#![allow(non_snake_case, unused_imports, unused_must_use)] use std::io::{self, prelude::*}; use std::str; fn main() { let (stdin, stdout) = (io::stdin(), io::stdout()); let mut scan = Scanner::new(stdin.lock()); let mut out = io::BufWriter::new(stdout.lock()); macro_rules! input { ($T: ty) => { scan.token::<$T>() }; ($T: ty, $N: expr) => { (0..$N).map(|_| scan.token::<$T>()).collect::>() }; } let N = input!(usize); let A = input!(usize, N); let mut dp = SegmentTree::new(100_001, |&x, &y| x + y, ModInt::<998244353>::new()); for i in 0..=100_000 { if A[0] <= i { dp.insert(i, ModInt::<998244353>::from_raw(1)); } } for i in 1..N { let mut nxtdp = SegmentTree::new(100_001, |&x, &y| x + y, ModInt::<998244353>::new()); for j in 0..=100_000 { let mut c = j as isize + A[i - 1] as isize - A[i] as isize; if c > 100_000 { c = 100_000; } else if c < 0 { continue; } let c = c as usize; nxtdp.insert(j, dp.prod(..=std::cmp::min(c, j))); } dp = nxtdp; } let ans = dp.prod(..); writeln!(out, "{}", ans); } pub struct SegmentTree { size: usize, tree: Vec, op: fn(&M, &M) -> M, id: M, } impl SegmentTree { /// self.tree = [id; size], self.op = op, self.id = id pub fn new(size: usize, op: fn(&M, &M) -> M, id: M) -> Self { return Self { size: size, tree: vec![id; 2 * size], op: op, id: id, }; } /// self.tree = arr, self.op = op, self.id = id pub fn from(arr: &[M], op: fn(&M, &M) -> M, id: M) -> Self { let size = arr.len(); let mut tree = vec![id; 2 * size]; for i in 0..size { tree[i + size] = arr[i]; assert!( op(&id, &arr[i]) == arr[i], "id is not the identity element of given operator" ); } for i in (1..size).rev() { tree[i] = op(&tree[i << 1], &tree[i << 1 | 1]); } return Self { size: size, tree: tree, op: op, id: id, }; } /// self.tree[pos] <- value pub fn insert(&mut self, mut pos: usize, value: M) -> () { pos += self.size; self.tree[pos] = value; while pos > 1 { pos >>= 1; self.tree[pos] = (self.op)(&self.tree[pos << 1], &self.tree[pos << 1 | 1]); } } /// return self.tree[pos] (syntax sugar: self[pos]) pub fn get_point(&self, pos: usize) -> M { return self[pos]; } /// return Π_{i ∈ [left, right)} self.tree[i] pub fn get(&self, left: usize, right: usize) -> M { let (mut l, mut r) = (left + self.size, right + self.size); let (mut vl, mut vr) = (self.id, self.id); while l < r { if l & 1 == 1 { vl = (self.op)(&vl, &self.tree[l]); l += 1; } if r & 1 == 1 { r -= 1; vr = (self.op)(&self.tree[r], &vr); } l >>= 1; r >>= 1; } return (self.op)(&vl, &vr); } /// return Π_{i ∈ range} self.tree[i] pub fn prod>(&self, range: R) -> M { let left = match range.start_bound() { std::ops::Bound::Included(&l) => l, std::ops::Bound::Excluded(&l) => l + 1, std::ops::Bound::Unbounded => 0, }; let right = match range.end_bound() { std::ops::Bound::Included(&r) => r + 1, std::ops::Bound::Excluded(&r) => r, std::ops::Bound::Unbounded => self.size, }; return self.get(left, right); } } impl std::ops::Index for SegmentTree { type Output = M; fn index(&self, index: usize) -> &Self::Output { &self.tree[index + self.size] } } impl std::fmt::Display for SegmentTree { fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result { write!( f, "{}", self.tree[self.size..] .iter() .map(|x| x.to_string()) .collect::>() .join(" ") ) } } #[derive(Clone, Copy, Eq, PartialEq, Debug)] pub struct ModInt { value: u32, } impl ModInt

{ pub fn value(&self) -> u32 { assert!(self.value < P); return self.value; } pub fn new() -> Self { return Self { value: 0 }; } pub fn from_raw(x: u32) -> Self { return Self { value: x }; } pub fn from_usize(x: usize) -> Self { return Self { value: (x % P as usize) as u32, }; } pub fn from_isize(x: isize) -> Self { let mut value = x % P as isize; if value < 0 { value += P as isize; } return Self { value: value as u32, }; } pub fn inv(&self) -> Self { pub fn ext_gcd(a: isize, b: isize) -> (isize, isize) { let mut a_k = a; let mut b_k = b; let mut q_k = a_k / b_k; let mut r_k = a_k % b_k; let mut x_k = 0; let mut y_k = 1; let mut z_k = 1; let mut w_k = -q_k; a_k = b_k; b_k = r_k; while r_k != 0 { q_k = a_k / b_k; r_k = a_k % b_k; a_k = b_k; b_k = r_k; let nx = z_k; let ny = w_k; let nz = x_k - q_k * z_k; let nw = y_k - q_k * w_k; x_k = nx; y_k = ny; z_k = nz; w_k = nw; } (x_k, y_k) } let val = self.value() as isize; let ret = ext_gcd(val, P as isize).0; return Self::from_isize(ret); } pub fn pow(&self, mut x: u64) -> Self { let mut ret = ModInt::from_raw(1); let mut a = self.clone(); while x > 0 { if (x & 1) == 1 { ret = ret * a; } a *= a; x >>= 1; } return ret; } } impl std::ops::Add for ModInt

{ type Output = Self; fn add(self, rhs: Self) -> Self::Output { let mut ret = self.value() + rhs.value(); if ret >= P { ret -= P; } return Self::from_raw(ret); } } impl std::ops::AddAssign for ModInt

{ fn add_assign(&mut self, rhs: Self) { self.value = (self.clone() + rhs).value(); } } impl std::ops::Sub for ModInt

{ type Output = Self; fn sub(self, rhs: Self) -> Self::Output { if self.value() >= rhs.value() { return Self::from_raw(self.value() - rhs.value()); } else { return Self::from_raw(P + self.value() - rhs.value()); } } } impl std::ops::SubAssign for ModInt

{ fn sub_assign(&mut self, rhs: Self) { self.value = (self.clone() - rhs).value(); } } impl std::ops::Mul for ModInt

{ type Output = Self; fn mul(self, rhs: Self) -> Self::Output { let ret = self.value() as usize * rhs.value() as usize; return Self::from_usize(ret); } } impl std::ops::MulAssign for ModInt

{ fn mul_assign(&mut self, rhs: Self) { self.value = (self.clone() * rhs).value(); } } impl std::ops::Div for ModInt

{ type Output = Self; fn div(self, rhs: Self) -> Self::Output { self * rhs.inv() } } impl std::ops::DivAssign for ModInt

{ fn div_assign(&mut self, rhs: Self) { self.value = (self.clone() / rhs).value(); } } impl std::ops::Neg for ModInt

{ type Output = Self; fn neg(self) -> Self::Output { let value = self.value(); return Self { value: P - value }; } } impl std::fmt::Display for ModInt

{ fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result { write!(f, "{}", self.value) } } struct Scanner { reader: R, buf_str: Vec, buf_iter: str::SplitWhitespace<'static>, } impl Scanner { fn new(reader: R) -> Self { Self { reader, buf_str: vec![], buf_iter: "".split_whitespace(), } } fn token(&mut self) -> T { loop { if let Some(token) = self.buf_iter.next() { return token.parse().ok().expect("Failed parse"); } self.buf_str.clear(); self.reader .read_until(b'\n', &mut self.buf_str) .expect("Failed read"); self.buf_iter = unsafe { let slice = str::from_utf8_unchecked(&self.buf_str); std::mem::transmute(slice.split_whitespace()) } } } }