#![allow(unused_imports, non_snake_case)] pub use __cargo_equip::prelude::*; use proconio::{marker::*, *}; use static_modint::ModInt998244353 as MInt; #[fastout] fn main() { input! { N: usize, } if N > 1_200_000 { return; } let mut ans = MInt::new(0); let two_inv = MInt::new(2).inv(); for j in 1..=N { // j*(1+2+...N/j-1) + N/j*(0..=余り) let nj = MInt::new(N / j); ans += (nj - 1) * nj * two_inv * j; ans += nj * (N % j + 1); } println!("{}", ans); } #[macro_export] macro_rules! mat { ($($e:expr),*) => { vec![$($e),*] }; ($($e:expr,)*) => { vec![$($e),*] }; ($e:expr; $d:expr) => { vec![$e; $d] }; ($e:expr; $d:expr $(; $ds:expr)+) => { vec![mat![$e $(; $ds)*]; $d] }; } #[macro_export] macro_rules! chmin { ($a:expr, $b:expr) => { if $a > $b { $a = $b; true } else { false } }; } #[macro_export] macro_rules! chmax { ($a:expr, $b:expr) => { if $a < $b { $a = $b; true } else { false } }; } /// https://maguro.dev/debug-macro/ #[macro_export] macro_rules! debug { ($($a:expr),* $(,)*) => { #[cfg(debug_assertions)] eprintln!(concat!($("| ", stringify!($a), "={:?} "),*, "|"), $(&$a),*); }; } // The following code was expanded by `cargo-equip`. /// # Bundled libraries /// /// - `internal_modint 0.1.0 (git+ssh://git@github.com/CoCo-Japan-pan/procon_lib_rs.git#66340933fd234b82f0daf7788b70bbaea1a40f5f)` licensed under `CC0-1.0` as `crate::__cargo_equip::crates::__internal_modint_0_1_0` /// - `internal_type_traits 0.1.0 (git+ssh://git@github.com/CoCo-Japan-pan/procon_lib_rs.git#66340933fd234b82f0daf7788b70bbaea1a40f5f)` licensed under `CC0-1.0` as `crate::__cargo_equip::crates::__internal_type_traits_0_1_0` /// - `static_modint 0.1.0 (git+ssh://git@github.com/CoCo-Japan-pan/procon_lib_rs.git#66340933fd234b82f0daf7788b70bbaea1a40f5f)` licensed under `CC0-1.0` as `crate::__cargo_equip::crates::static_modint` #[cfg_attr(any(), rustfmt::skip)] #[allow(unused)] mod __cargo_equip { pub(crate) mod crates { pub mod __internal_modint_0_1_0 {use crate::__cargo_equip::preludes::__internal_modint_0_1_0::*;use internal_type_traits::{One,Zero};use std::fmt::{Debug,Display};use std::ops::{Add,AddAssign,Div,DivAssign,Mul,MulAssign,Neg,Sub,SubAssign};use std::str::FromStr;pub trait ModInt:Debug+Default+Clone+PartialEq+Eq+Display+Copy+Add+Sub+Mul+Div+AddAssign+SubAssign+MulAssign+DivAssign+Neg+FromStr+Zero+One{fn new(x:T)->Self;fn raw(x:u32)->Self;fn value(&self)->u32;fn modulus()->u32;fn pow(&self,mut n:u64)->Self{let mut ret=Self::new(1);let mut base=*self;while n>0{if n&1==1{ret*=base;}base*=base;n>>=1;}ret}#[inline]fn inv(&self)->Self{let(g,x)=inv_gcd(self.value()as i64,Self::modulus()as i64);assert_eq!(g,1);Self::raw(x as u32)}}pub const fn safe_mod(mut x:i64,m:i64)->i64{x%=m;if x<0{x+=m;}x}pub const fn inv_gcd(a:i64,b:i64)->(i64,i64){let a=safe_mod(a,b);if a==0{return(b,0);}let mut s=b;let mut t=a;let mut m0=0;let mut m1=1;while t!=0{let u=s/t;s-=t*u;m0-=m1*u;let tmp=s;s=t;t=tmp;let tmp=m0;m0=m1;m1=tmp;}if m0<0{m0+=b/s;}(s,m0)}pub trait RemEuclidU32:Copy{fn rem_euclid_u32(self,modulus:u32)->u32;}impl RemEuclidU32 for u8{#[inline]fn rem_euclid_u32(self,modulus:u32)->u32{self as u32%modulus}}impl RemEuclidU32 for u16{#[inline]fn rem_euclid_u32(self,modulus:u32)->u32{self as u32%modulus}}impl RemEuclidU32 for u32{#[inline]fn rem_euclid_u32(self,modulus:u32)->u32{self%modulus}}impl RemEuclidU32 for u64{#[inline]fn rem_euclid_u32(self,modulus:u32)->u32{(self%modulus as u64)as u32}}impl RemEuclidU32 for usize{#[inline]fn rem_euclid_u32(self,modulus:u32)->u32{let casted:u64=self.try_into().unwrap();casted.rem_euclid_u32(modulus)}}impl RemEuclidU32 for u128{#[inline]fn rem_euclid_u32(self,modulus:u32)->u32{(self%modulus as u128)as u32}}#[inline]fn neg(val:u32,modulus:u32)->u32{if val==0{0}else{modulus-val}}macro_rules!impl_rem_euclid_u32_for_signed{($($t:ty),*)=>{$(impl RemEuclidU32 for$t{#[inline]fn rem_euclid_u32(self,modulus:u32)->u32{if self<0{neg(self.unsigned_abs().rem_euclid_u32(modulus),modulus)}else{self.unsigned_abs().rem_euclid_u32(modulus)}}})*};}impl_rem_euclid_u32_for_signed!(i8,i16,i32,i64,isize,i128);macro_rules!impl_rem_for_borrow{($($t:ty),*)=>{$(impl RemEuclidU32 for&$t{#[inline]fn rem_euclid_u32(self,modulus:u32)->u32{(*self).rem_euclid_u32(modulus)}})*};}impl_rem_for_borrow!(u8,u16,u32,u64,usize,u128,i8,i16,i32,i64,isize,i128);} pub mod __internal_type_traits_0_1_0 {use std::fmt::{Debug,Display};use std::ops::{Add,AddAssign,Sub,SubAssign};pub trait Integral:Copy+Add+AddAssign+Sub+SubAssign+Ord+Zero+One+BoundedBelow+BoundedAbove+Display+Debug{}pub trait Zero{fn zero()->Self;}pub trait One{fn one()->Self;}pub trait BoundedBelow{fn min_value()->Self;}pub trait BoundedAbove{fn max_value()->Self;}macro_rules!impl_integral{($($ty:ty),*)=>{$(impl Zero for$ty{#[inline]fn zero()->Self{0}}impl One for$ty{#[inline]fn one()->Self{1}}impl BoundedBelow for$ty{#[inline]fn min_value()->Self{Self::MIN}}impl BoundedAbove for$ty{#[inline]fn max_value()->Self{Self::MAX}}impl Integral for$ty{})*};}impl_integral!(i8,i16,i32,i64,i128,isize,u8,u16,u32,u64,u128,usize);} pub mod static_modint {use crate::__cargo_equip::preludes::static_modint::*;use internal_modint::{ModInt,RemEuclidU32};use internal_type_traits::{One,Zero};use std::fmt::{Debug,Display};use std::iter::{Product,Sum};use std::ops::{Add,AddAssign,Div,DivAssign,Mul,MulAssign,Neg,Sub,SubAssign};use std::str::FromStr;pub type ModInt998244353=StaticModInt<998244353>;pub type ModInt1000000007=StaticModInt<1000000007>;#[derive(Clone,Copy,PartialEq,Eq,Hash,Default)]pub struct StaticModInt{value:u32,}implZero for StaticModInt{fn zero()->Self{Self::raw(0)}}implOne for StaticModInt{fn one()->Self{Self::new(1)}}implDebug for StaticModInt{fn fmt(&self,f:&mut std::fmt::Formatter<'_>)->std::fmt::Result{write!(f,"{}",self.value)}}implDisplay for StaticModInt{fn fmt(&self,f:&mut std::fmt::Formatter<'_>)->std::fmt::Result{write!(f,"{}",self.value)}}implSumfor StaticModIntwhere Self:Add,{fn sum>(iter:I)->Self{iter.fold(Self::raw(0),Add::add)}}implProductfor StaticModIntwhere Self:Mul,{fn product>(iter:I)->Self{iter.fold(Self::new(1),Mul::mul)}}implFromStr for StaticModInt{type Err=::Err;fn from_str(s:&str)->Result{i64::from_str(s).map(Self::new)}}implStaticModInt{#[inline]pub fn value(&self)->u32{self.value}#[inline]pub fn modulus()->u32{MOD}#[inline]pub fn new(x:T)->Self{ModInt::new(x)}#[inline]pub fn raw(x:u32)->Self{Self{value:x}}#[inline]pub fn pow(&self,n:u64)->Self{ModInt::pow(self,n)}#[inline]pub fn inv(&self)->Self{ModInt::inv(self)}}implModInt for StaticModInt{#[inline]fn value(&self)->u32{self.value}#[inline]fn modulus()->u32{MOD}#[inline]fn raw(x:u32)->Self{Self{value:x}}#[inline]fn new(x:T)->Self{Self{value:x.rem_euclid_u32(MOD),}}}implNeg for StaticModInt{type Output=Self;#[inline]fn neg(self)->Self{if self.value==0{Self{value:0}}else{Self{value:MOD-self.value,}}}}macro_rules!impl_ops{($trait:ident,$method:ident,$assign_trait:ident,$assign_method:ident)=>{impl$traitfor StaticModIntwhere Self:$assign_trait,{type Output=Self;fn$method(mut self,rhs:T)->Self{StaticModInt::::$assign_method(&mut self,rhs);self}}impl$assign_traitfor StaticModInt{fn$assign_method(&mut self,rhs:T){StaticModInt::::$assign_method(self,Self::new(rhs));}}};}impl_ops!(Add,add,AddAssign,add_assign);impl_ops!(Sub,sub,SubAssign,sub_assign);impl_ops!(Mul,mul,MulAssign,mul_assign);impl_ops!(Div,div,DivAssign,div_assign);implAddAssign for StaticModInt{fn add_assign(&mut self,rhs:Self){self.value+=rhs.value;if self.value>=MOD{self.value-=MOD;}}}implSubAssign for StaticModInt{fn sub_assign(&mut self,rhs:Self){if self.valueMulAssign for StaticModInt{fn mul_assign(&mut self,rhs:Self){self.value=(self.value as u64*rhs.value as u64).rem_euclid_u32(MOD);}}#[allow(clippy::suspicious_op_assign_impl)]implDivAssign for StaticModInt{fn div_assign(&mut self,rhs:Self){*self*=rhs.inv();}}macro_rules!impl_from_primitive{($($t:ty),*)=>{$(implFrom<$t>for StaticModInt{fn from(x:$t)->Self{Self::new(x)}})*};}impl_from_primitive!(u8,u16,u32,u64,usize,u128,i8,i16,i32,i64,isize,i128);} } pub(crate) mod macros { pub mod __internal_modint_0_1_0 {} pub mod __internal_type_traits_0_1_0 {} pub mod static_modint {} } pub(crate) mod prelude {pub use crate::__cargo_equip::crates::*;} mod preludes { pub mod __internal_modint_0_1_0 {pub(in crate::__cargo_equip)use crate::__cargo_equip::crates::__internal_type_traits_0_1_0 as internal_type_traits;} pub mod __internal_type_traits_0_1_0 {} pub mod static_modint {pub(in crate::__cargo_equip)use crate::__cargo_equip::crates::{__internal_modint_0_1_0 as internal_modint,__internal_type_traits_0_1_0 as internal_type_traits};} } }