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++ (Clang 10.0.0) (judge verdict: Time Limit Exceeded)

/*
                                                                                                     
                                             `-:://:::-                                             
                                           `//:-------:/:`                                          
                                          .+:--.......--:+`                                         
                                         `+:--..`````..--//`                                        
                                         .o:--..`` ``..--:o`                                        
                                         .o:--...```..---+/`                                        
                                       `/y+o/---....---:+o.                                         
                                   `...````-os+/:---:/+o/--.`                                       
              `-/+++++/:.      `...`       :h+d+oooo+/+-`   ...                                     
            `/++//:::://++-`....`         -.`//````````:`     `..`                                  
           `o+/::------://o/`           `-` -.          -`       `..`                               
 `---.-o/:./o/::-..``..-ЗАПУСКАЕМ      ..  ..            -`        `...       ``..``                
  `....o+:-++/:--.```..-://s.        `-`  .-              -`          `-o: .-//::::/:-`             
          `:s+/:--....-::/+s-`      .-   `-                -`           -///:--------:/:`           
           ./s+//:::::://oo-``..НЕЙРОННУЮ: СЕТЬ:::::::-`РАБОТЯГИ        `+:--........--:/`          
            .:ooo+++++osso-`    `.:-...`/` ./::-------:/:`   -`         :+--..``````.--:+:...-+:-`  
             `.-/+++++/+-.-`    -.   ``:so:/:--.......--:+`  `-```````o+/+--..`````..--:o/-..:s+:.  
                 ```````:``.. `-`     -` `+:--..`````..--/+-.../.`````..-o:--.......---/o.    `     
                        `:  `:-      -.  .o:--..`` ``..--:o`   `-`      `:o+:--------:+o-`          
                         `-`-...    ..   .o/--...```..--:+/`    `-`     `oy/so/////++o/.`           
                          -/`  `-` `- ``+s/o/:---...---:++.      `-`   .-../d://///:-.`             
                `.---..``-..-    .-/..`````-oo+/:::::/+o+-        `-``-`  `-.  ````                 
             `:++++/+++++-  ..``.-/:`      /y-:/++o++/:.`..`       ./.   `-                         
            -++/::::::://+/..:-``:` ..   `-.`  ```.```    `..`   `..`-` `-                          
       ``  -o//:--....-::/++` -.-`   `-`.-`                 `..`..`  `-.-                           
  -----ss+:++/:--.```..-://s.  /.     `::                    `-:.     ./`                           
  `````/:..+o/::-..``.--:/+s. ..-`   `-``-`                 ..` `-`  `-`-`                          
          `-s+/::-----::/+oo---``-` ..    .:-    ```      .-`     .-.-  `-`                         
           `:oo+//::://+os/..:`..-/:`      :y.-:::::::.`.-`        ./-`  `-`                        
            `./+oooooooo+/.`-    .-:...`.. .//:-------://`        `- `..` `:.                       
              ``.-::::-.``-/`  `-` `-  `oo:+:--.......--:/`      `-    `.:--h.``..```               
                          -.-`.-    .-   `+:--..`````..--//`    `-       /s-//::::::::.             
                         -` `/-      ..  .o:--..`` ``..--:o.```.-        `//:--------://`           
                        -` .-`.-`     -.`-o/--...```..--:+/.``-:....``:-.+:--....`...--:+`          
                       ..`-.   `-.   ``:os:o/:---...---:++.  `-     ``///+:-..``````.--:+-````-.`   
              `.:///////.-`      .:-..` -``-+o+/:::::/+o/.  `-         `:+:-..`````..--:o/:--/ys+-  
            `-++///////+o/. ``....`-.    :` `.:++++++/:.`  .-           -o/---......---/o.   `.`    
           `++//:-----::/+o:..`     .-`   :    ```````    .-           `+so+:--------:++-`          
  `````:-``:o/::-..`..--:/+o`         -.  `-             .-          `../../+o+////+o+:.`           
  -----syo/o+/:--.```..-://s.          .-` `-           .-        `...     ``-:////:-``             
       .` `/s//:--....-::/+s.            -. `-`        .-       `..`                                
           .+o+/:::--:://+s/-..`          .::+y  ```  .-     `..`                                   
            ./oo++////+oso-`   `....       :y-+:::::::/`   ...                                      
             `.:+oooooo/-`         `....-. .//:-------:/:-.`                                        
                ``...``                 /+:+:--.......--:+`                                         
                                         `+:--..`````..--//`                                        
                                         .o:--..`` ``..--:o`                                        
                                         .+/--...```..--:+/`                                        
                                         `-o/:---...---:++.                                         
                                          `-+o+/:---:/+o/.                                          
                                            `.:+oooo+/-.`                                           
                                               ``````                                               
*/

#ifdef aimbot
#pragma GCC optimize("Ofast")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,avx,avx2")
#include <immintrin.h>
#endif

#define hur(f, g) template<class c> int f(c a) {if (sizeof(c) == 8) return g##ll(a); else return g(a);}
hur(popc, __builtin_popcount) hur(ctz, __builtin_ctz) hur(clz, __builtin_clz)

/*
	- place bitset modifications here
*/

#include <iostream>
#include <vector>
#include <algorithm>
#include <cmath>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <map>
#include <set>
#include <queue>
#include <ostream>
#include <istream>
#include <typeinfo>
#include <iomanip>
#include <cstdio>
#include <cstdlib>
#include <cassert>
#include <limits>
#include <fstream>
#include <array>
#include <list>
#include <bitset>
#include <functional>
#include <random>
#include <cstring>
#include <chrono>

#define random escape__from__random__aetuhoetnuhshe
#define mt make_tuple
#define x first
#define y second
#define pb push_back
#define mp make_pair
#define le(v) ((int)v.size())
#define f(i, n) for (int i = 0; i < (n); i++)
#define rof(i, n) for (int i = ((n) - 1); i >= 0; i--)
#define apply(v, act) for (auto &x : v) { act; }
#define log(args...) {string s = #args;deque<string> deq;\
string buf = "";int bal = 0;for (char c : s) {\
if (c == '(' || c == '[' || c == '{') {bal++;\
} else if (c == ')' || c == ']' || c == '}') {\
bal--;} else {if (bal == 0) {if (c == ',') {\
deq.pb(buf);buf = "";} else {if (c != ' ') {\
buf += c;}}}}}if (!buf.empty()) {deq.pb(buf);}\
smart_io::precall_print();smart_io::_print(deq, args);}

inline int min(const int &x, const int &y) { return (((y-x)>>(32-1))&(x^y))^x; }
inline int max(const int &x, const int &y) { return (((y-x)>>(32-1))&(x^y))^y; }
inline long long min(const long long &x, const long long &y) { return (((y-x)>>(64-1))&(x^y))^x; }
inline long long max(const long long &x, const long long &y) { return (((y-x)>>(64-1))&(x^y))^y; }

#define print    \
smart_io::precall_print(); \
cout,

#define scan cin,

#ifdef fast_allocator
const int MAXMEM = 200 * 1000 * 1024;
char _memory[MAXMEM];
size_t _ptr = 0;
void* operator new(size_t _x) { _ptr += _x; assert(_ptr < MAXMEM); return _memory + _ptr - _x; }
void operator delete (void*) noexcept {}
#endif

using namespace std;

char string_in_buffer[(int)2e6];


void fast_scan(int &x) { scanf("%d", &x); }
void fast_scan(long long &x) { scanf("%lld", &x); }
void fast_scan(unsigned long long &x) { scanf("%llu", &x); }
void fast_scan(double &x) { scanf("%lf", &x); }
void fast_scan(long double &x) { scanf("%Lf", &x); }
void fast_scan(char &x) {
	scanf("%c", &x);
	if (x == '\n') {
		fast_scan(x);
	}
}
void fast_scan(string &x) {
	scanf("%s", string_in_buffer);
	x = string(string_in_buffer);
}

template<class TFirst, class TSecond>
void fast_scan(pair<TFirst, TSecond> &p) {
	fast_scan(p.first);
	fast_scan(p.second);
}

template <class T>
void fast_scan(vector<T> &v) {
	for (auto &x : v) fast_scan(x);
}

void fast_print(const int &x) { printf("%d", x); }
void fast_print(const unsigned int &x) { printf("%u", x); }
void fast_print(const long long &x) { printf("%lld", x); }
void fast_print(const unsigned long long &x) { printf("%llu", x); }
void fast_print(const char &x) { printf("%c", x); };
// void fast_print(__int128 x) {
// 	if (x == 0) { fast_print('0'); return; }
// 	if (x < 0) {
// 		fast_print('-');
// 		x = -x;
// 	}
// 	__int128 p = 1;
// 	while (x / (p * 10)) p *= 10;
// 	while (p) {
// 		__int128 symb = x / p;
// 		fast_print((int)symb);
// 		x -= p * symb;
// 		p /= 10;
// 	}
// };
void fast_print(const double &x) { printf("%.15lf", x); }
void fast_print(const long double &x) { printf("%.15Lf", x); }
void fast_print(const string &x) { printf("%s", x.c_str());}
void fast_print(const char v[]) { fast_print((string)v); }

template<class TFirst, class TSecond>
void fast_print(const pair<TFirst, TSecond> &p) {
	fast_print(p.first);
	fast_print(' ');
	fast_print(p.second);
}

template <class T>
void fast_print(const vector<T> &v) {
	if (v.empty()) return;
	fast_print(v[0]);
	for (int i = 1; i < v.size(); i++) {
		fast_print(' ');
		fast_print(v[i]);
	}
}

template <class T>
void fast_print(const vector<vector<T>> &v) {
	if (v.empty()) return;
	fast_print(v[0]);
	for (int i = 1; i < v.size(); i++) {
		fast_print('\n');
		fast_print(v[i]);
	}
}

template <class T>
void fast_print(const T &v) {
	for (const auto &x : v) {
		fast_print(x);
		fast_print(' ');
	}
}


using namespace std;


namespace smart_io {
	string print_start = "";
	string sep = " ";
	bool first_print = false;
	
	void precall_print() {
		fast_print(print_start);
		print_start = "\n";
		first_print = true;
	}
	
	void _print(deque<string>) {}
	template<class T, class... Args>
	void _print(deque<string> names, T elem, Args... args) {
		if (!first_print) {
			fast_print("\n");
		} else {
			first_print = false;
		}
		fast_print(names.front());
		fast_print(" = ");
		fast_print(elem);
		names.pop_front();
		_print(names, args...);
	}
} //namespace smart_io


template <class T>
ostream &operator,(ostream &os, const T &object) {
	if (!smart_io::first_print) {
		fast_print(smart_io::sep);
	} else {
		smart_io::first_print = false;
	}
	fast_print(object);
	return os;
}

template <class T>
istream &operator,(istream &is, T &object) {
	fast_scan(object);
	return is;
}

namespace random {
	using namespace std::chrono;
	mt19937 rng(duration_cast< milliseconds >(
											  system_clock::now().time_since_epoch()
											  ).count());
	uniform_real_distribution<> prob_dist(0.0, 1.0);
};

namespace typedefs {
	typedef long long ll;
	typedef unsigned long long ull;
	typedef pair<int, int> pii;
	typedef long double ld;
}

namespace numbers_operation {
	template<class T>
	inline T floor_mod(T a, const T &b) {
		a %= b;	
		if (a < 0) a += b;
		return a;
	}
}

using namespace numbers_operation;
using namespace typedefs;
using namespace random;

// const ll MOD = 1e9 + 7;
const ll MOD = 998244353;
template<ll MOD>
struct Ring {
	ll value = 0;
	Ring() {}
	Ring(int _value) {
		value = _value;
		value = floor_mod(value, MOD);
	}
	Ring(ll _value) {
		value = _value;
		value = floor_mod(value, MOD);
	}
	Ring pow(ll p) const {
		Ring r = 1;
		Ring x; x.value = value;
		while (p) {
			if (p & 1) r *= x;
			x *= x;
			p /= 2;
		}
		return r;
	}
	Ring inv() const {
		return pow(MOD - 2);
	}
	void operator*=(const Ring<MOD> &b) {
		value *= b.value;
		value = floor_mod(value, MOD);
	}
	friend Ring operator*(Ring<MOD> a, const Ring<MOD> &b) {
		a *= b;
		return a;
	}
	void operator+=(const Ring<MOD> &b) {
		value += b.value;
		value -= (value >= MOD) * MOD;
	}
	friend Ring operator+(Ring a, const Ring &b) {
		a += b;
		return a;
	}
	void operator-=(const Ring<MOD> &b) {
		value -= b.value;
		value += (value < 0) ? MOD : 0;
	}
	friend Ring operator-(Ring a, const Ring &b) {
		a -= b;
		return a;
	}
	void operator/=(const Ring<MOD> &b) {
		(*this) *= b.inv();	
	}
	friend Ring operator/(Ring a, const Ring &b) {
		a /= b;
		return a;
	}
	bool operator==(const Ring<MOD> &b) {
		return value == b.value;
	}
	bool operator!=(const Ring<MOD> &b) {
		return value != b.value;
	}
	friend void fast_print(const Ring<MOD> &b) {
		fast_print(b.value);
	}
};

typedef Ring<MOD> num;

string s;

vector<string> perform(string s, int steps) {
	vector<string> v{s};	
	f(i, steps) {
		vector<string> u;
		for (string s : v) {
			char a = s[0]; char b = s[1];
			s.erase(s.begin());
			s.erase(s.begin());
			for (char c : {a, b}) {
				for (int i = 0; i <= le(s); i++) {
					string t = s;
					t.insert(t.begin() + i, c);
					u.pb(t);
				}
			}
		}
		sort(u.begin(), u.end());
		u.resize(unique(u.begin(), u.end()) - u.begin());
		v = u;
	}
	return v;
}

vector<string> perform2(string s, int steps) {
	vector<string> v{s};
	int adj = steps * 2;
	f(i, steps) {
		vector<string> u;
		for (string s : v) {
			char a = s[0]; char b = s[1];
			s.erase(s.begin());
			s.erase(s.begin());
			for (char c : {a, b}) {
				for (int i = adj - 1; i <= le(s); i++) {
					string t = s;
					t.insert(t.begin() + i, c);
					u.pb(t);
				}
			}
		}
		sort(u.begin(), u.end());
		u.resize(unique(u.begin(), u.end()) - u.begin());
		v = u;
		adj -= 2;
	}
	return v;
}

// vector<string> perform2(string s, int steps) {
// 	for (int i = 0; i < steps; i += 2) {

// 	}
// }
const int N = 310;
int mem[2 * N][2 * N];
num binom(int n, int k) {
	if (k > n) return 0;
	if (n == 0 || k == 0) return 1;
	if (mem[n][k] != -1) return mem[n][k];
	mem[n][k] = (binom(n - 1, k - 1) + binom(n - 1, k)).value;
	return mem[n][k];
}

int mem2[N][N][N];
num dp(int i, int a, int b) {
	if (a < 0 || b < 0) return 0;
	if (i >= le(s)) return binom(a + b, b);
	if (mem2[i][a][b] != -1) return mem2[i][a][b];
	num rez = 0;
	// place 0
	{
		if (s[i] == '0') {
			rez += dp(i + 1, a, b);
		} else rez += dp(i, a - 1, b);
	}
	// place 1
	{
		if (s[i] == '1') {
			rez += dp(i + 1, a, b);
		} else {
			rez += dp(i, a, b - 1);
		}
	}
	mem2[i][a][b] = rez.value;
	return rez;
}

int mem3[N][N][N];
bool obt(int i, vector<int> c) {
	if (c[0] < 0 || c[1] < 0) return false;
	if (i < 0) return c == vector<int>{0, 0};
	if (mem3[i][c[0]][c[1]] != -1) return mem3[i][c[0]][c[1]];
	if (i - 1 >= 0) {
		// rem i - 1
		{
			vector<int> nc = c;
			nc[s[i] - '0']--;
			if (obt(i - 2, nc)) return mem3[i][c[0]][c[1]] = true;
		}
		{
			vector<int> nc = c;
			nc[s[i - 1] - '0']--;
			if (obt(i - 2, nc)) return mem3[i][c[0]][c[1]] = true;
		}
	}
	f(in, 2) {
		{
			vector<int> nc = c;
			nc[s[i] - '0']--;
			nc[in]++;
			if (obt(i - 1, nc)) return mem3[i][c[0]][c[1]] = true;
		}
		{
			vector<int> nc = c;
			// nc[s[i] - '0']++;
			// nc[in]--;
			if (obt(i - 1, nc)) return mem3[i][c[0]][c[1]] = true;
		}
	}
	return mem3[i][c[0]][c[1]] = false;
}


signed main(signed argc, char *argv[]) {
	memset(mem, -1, sizeof mem);
	memset(mem2, -1, sizeof mem2);
	memset(mem3, -1, sizeof mem3);
	scan s;
	num rez = 0;
	for (int a = 0; a <= le(s); a++) {
		for (int b = 0; a + b <= le(s); b++) {
			if (a + b == 0) continue;
			int c = a; int d = b;
			for (int i = le(s); i >= 0; i--) {
				if (i < le(s)) {
					if (s[i] == '0') c--;
					else d--;
				}
				if (obt(i - 1, {c, d})) {
					// print i, c, d;
					rez += dp(i, c, d);
					break;
				}
			}
		}
	}
	print rez;
}