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 C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>

int ri() {
	int n;
	scanf("%d", &n);
	return n;
}

template<int mod>
struct ModInt{
	int x;
	ModInt () : x(0) {}
	ModInt (int64_t x) : x(x >= 0 ? x % mod : (mod - -x % mod) % mod) {}
	ModInt &operator += (const ModInt &p){
		if ((x += p.x) >= mod) x -= mod;
		return *this;
	}
	ModInt &operator -= (const ModInt &p) {
		if ((x += mod - p.x) >= mod) x -= mod;
		return *this;
	}
	ModInt &operator *= (const ModInt &p) {
		x = (int64_t) x * p.x % mod;
		return *this;
	}
	ModInt &operator /= (const ModInt &p) {
		*this *= p.inverse();
		return *this;
	}
	ModInt &operator ^= (int64_t p) {
		ModInt res = 1;
		for (; p; p >>= 1) {
			if (p & 1) res *= *this;
			*this *= *this;
		}
		return *this = res;
	}
	ModInt operator - () const { return ModInt(-x); }
	ModInt operator + (const ModInt &p) const { return ModInt(*this) += p; }
	ModInt operator - (const ModInt &p) const { return ModInt(*this) -= p; }
	ModInt operator * (const ModInt &p) const { return ModInt(*this) *= p; }
	ModInt operator / (const ModInt &p) const { return ModInt(*this) /= p; }
	ModInt operator ^ (int64_t p) const { return ModInt(*this) ^= p; }
	bool operator == (const ModInt &p) const { return x == p.x; }
	bool operator != (const ModInt &p) const { return x != p.x; }
	explicit operator int() const { return x; }
	ModInt &operator = (const int p) { x = p; return *this;}
	ModInt inverse() const {
		int a = x, b = mod, u = 1, v = 0, t;
		while (b > 0) {
			t = a / b;
			a -= t * b;
			std::swap(a, b);
			u -= t * v;
			std::swap(u, v);
		}
		return ModInt(u);
	}
	friend std::ostream & operator << (std::ostream &stream, const ModInt<mod> &p) {
		return stream << p.x;
	}
	friend std::istream & operator >> (std::istream &stream, ModInt<mod> &a) {
		int64_t x;
		stream >> x;
		a = ModInt<mod>(x);
		return stream;
	}
};

template<int mod> struct MComb {
	using mint = ModInt<mod>;
	std::vector<mint> fact;
	std::vector<mint> inv;
	MComb (int n) { // O(n + log(mod))
		fact = std::vector<mint>(n + 1, 1);
		for (int i = 1; i <= n; i++) fact[i] = fact[i - 1] * mint(i);
		inv.resize(n + 1);
		inv[n] = fact[n] ^ (mod - 2);
		for (int i = n; i--; ) inv[i] = inv[i + 1] * mint(i + 1);
	}
	mint ncr(int n, int r) {
		return fact[n] * inv[r] * inv[n - r];
	}
	mint npr(int n, int r) {
		return fact[n] * inv[n - r];
	}
	mint nhr(int n, int r) {
		assert(n + r - 1 < (int) fact.size());
		return ncr(n + r - 1, r);
	}
};

typedef ModInt<998244353> mint;

int main() {
	std::string s;
	std::cin >> s;
	int n = s.size();
	std::vector<std::vector<int> > ok(n + 1, std::vector<int>(n + 1, -1)); // white, black : max start
	{
		std::vector<std::vector<std::vector<int> > > dp(n + 1, std::vector<std::vector<int> >(n + 1, std::vector<int>(n + 1, -1)));
		dp[0][0][0] = 0;
		for (int i = 0; i < n; i++) {
			for (int j = 0; j <= n; j++) {
				for (int k = 0; k <= n; k++) {
					if (dp[i][j][k] == -1) continue;
					
					auto go = [&] (int i, int j, int k, int val) {
						dp[i][j][k] = std::max(dp[i][j][k], val);
					};
					
					int stock = dp[i][j][k];
					// normal use
					if (i + 1 < n) go(i + 2, j + (s[i] == '0'), k + (s[i] == '1'), stock);
					if (i + 1 < n) go(i + 2, j + (s[i + 1] == '0'), k + (s[i + 1] == '1'), stock);
					// use stock
					if (stock) go(i + 1, j + (s[i] == '0'), k + (s[i] == '1'), stock - 1);
					// stock
					if (i + 1 < n) go(i + 2, j, k, stock + 1);
				}
			}
		}
		dp[n][0][0] = -1; // special
		/*
		for (int i = 0; i <= n; i++) {
			for (int j = 0; j <= n; j++) for (int k = 0; k <= n; k++) if (dp[i][j][k] != -1) {
				std::cerr << "at " << i << " w:" << j << " b:" << k << " " << std::endl;
			}
		}*/
		int sum[n + 1][2];
		memset(sum, 0, sizeof(sum));
		for (int i = 0; i < n; i++) sum[i + 1][s[i] - '0']++;
		for (int i = 0; i < n; i++) for (int j = 0; j < 2; j++) sum[i + 1][j] += sum[i][j];
		
		for (int i = 0; i <= n; i++) for (int j = 0; j <= n; j++) for (int k = 0; k <= n; k++) if (dp[i][j][k] != -1) {
			int white = j + sum[n][0] - sum[i][0];
			int black = k + sum[n][1] - sum[i][1];
			ok[white][black] = std::max(ok[white][black], i);
		}
	}
	
	std::reverse(s.begin(), s.end());
	mint dp[n + 1][n + 1][n + 1]; // pos, white, black
	dp[0][0][0] = 1;
	for (int i = 0; i <= n; i++) for (int j = 0; j <= n; j++) for (int k = 0; k <= n; k++) if (dp[i][j][k] != 0) {
		// white
		if (j < n) dp[i + (i < n && s[i] == '0')][j + 1][k] += dp[i][j][k];
		if (k < n) dp[i + (i < n && s[i] == '1')][j][k + 1] += dp[i][j][k];
	}
	
	mint res = 0;
	for (int i = 0; i <= n; i++) for (int j = 0; j <= n; j++) {
		if (ok[i][j] == -1) continue;
		int len = n - ok[i][j];
		// dp[len...][i][j]
		for (int k = len; k <= n; k++) res += dp[k][i][j];
	}
	std::cout << res << std::endl;
	return 0;
}