Problem:
Score : 1100 points

Problem Statement

Given is a string S consisting of 0 and 1. Find the number of strings, modulo 998244353, that can result from applying the following operation on S zero or more times:

Remove the two characters at the beginning of S, erase one of them, and reinsert the other somewhere in S. This operation can be applied only when S has two or more characters.

Constraints

1 \leq |S| \leq 300

S consists of 0 and 1.

Input

Input is given from Standard Input in the following format:

S

Output

Print the number of strings, modulo 998244353, that can result from applying the operation on S zero or more times.

Sample Input 1

0001

Sample Output 1

8

Eight strings, 0001, 001, 010, 00, 01, 10, 0, and 1, can result.

Sample Input 2

110001

Sample Output 2

24

Sample Input 3

11101111011111000000000110000001111100011111000000001111111110000000111111111

Sample Output 3

697354558

Solution in Rust (1.42.0) (judge verdict: Accepted)

// ---------- begin ModInt ----------
mod modint {

    #[allow(dead_code)]
    pub struct Mod;
    impl ConstantModulo for Mod {
        const MOD: u32 = 998_244_353;
    }

    #[allow(dead_code)]
    pub struct StaticMod;
    static mut STATIC_MOD: u32 = 0;
    impl Modulo for StaticMod {
        fn modulo() -> u32 {
            unsafe { STATIC_MOD }
        }
    }

    #[allow(dead_code)]
    impl StaticMod {
        pub fn set_modulo(p: u32) {
            unsafe {
                STATIC_MOD = p;
            }
        }
    }

    use std::marker::*;
    use std::ops::*;

    pub trait Modulo {
        fn modulo() -> u32;
    }

    pub trait ConstantModulo {
        const MOD: u32;
    }

    impl<T> Modulo for T
    where
        T: ConstantModulo,
    {
        fn modulo() -> u32 {
            T::MOD
        }
    }

    pub struct ModInt<T>(pub u32, PhantomData<T>);

    impl<T> Clone for ModInt<T> {
        fn clone(&self) -> Self {
            ModInt::new_unchecked(self.0)
        }
    }

    impl<T> Copy for ModInt<T> {}

    impl<T: Modulo> Add for ModInt<T> {
        type Output = ModInt<T>;
        fn add(self, rhs: Self) -> Self::Output {
            let mut d = self.0 + rhs.0;
            if d >= T::modulo() {
                d -= T::modulo();
            }
            ModInt::new_unchecked(d)
        }
    }

    impl<T: Modulo> AddAssign for ModInt<T> {
        fn add_assign(&mut self, rhs: Self) {
            *self = *self + rhs;
        }
    }

    impl<T: Modulo> Sub for ModInt<T> {
        type Output = ModInt<T>;
        fn sub(self, rhs: Self) -> Self::Output {
            let mut d = T::modulo() + self.0 - rhs.0;
            if d >= T::modulo() {
                d -= T::modulo();
            }
            ModInt::new_unchecked(d)
        }
    }

    impl<T: Modulo> SubAssign for ModInt<T> {
        fn sub_assign(&mut self, rhs: Self) {
            *self = *self - rhs;
        }
    }

    impl<T: Modulo> Mul for ModInt<T> {
        type Output = ModInt<T>;
        fn mul(self, rhs: Self) -> Self::Output {
            let v = self.0 as u64 * rhs.0 as u64 % T::modulo() as u64;
            ModInt::new_unchecked(v as u32)
        }
    }

    impl<T: Modulo> MulAssign for ModInt<T> {
        fn mul_assign(&mut self, rhs: Self) {
            *self = *self * rhs;
        }
    }

    impl<T: Modulo> Neg for ModInt<T> {
        type Output = ModInt<T>;
        fn neg(self) -> Self::Output {
            if self.0 == 0 {
                Self::zero()
            } else {
                Self::new_unchecked(T::modulo() - self.0)
            }
        }
    }

    impl<T> std::fmt::Display for ModInt<T> {
        fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result {
            write!(f, "{}", self.0)
        }
    }

    impl<T: Modulo> std::str::FromStr for ModInt<T> {
        type Err = std::num::ParseIntError;
        fn from_str(s: &str) -> Result<Self, Self::Err> {
            let val = s.parse::<u32>()?;
            Ok(ModInt::new(val))
        }
    }

    impl<T: Modulo> From<usize> for ModInt<T> {
        fn from(val: usize) -> ModInt<T> {
            ModInt::new_unchecked((val % T::modulo() as usize) as u32)
        }
    }

    impl<T: Modulo> From<u64> for ModInt<T> {
        fn from(val: u64) -> ModInt<T> {
            ModInt::new_unchecked((val % T::modulo() as u64) as u32)
        }
    }

    impl<T: Modulo> From<i64> for ModInt<T> {
        fn from(val: i64) -> ModInt<T> {
            let m = T::modulo() as i64;
            ModInt::new((val % m + m) as u32)
        }
    }

    #[allow(dead_code)]
    impl<T> ModInt<T> {
        pub fn new_unchecked(d: u32) -> Self {
            ModInt(d, PhantomData)
        }
        pub fn zero() -> Self {
            ModInt::new_unchecked(0)
        }
        pub fn one() -> Self {
            ModInt::new_unchecked(1)
        }
        pub fn is_zero(&self) -> bool {
            self.0 == 0
        }
    }

    #[allow(dead_code)]
    impl<T: Modulo> ModInt<T> {
        pub fn new(d: u32) -> Self {
            ModInt::new_unchecked(d % T::modulo())
        }
        pub fn pow(&self, mut n: u64) -> Self {
            let mut t = Self::one();
            let mut s = *self;
            while n > 0 {
                if n & 1 == 1 {
                    t *= s;
                }
                s *= s;
                n >>= 1;
            }
            t
        }
        pub fn inv(&self) -> Self {
            assert!(self.0 != 0);
            self.pow(T::modulo() as u64 - 2)
        }
    }

    #[allow(dead_code)]
    pub fn mod_pow(r: u64, mut n: u64, m: u64) -> u64 {
        let mut t = 1 % m;
        let mut s = r % m;
        while n > 0 {
            if n & 1 == 1 {
                t = t * s % m;
            }
            s = s * s % m;
            n >>= 1;
        }
        t
    }
}
// ---------- end ModInt ----------

use proconio::*;
use proconio::marker::*;

use modint::*;

type M = ModInt<Mod>;

fn run() {
    input! {
        s: Bytes,
    }
    let s: Vec<usize> = s.into_iter().map(|c| (c - b'0') as usize).collect();
    let mut cnt = [0; 2];
    for c in s.iter() {
        cnt[*c] += 1;
    }
    let (a, b) = (cnt[0], cnt[1]);
    let len = s.len();
    let mut dp = vec![vec![vec![M::zero(); b + 1]; a + 1]; len + 1];
    dp[len][0][0] = M::one();
    for i in (0..=len).rev() {
        for j in 0..=a {
            for k in 0..=b {
                let v = dp[i][j][k];
                if v.is_zero() {
                    continue;
                }
                if i > 0 {
                    dp[i - 1][j][k] += v;
                }
                if k + 1 <= b && (i == 0 || s[i - 1] == 0) {
                    dp[i][j][k + 1] += v;
                }
                if j + 1 <= a && (i == 0 || s[i - 1] == 1) {
                    dp[i][j + 1][k] += v;
                }
            }
        }
    }
    let way = dp;
    let mut ok = vec![vec![vec![false; b + 1]; a + 1]; len + 1];
    ok[0][0][0] = true;
    let mut ans = M::zero();
    for i in 0..=len {
        for j in (0..=a).rev() {
            for k in (0..=b).rev() {
                if !ok[i][j][k] {
                    continue;
                }
                ans += way[i][j][k];
                if j + k >= 2 {
                    if j > 0 {
                        ok[i][j - 1][k] = true;
                    }
                    if k > 0 {
                        ok[i][j][k - 1] = true;
                    }
                }
                if j + k >= 1 && i + 1 <= len {
                    if j > 0 {
                        ok[i][j - 1][k] = true;
                    }
                    if k > 0 {
                        ok[i][j][k - 1] = true;
                    }
                    let mut cnt = [j, k];
                    cnt[s[i]] += 1;
                    if cnt[0] > 0 {
                        ok[i + 1][cnt[0] - 1][cnt[1]] = true;
                    }
                    if cnt[1] > 0 {
                        ok[i + 1][cnt[0]][cnt[1] - 1] = true;
                    }
                }
                if i + 2 <= len {
                    ok[i + 1][j][k] = true;
                    let mut cnt = [j, k];
                    cnt[s[i]] += 1;
                    cnt[s[i + 1]] += 1;
                    if s[i] == 0 || s[i + 1] == 0 {
                        ok[i + 2][cnt[0] - 1][cnt[1]] = true;
                    }
                    if s[i] == 1 || s[i + 1] == 1 {
                        ok[i + 2][cnt[0]][cnt[1] - 1] = true;
                    }
                }
            }
        }
    }
    println!("{}", ans);
}

fn main() {
    run();
}