#[allow(unused_imports)] use std::cmp::*; #[allow(unused_imports)] use std::collections::*; use std::io::Read; fn getline() -> String { let mut ret = String::new(); std::io::stdin().read_line(&mut ret).ok().unwrap(); ret } /// 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 Default for ModInt { fn default() -> Self { Self::new_internal(0) } } 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)] pub 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

; // https://yukicoder.me/problems/no/2437 (3.5) // 壊れやすくない 11 の倍数について、以下が成り立つ: // 取り除く桁を b とすると 10^k(10a + b) + c と 10^k a + c がともに 11 の倍数であるため、10a + b = a (mod 11) である。 // つまり b = 2a (mod 11) である。 // そのため、桁 DP で以下の情報を持てば良い: // dp[X と等しい?][mod 11][壊れやすい?] 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 solve() { getline(); let x: Vec<_> = getline().trim().bytes().collect(); let n = x.len(); let mut dp = vec![[[[MInt::new(0); 2]; 11]; 2]; n + 1]; dp[0][1][0][1] += 1; for i in 0..n { for eq in 0..2 { for m in 0..11 { for fr in 0..2 { let old = dp[i][eq][m][fr]; for j in 0..[10, (x[i] - b'0') as usize + 1][eq] { let neq = eq & if (x[i] - b'0') as usize == j { 1 } else { 0 }; let nfr = fr & if (9 * m + j) % 11 == 0 { 0 } else { 1 }; dp[i + 1][neq][(10 * m + j) % 11][nfr] += old; } } } } if i > 0 { for j in 1..10 { dp[i + 1][0][j][1] += 1; } } } let ans = dp[n][0][0][1] + dp[n][1][0][1]; println!("{}", ans); }