#ifdef LOCAL
//#define _GLIBCXX_DEBUG
#endif

#include <bits/stdc++.h>

using namespace std;
using ll = long long;

const int mod = 998244353;

void add(int &a, int b)
{
	a += b;
	if (a >= mod)
		a -= mod;
}

void sub(int &a, int b)
{
	a -= b;
	if (a < 0)
		a += mod;
}

int mult(int a, int b)
{
	return ll(a) * b % mod;
}

vector<vector<vector<int>>> calc(const string &s)
{
	const int n = int(s.size());

	vector<vector<vector<int>>> ans(n + 1);
	for (int i = 0; i <= n; i++)
	{
		ans[i].resize(n - i + 1);
		for (int j = 0; j <= n - i; j++)
			ans[i][j].resize(n - i - j + 1);
	}

	const int N = 300;
	static int dp[N + 1][N + 1][N + 1][2];
	memset(dp, 0, sizeof dp);
	dp[0][0][0][0] = dp[0][0][0][1] = 1;

	for (int len = 0; len <= n; len++)
		for (int zero = 0; zero <= n - len; zero++)
			for (int one = 0; one <= n - len - zero; one++)
				for (int fin = 0; fin < 2; fin++)
				{
					const int cur = dp[len][zero][one][fin];

					if (fin == 1)
						add(ans[len][zero][one], cur);
					if (cur == 0 || len + zero + one >= n)
						continue;

					if (fin == 1)
					{
						add(dp[len][zero + 1][one][1], cur);
						add(dp[len][zero][one + 1][1], cur);
					}

					if (fin == 0)
					{
						add(dp[len + 1][zero][one][0], cur);
						add(dp[len + 1][zero][one][1], cur);

						if (s[len] == '0')
							add(dp[len][zero][one + 1][0], cur);
						else
							add(dp[len][zero + 1][one][0], cur);
					}
				}

	return ans;
}

void solve(istream &cin = std::cin, ostream &cout = std::cout)
{
	string s;

	while (cin >> s)
	{
		const int n = int(s.size());

		string rev_s = s;
		reverse(rev_s.begin(), rev_s.end());

		auto dp_ways = calc(rev_s);

		cerr << double(clock()) / CLOCKS_PER_SEC << endl;

		vector<vector<vector<bool>>> reach(n + 1, vector<vector<bool>>(n + 1, vector<bool>(n + 1)));
		reach[0][0][0] = true;


		for (int i = 0; i <= n; i++)
		{
			for (int j = n; j >= 0; j--)
				for (int k = n; k >= 0; k--)
					if (reach[i][j][k])
					{
						if (j >= 2)
							reach[i][j - 1][k] = true;
						if (k >= 2)
							reach[i][j][k - 1] = true;
						if (j >= 1 && k >= 1)
							reach[i][j][k - 1] = reach[i][j - 1][k] = true;
					}

			if (i + 1 <= n)
			{
				for (int j = 0; j <= n; j++)
					for (int k = 0; k <= n; k++)
						if (reach[i][j][k])
						{
							const int nj = j + (s[i] == '0'), nk = k + (s[i] == '1');

							if (nj > 0)
								reach[i + 1][nj - 1][nk] = true;
							if (nk > 0)
								reach[i + 1][nj][nk - 1] = true;
						}
			}

			if (i + 2 <= n)
			{
				for (int j = 0; j <= n; j++)
					for (int k = 0; k <= n; k++)
						if (reach[i][j][k])
						{
							for (int x = 0; x < 2; x++)
								if (s[i] == x + '0' || s[i + 1] == x + '0')
									(x == 0 ? reach[i + 2][j + 1][k] : reach[i + 2][j][k + 1]) = true;
						}
			}
		}

		int ans = 0;
		vector<int> cnt(2);
		vector<vector<bool>> used(n + 1, vector<bool>(n + 1, false));

		for (int suff = 0; suff <= n; suff++)
		{
			for (int zero = 0; zero <= n; zero++)
				for (int one = 0; one <= n; one++)
					if (reach[n - suff][zero][one])
					{
						if (!used[cnt[0] + zero][cnt[1] + one])
						{
							used[cnt[0] + zero][cnt[1] + one] = true;
							add(ans, dp_ways[suff][zero][one]);
						}
					}

			if (suff < n)
				cnt[rev_s[suff] - '0']++;
		}

		sub(ans, 1);
		cout << ans << endl;
	}
}

void gen (stringstream &cout)
{
	const int n = 300;

	static mt19937 rng;
	string ans(n, '-');
	for (auto &ch : ans)
		ch = rng() % 2 + '0';

	cout << ans << endl;
}

int main()
{
	ios_base::sync_with_stdio(false);
	cin.tie(nullptr);

#ifdef LOCAL
	auto st = clock();

//	stringstream test, out;
//	gen(test);
//	solve(test, out);

	ifstream fin("../input.txt");
	solve(fin);

	cout << "clock: " << (clock() - st) / (double) CLOCKS_PER_SEC << endl;
#else
	solve();
#endif

	return 0;
}
### Prompt

Please formulate a Cpp solution to the following problem:

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.

Examples

Input

0001


Output

8


Input

110001


Output

24


Input

11101111011111000000000110000001111100011111000000001111111110000000111111111


Output

697354558

### Response

```cpp
#ifdef LOCAL
//#define _GLIBCXX_DEBUG
#endif

#include <bits/stdc++.h>

using namespace std;
using ll = long long;

const int mod = 998244353;

void add(int &a, int b)
{
	a += b;
	if (a >= mod)
		a -= mod;
}

void sub(int &a, int b)
{
	a -= b;
	if (a < 0)
		a += mod;
}

int mult(int a, int b)
{
	return ll(a) * b % mod;
}

vector<vector<vector<int>>> calc(const string &s)
{
	const int n = int(s.size());

	vector<vector<vector<int>>> ans(n + 1);
	for (int i = 0; i <= n; i++)
	{
		ans[i].resize(n - i + 1);
		for (int j = 0; j <= n - i; j++)
			ans[i][j].resize(n - i - j + 1);
	}

	const int N = 300;
	static int dp[N + 1][N + 1][N + 1][2];
	memset(dp, 0, sizeof dp);
	dp[0][0][0][0] = dp[0][0][0][1] = 1;

	for (int len = 0; len <= n; len++)
		for (int zero = 0; zero <= n - len; zero++)
			for (int one = 0; one <= n - len - zero; one++)
				for (int fin = 0; fin < 2; fin++)
				{
					const int cur = dp[len][zero][one][fin];

					if (fin == 1)
						add(ans[len][zero][one], cur);
					if (cur == 0 || len + zero + one >= n)
						continue;

					if (fin == 1)
					{
						add(dp[len][zero + 1][one][1], cur);
						add(dp[len][zero][one + 1][1], cur);
					}

					if (fin == 0)
					{
						add(dp[len + 1][zero][one][0], cur);
						add(dp[len + 1][zero][one][1], cur);

						if (s[len] == '0')
							add(dp[len][zero][one + 1][0], cur);
						else
							add(dp[len][zero + 1][one][0], cur);
					}
				}

	return ans;
}

void solve(istream &cin = std::cin, ostream &cout = std::cout)
{
	string s;

	while (cin >> s)
	{
		const int n = int(s.size());

		string rev_s = s;
		reverse(rev_s.begin(), rev_s.end());

		auto dp_ways = calc(rev_s);

		cerr << double(clock()) / CLOCKS_PER_SEC << endl;

		vector<vector<vector<bool>>> reach(n + 1, vector<vector<bool>>(n + 1, vector<bool>(n + 1)));
		reach[0][0][0] = true;


		for (int i = 0; i <= n; i++)
		{
			for (int j = n; j >= 0; j--)
				for (int k = n; k >= 0; k--)
					if (reach[i][j][k])
					{
						if (j >= 2)
							reach[i][j - 1][k] = true;
						if (k >= 2)
							reach[i][j][k - 1] = true;
						if (j >= 1 && k >= 1)
							reach[i][j][k - 1] = reach[i][j - 1][k] = true;
					}

			if (i + 1 <= n)
			{
				for (int j = 0; j <= n; j++)
					for (int k = 0; k <= n; k++)
						if (reach[i][j][k])
						{
							const int nj = j + (s[i] == '0'), nk = k + (s[i] == '1');

							if (nj > 0)
								reach[i + 1][nj - 1][nk] = true;
							if (nk > 0)
								reach[i + 1][nj][nk - 1] = true;
						}
			}

			if (i + 2 <= n)
			{
				for (int j = 0; j <= n; j++)
					for (int k = 0; k <= n; k++)
						if (reach[i][j][k])
						{
							for (int x = 0; x < 2; x++)
								if (s[i] == x + '0' || s[i + 1] == x + '0')
									(x == 0 ? reach[i + 2][j + 1][k] : reach[i + 2][j][k + 1]) = true;
						}
			}
		}

		int ans = 0;
		vector<int> cnt(2);
		vector<vector<bool>> used(n + 1, vector<bool>(n + 1, false));

		for (int suff = 0; suff <= n; suff++)
		{
			for (int zero = 0; zero <= n; zero++)
				for (int one = 0; one <= n; one++)
					if (reach[n - suff][zero][one])
					{
						if (!used[cnt[0] + zero][cnt[1] + one])
						{
							used[cnt[0] + zero][cnt[1] + one] = true;
							add(ans, dp_ways[suff][zero][one]);
						}
					}

			if (suff < n)
				cnt[rev_s[suff] - '0']++;
		}

		sub(ans, 1);
		cout << ans << endl;
	}
}

void gen (stringstream &cout)
{
	const int n = 300;

	static mt19937 rng;
	string ans(n, '-');
	for (auto &ch : ans)
		ch = rng() % 2 + '0';

	cout << ans << endl;
}

int main()
{
	ios_base::sync_with_stdio(false);
	cin.tie(nullptr);

#ifdef LOCAL
	auto st = clock();

//	stringstream test, out;
//	gen(test);
//	solve(test, out);

	ifstream fin("../input.txt");
	solve(fin);

	cout << "clock: " << (clock() - st) / (double) CLOCKS_PER_SEC << endl;
#else
	solve();
#endif

	return 0;
}
```