#![allow(unused_imports, dead_code, unused_macros, unused_variables, non_snake_case, unused_parens)] use proconio::{input,marker::{Bytes, Chars, Usize1,Isize1}}; use std::ops::*; use std::cmp::*; use std::mem::swap; use std::collections::*; const MOD:i64 = 998244353; const INF:i64 = 0x3fff_ffff_ffff_ffff; macro_rules! min {($a:expr $(,)*) => {{$a}};($a:expr, $b:expr $(,)*) => {{std::cmp::min($a, $b)}};($a:expr, $($rest:expr),+ $(,)*) => {{std::cmp::min($a, min!($($rest),+))}};} macro_rules! max {($a:expr $(,)*) => {{$a}};($a:expr, $b:expr $(,)*) => {{std::cmp::max($a, $b)}};($a:expr, $($rest:expr),+ $(,)*) => {{std::cmp::max($a, max!($($rest),+))}};} macro_rules! chmin {($base:expr, $($cmps:expr),+ $(,)*) => {{let cmp_min = min!($($cmps),+);if $base > cmp_min {$base = cmp_min;true} else {false}}};} macro_rules! chmax {($base:expr, $($cmps:expr),+ $(,)*) => {{let cmp_max = max!($($cmps),+);if $base < cmp_max {$base = cmp_max;true} else {false}}};} macro_rules! mulvec {($x:expr; $s:expr) => {vec![$x; $s]};($x:expr; $s0:expr; $( $s:expr );+) => {mulvec![vec![$x; $s0]; $( $s );+ ]};} macro_rules! outputln {($var:expr)=>{println!("{}",$var)};($var:expr,$($vars:expr),+)=>{print!("{} ",$var);outputln!($($vars),+);};} macro_rules! debug {($($a:expr),* $(,)*) => {eprintln!(concat!($("| ",stringify!($a), "={:?} "),*, "|"),$(&$a),*);};} fn solve() { input! { n: usize, mut A:[usize;n], } let mut ah = vec![0;100_000+10]; let cmb = combination::ModCombination::new(200_000+100); let mut ans = 0; for (h, &a) in A.iter().take(n).enumerate() { ah[a] += 1; ans += cmb.nCr(a+h-1, h); ans %= MOD; } let mut h = n; for x in 1..=100_000 { ans += cmb.nCr(x+h-2, h-1); ans %= MOD; h -= ah[x]; if h == 0 {break;} } println!("{}", ans); } fn main() { std::thread::Builder::new() .stack_size(128 * 1024 * 1024) .spawn(|| solve()).unwrap() .join().unwrap(); } pub mod combination { type Int = i64; const MOD: Int = 998244353; const fn pow_mod(x: Int, mut n: Int, m: Int) -> Int { if m == 1 { return 0; } let mut r: u64 = 1; let mut y: u64 = x.rem_euclid(m) as u64; while n != 0 { if (n & 1) > 0 { r = (r * y) % (m as u64); } y = (y * y) % (m as u64); n >>= 1; } r as Int } pub struct ModCombination { fac: Vec, ifac: Vec, } impl ModCombination { pub fn new(size: usize) -> Self { let mut fac = vec![1; size + 1]; let mut f = 1; let mut i = 2; while i <= size { f = f * i as Int % MOD; fac[i] = f; i += 1; } let mut ifac = vec![1; size + 1]; let mut f = pow_mod(fac[size], MOD - 2, MOD); ifac[size] = f; let mut i = size; while i > 0 { f = f * i as Int % MOD; i -= 1; ifac[i] = f; } Self { fac, ifac } } #[inline] pub fn nCr(&self, n: usize, r: usize) -> Int { if n < r { return 0; } self.fac[n] * self.ifac[r] % MOD * self.ifac[n - r] % MOD } #[inline] pub fn nPr(&self, n: usize, r: usize) -> Int { if n < r { return 0; } self.fac[n] * self.ifac[n - r] % MOD } #[inline] pub fn nHr(&self, n: usize, r: usize) -> Int { if n == 0 && r == 0 { return 1; } self.nCr(n + r - 1, r) } } }