pub fn sum>(&self, rng: R) -> T { let Range { start, end } = bounds_within(rng, self.0.len() - 1); self.prefix_sum(end) + -self.prefix_sum(start) } } use std::ops::Bound::{Excluded, Included, Unbounded}; use std::ops::{Range, RangeBounds}; /// 区間を配列サイズに収まるように丸める。 /// /// 与えられた区間 `r` と `0..len` の共通部分を、有界な半開区間として返す。 /// /// # Examples /// ``` /// use bibliotheca::utils::bounds::bounds_within; /// /// assert_eq!(bounds_within(.., 7), 0..7); /// assert_eq!(bounds_within(..=4, 7), 0..5); /// ``` pub fn bounds_within>(r: R, len: usize) -> Range { let e_ex = match r.end_bound() { Included(&e) => e + 1, Excluded(&e) => e, Unbounded => len, } .min(len); let s_in = match r.start_bound() { Included(&s) => s, Excluded(&s) => s + 1, Unbounded => 0, } .min(e_ex); s_in..e_ex } // ------------ FenwickTree with generics end ------------ // ------------ libraries end ------------ // ------------ traits start ------------ use std::{ fmt::{Debug, Display}, hash::Hash, iter, marker::PhantomData, ops, }; crate::define_fp!(pub F998244353, Mod998244353, 998244353); crate::define_fp!(pub F1000000007, Mod1000000007, 1000000007); #[derive(Clone, PartialEq, Copy, Eq, Hash)] pub struct Fp(i64, PhantomData); pub trait Mod: Debug + Clone + PartialEq + Copy + Eq + Hash { const MOD: i64; } impl Fp { pub fn new(mut x: i64) -> Self { x %= T::MOD; Self::unchecked(if x < 0 { x + T::MOD } else { x }) } pub fn into_inner(self) -> i64 { self.0 } pub fn r#mod() -> i64 { T::MOD } pub fn inv(self) -> Self { assert_ne!(self.0, 0, "Zero division"); let (sign, x) = if self.0 * 2 < T::MOD { (1, self.0) } else { (-1, T::MOD - self.0) }; let (g, _a, b) = ext_gcd(T::MOD, x); let ans = sign * b; assert_eq!(g, 1); Self::unchecked(if ans < 0 { ans + T::MOD } else { ans }) } pub fn frac(x: i64, y: i64) -> Self { Fp::new(x) / Fp::new(y) } pub fn pow(mut self, mut p: u64) -> Self { let mut ans = Fp::new(1); while p != 0 { if p & 1 == 1 { ans *= self; } self *= self; p >>= 1; } ans } fn unchecked(x: i64) -> Self { Self(x, PhantomData) } } impl iter::Sum> for Fp { fn sum(iter: I) -> Self where I: iter::Iterator>, { iter.fold(Fp::new(0), ops::Add::add) } } impl<'a, T: 'a + Mod> iter::Sum<&'a Fp> for Fp { fn sum(iter: I) -> Self where I: iter::Iterator>, { iter.fold(Fp::new(0), ops::Add::add) } } impl iter::Product> for Fp { fn product(iter: I) -> Self where I: iter::Iterator>, { iter.fold(Self::new(1), ops::Mul::mul) } } impl<'a, T: 'a + Mod> iter::Product<&'a Fp> for Fp { fn product(iter: I) -> Self where I: iter::Iterator>, { iter.fold(Self::new(1), ops::Mul::mul) } } impl Debug for Fp { fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> Result<(), std::fmt::Error> { write!(f, "{}", self.0) } } impl Display for Fp { fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> Result<(), std::fmt::Error> { write!(f, "{}", self.0) } } // ax + by = gcd(x, y) なる、互いに素な (a, b) を一組探して、(g, a, b) を返します。 // // | 0 -x | | y -x | | x 0 | // | 1 b | = | a b | | y 1 | fn ext_gcd(x: i64, y: i64) -> (i64, i64, i64) { let (b, g) = { let mut x = x; let mut y = y; let mut u = 0; let mut v = 1; while x != 0 { let q = y / x; y -= q * x; v -= q * u; std::mem::swap(&mut x, &mut y); std::mem::swap(&mut u, &mut v); } (v, y) }; assert_eq!((g - b * y) % x, 0); let a = (g - b * y) / x; (g, a, b) } #[macro_export] macro_rules! define_fp { ($vis:vis $fp:ident, $t:ident, $mod:expr) => { #[derive(Debug, Clone, PartialEq, Copy, Eq, Hash)] $vis struct $t; // NOTE: `$crate::` があるとうまく展開できません。 impl Mod for $t { const MOD: i64 = $mod; } // NOTE: `$crate::` があるとうまく展開できません。 $vis type $fp = Fp<$t>; } } use std::ops::*; impl Associative for Fp {} impl Zero for Fp { fn zero() -> Self { Self::unchecked(0) } fn is_zero(&self) -> bool { self.0 == 0 } } impl One for Fp { fn one() -> Self { Self::unchecked(1) } fn is_one(&self) -> bool { self.0 == 1 } } impl Add for Fp { type Output = Self; fn add(self, rhs: Self) -> Self { let res = self.0 + rhs.0; Self::unchecked(if T::MOD <= res { res - T::MOD } else { res }) } } impl Sub for Fp { type Output = Self; fn sub(self, rhs: Self) -> Self { let res = self.0 - rhs.0; Self::unchecked(if res < 0 { res + T::MOD } else { res }) } } impl Mul for Fp { type Output = Self; fn mul(self, rhs: Self) -> Self { Self::new(self.0 * rhs.0) } } #[allow(clippy::suspicious_arithmetic_impl)] impl Div for Fp { type Output = Self; fn div(self, rhs: Self) -> Self { self * rhs.inv() } } impl Neg for Fp { type Output = Self; fn neg(self) -> Self { if self.0 == 0 { Self::unchecked(0) } else { Self::unchecked(M::MOD - self.0) } } } impl Neg for &Fp { type Output = Fp; fn neg(self) -> Self::Output { if self.0 == 0 { Fp::unchecked(0) } else { Fp::unchecked(M::MOD - self.0) } } } macro_rules! forward_assign_biop { ($(impl $trait:ident, $fn_assign:ident, $fn:ident)*) => { $( impl $trait for Fp { fn $fn_assign(&mut self, rhs: Self) { *self = self.$fn(rhs); } } )* }; } forward_assign_biop! { impl AddAssign, add_assign, add impl SubAssign, sub_assign, sub impl MulAssign, mul_assign, mul impl DivAssign, div_assign, div } macro_rules! forward_ref_binop { ($(impl $imp:ident, $method:ident)*) => { $( impl<'a, T: Mod> $imp> for &'a Fp { type Output = Fp; fn $method(self, other: Fp) -> Self::Output { $imp::$method(*self, other) } } impl<'a, T: Mod> $imp<&'a Fp> for Fp { type Output = Fp; fn $method(self, other: &Fp) -> Self::Output { $imp::$method(self, *other) } } impl<'a, T: Mod> $imp<&'a Fp> for &'a Fp { type Output = Fp; fn $method(self, other: &Fp) -> Self::Output { $imp::$method(*self, *other) } } )* }; } forward_ref_binop! { impl Add, add impl Sub, sub impl Mul, mul impl Div, div } use std::marker::Sized; /// 元 pub trait Element: Sized + Clone + PartialEq {} impl Element for T {} /// 結合性 pub trait Associative: Magma {} /// マグマ pub trait Magma: Element + Add {} impl> Magma for T {} /// 半群 pub trait SemiGroup: Magma + Associative {} impl SemiGroup for T {} /// モノイド pub trait Monoid: SemiGroup + Zero {} impl Monoid for T {} pub trait ComMonoid: Monoid + AddAssign {} impl ComMonoid for T {} /// 群 pub trait Group: Monoid + Neg {} impl> Group for T {} pub trait ComGroup: Group + ComMonoid {} impl ComGroup for T {} /// 半環 pub trait SemiRing: ComMonoid + Mul + One {} impl + One> SemiRing for T {} /// 環 pub trait Ring: ComGroup + SemiRing {} impl Ring for T {} pub trait ComRing: Ring + MulAssign {} impl ComRing for T {} /// 体 pub trait Field: ComRing + Div + DivAssign {} impl + DivAssign> Field for T {} /// 加法単元 pub trait Zero: Element { fn zero() -> Self; fn is_zero(&self) -> bool; } /// 乗法単元 pub trait One: Element { fn one() -> Self; fn is_one(&self) -> bool; } macro_rules! impl_integer { ($($T:ty,)*) => { $( impl Associative for $T {} impl Zero for $T { fn zero() -> Self { 0 } fn is_zero(&self) -> bool { *self == 0 } } impl<'a> Zero for &'a $T { fn zero() -> Self { &0 } fn is_zero(&self) -> bool { *self == &0 } } impl One for $T { fn one() -> Self { 1 } fn is_one(&self) -> bool { *self == 1 } } impl<'a> One for &'a $T { fn one() -> Self { &1 } fn is_one(&self) -> bool { *self == &1 } } )* }; } impl_integer! { i8, i16, i32, i64, i128, isize, u8, u16, u32, u64, u128, usize, } // ------------ traits end ------------ // ------------ io module start ------------ use std::io::{stdout, BufWriter, Read, StdoutLock, Write}; pub struct IO { iter: std::str::SplitAsciiWhitespace<'static>, buf: BufWriter>, } impl IO { pub fn new() -> Self { let mut input = String::new(); std::io::stdin().read_to_string(&mut input).unwrap(); let input = Box::leak(input.into_boxed_str()); let out = Box::new(stdout()); IO { iter: input.split_ascii_whitespace(), buf: BufWriter::new(Box::leak(out).lock()), } } fn scan_str(&mut self) -> &'static str { self.iter.next().unwrap() } fn scan_raw(&mut self) -> &'static [u8] { self.scan_str().as_bytes() } pub fn scan(&mut self) -> T { T::scan(self) } pub fn scan_vec(&mut self, n: usize) -> Vec { (0..n).map(|_| self.scan()).collect() } } impl IO { pub fn print(&mut self, x: T) { T::print(self, x); } pub fn println(&mut self, x: T) { self.print(x); self.print("\n"); } pub fn iterln>(&mut self, mut iter: I, delim: &str) { if let Some(v) = iter.next() { self.print(v); for v in iter { self.print(delim); self.print(v); } } self.print("\n"); } pub fn flush(&mut self) { self.buf.flush().unwrap(); } } impl Default for IO { fn default() -> Self { Self::new() } } pub trait Scan { fn scan(io: &mut IO) -> Self; } macro_rules! impl_parse_int { ($($t:tt),*) => { $( impl Scan for $t { fn scan(s: &mut IO) -> Self { let mut res = 0; let mut neg = false; for d in s.scan_raw() { if *d == b'-' { neg = true; } else { res *= 10; res += (*d - b'0') as $t; } } if neg { res = res.wrapping_neg(); } res } } )* }; } impl_parse_int!(i16, i32, i64, isize, u16, u32, u64, usize); impl Scan for (T, U) { fn scan(s: &mut IO) -> Self { (T::scan(s), U::scan(s)) } } impl Scan for (T, U, V) { fn scan(s: &mut IO) -> Self { (T::scan(s), U::scan(s), V::scan(s)) } } impl Scan for (T, U, V, W) { fn scan(s: &mut IO) -> Self { (T::scan(s), U::scan(s), V::scan(s), W::scan(s)) } } pub trait Print { fn print(w: &mut IO, x: Self); } macro_rules! impl_print_int { ($($t:ty),*) => { $( impl Print for $t { fn print(w: &mut IO, x: Self) { w.buf.write_all(x.to_string().as_bytes()).unwrap(); } } )* }; } impl_print_int!(i16, i32, i64, isize, u16, u32, u64, usize); impl Print for u8 { fn print(w: &mut IO, x: Self) { w.buf.write_all(&[x]).unwrap(); } } impl Print for &[u8] { fn print(w: &mut IO, x: Self) { w.buf.write_all(x).unwrap(); } } impl Print for &str { fn print(w: &mut IO, x: Self) { w.print(x.as_bytes()); } } impl Print for (T, U) { fn print(w: &mut IO, (x, y): Self) { w.print(x); w.print(" "); w.print(y); } } impl Print for (T, U, V) { fn print(w: &mut IO, (x, y, z): Self) { w.print(x); w.print(" "); w.print(y); w.print(" "); w.print(z); } } impl Print for (T, U, V, W) { fn print(w: &mut IO, (x, y, z, a): Self) { w.print(x); w.print(" "); w.print(y); w.print(" "); w.print(z); w.print(" "); w.print(a); } } // ------------ io module end ------------