//Author:xht37
#include <bits/stdc++.h>

#define ui unsigned int
#define ll long long
#define ul unsigned ll
#define ld long double

#define pi pair <int, int>
#define fi first
#define se second
#define mp make_pair

#define ls (p << 1)
#define rs (ls | 1)
#define md ((t[p].l + t[p].r) >> 1)

#define vi vector <int>
#define pb push_back
#define pq priority_queue

#define dbg(x) cerr << #x" = " << x << endl
#define debug(...) fprintf(stderr, __VA_ARGS__)

#define fl(x) freopen(x".in", "r", stdin), freopen(x".out", "w", stdout)

using namespace std;

namespace io {
	const int SI = 1 << 21 | 1;
	char IB[SI], *IS, *IT, OB[SI], *OS = OB, *OT = OS + SI - 1, c, ch[100];
	int f, t;
	#define gc() (IS == IT ? (IT = (IS = IB) + fread(IB, 1, SI, stdin), IS == IT ? EOF : *IS++) : *IS++)
	inline void flush() {
		fwrite(OB, 1, OS - OB, stdout), OS = OB;
	}
	inline void pc(char x) {
		*OS++ = x;
		if (OS == OT) flush();
	}

	template <class I>
	inline void rd(I &x) {
		for (f = 1, c = gc(); c < '0' || c > '9'; c = gc()) if (c == '-') f = -1;
		for (x = 0; c >= '0' && c <= '9'; x = (x << 3) + (x << 1) + (c & 15), c = gc());
		x *= f;
	}
	template <class I>
	inline void rd(I &x, I &y) {
		rd(x), rd(y);
	}
	template <class I>
	inline void rd(I &x, I &y, I &z) {
		rd(x), rd(y), rd(z);
	}
	template <class I>
	inline void rda(I *a, int n) {
		for (int i = 1; i <= n; i++) rd(a[i]);
	}
	inline void rdc(char &c) {
		for (c = gc(); c < 33 || c > 126; c = gc());
	}
	inline void rds(char *s, int &n) {
		for (c = gc(); c < 33 || c > 126; c = gc());
		for (n = 0; c >= 33 && c <= 126; s[++n] = c, c = gc());
		s[n+1] = '\0';
	}
	inline void rds(string &s) {
		for (c = gc(); c < 33 || c > 126; c = gc());
		for (s.clear(); c >= 33 && c <= 126; s.pb(c), c = gc());
	}

	template <class I>
	inline void print(I x, char k = '\n') {
		if (!x) pc('0');
		if (x < 0) pc('-'), x = -x;
		while (x) ch[++t] = x % 10 + '0', x /= 10;
		while (t) pc(ch[t--]);
		pc(k);
	}
	template <class I>
	inline void print(I x, I y) {
		print(x, ' '), print(y);
	}
	template <class I>
	inline void print(I x, I y, I z) {
		print(x, ' '), print(y, ' '), print(z);
	}
	template <class I>
	inline void printa(I *a, int n) {
		for (int i = 1; i <= n; i++) print(a[i], " \n"[i==n]);
	}
	inline void printc(char c) {
		pc(c);
	}
	inline void prints(char *s, int n) {
		for (int i = 1; i <= n; i++) pc(s[i]);
		pc('\n');
	}
	inline void prints(string s) {
		int n = s.length();
		while (t < n) pc(s[t++]);
		pc('\n'), t = 0;
	}
	struct Flush {
		~Flush() {
			flush();
		}
	} flusher;
}
using io::rd;
using io::rda;
using io::rdc;
using io::rds;
using io::print;
using io::printa;
using io::printc;
using io::prints;

const int P = 998244353;

struct modint {
    int x;
    inline modint(int x = 0) : x(x) {}
    inline modint &operator = (int o) { return x = o, *this; }
    inline modint &operator += (modint o) { return (x += o.x) >= P && (x -= P), *this; }
    inline modint &operator -= (modint o) { return (x -= o.x) < 0 && (x += P), *this; }
    inline modint &operator *= (modint o) { return x = 1ll * x * o.x % P, *this; }
    template <class I>
    inline modint &operator ^= (I b) {
        modint a = *this, c;
        if (!~b) b = P - 2;
        c.x = 1 % P;
        while (b) {
            if (b & 1) c *= a;
            a *= a, b >>= 1;
        }
        return x = c.x, *this;
    }
    inline modint &operator /= (modint o) { return *this *= o ^ -1; }
    inline modint &operator += (int o) { return (x += o) >= P && (x -= P), *this; }
    inline modint &operator -= (int o) { return (x -= o) < 0 && (x += P), *this; }
    inline modint &operator *= (int o) { return x = 1ll * x * o % P, *this; }
    inline modint &operator /= (int o) { return *this *= (modint)o ^ -1; }
    template <class I>
    inline friend modint operator + (modint a, I b) { return a += b; }
    template <class I>
    inline friend modint operator - (modint a, I b) { return a -= b; }
    template <class I>
    inline friend modint operator * (modint a, I b) { return a *= b; }
    template <class I>
    inline friend modint operator ^ (modint a, I b) { return a ^= b; }
    template <class I>
    inline friend modint operator / (modint a, I b) { return a /= b; }
    inline friend bool operator == (modint a, int b) { return a.x == b; }
    inline friend bool operator != (modint a, int b) { return a.x != b; }
    inline friend bool operator < (modint a, int b) { return a.x < b; }
    inline friend bool operator <= (modint a, int b) { return a.x <= b; }
    inline friend bool operator > (modint a, int b) { return a.x > b; }
    inline friend bool operator >= (modint a, int b) { return a.x >= b; }
    inline friend bool operator == (modint a, modint b) { return a.x == b.x; }
    inline friend bool operator != (modint a, modint b) { return a.x != b.x; }
    inline friend bool operator < (modint a, modint b) { return a.x < b.x; }
    inline friend bool operator <= (modint a, modint b) { return a.x <= b.x; }
    inline friend bool operator > (modint a, modint b) { return a.x > b.x; }
    inline friend bool operator >= (modint a, modint b) { return a.x >= b.x; }
    inline bool operator ! () { return !x; }
    inline modint operator - () { return x ? P - x : 0; }
};
inline void rd(modint &x) { rd(x.x); }
inline void print(modint x, char k = '\n') { print(x.x, k); }

//const int NP = 1e6 + 7;
//modint p[NP], v[NP], vp[NP];
//inline void init(int n) {
//  p[0] = v[0] = 1;
//  for (int i = 1; i <= n; i++) p[i] = p[i-1] * i;
//  vp[n] = 1 / p[n];
//  for (int i = n; i; i--) v[i] = vp[i] * p[i-1], vp[i-1] = vp[i] * i;
//}
//inline modint binom(int n, int m) {
//  return (m < 0 || n < m) ? 0 : p[n] * vp[m] * vp[n-m];
//}

const int N = 307;
int n;
char s[N];
modint f[N][N][N], ans;
int g[N][N][N];
bool v[N][N][N];

inline void upd(int &x, int y) {
	x = max(x, y);
} 

int main() {
	rds(s, n);
	f[n][0][0] = 1;
	for (int i = n; i; i--)
		for (int j = 0; j < i; j++)
			for (int k = 0; j + k < i; k++) {
				f[i-1][j][k] += f[i][j][k];
				if (s[i] == '0') f[i][j][k+1] += f[i][j][k];
				else f[i][j+1][k] += f[i][j][k];
			}
	for (int i = 0; i <= n; i++)
		for (int j = 0; j <= n; j++)
			for (int k = 0; k <= n; k++)
				g[i][j][k] = -1;
	g[0][0][0] = 0;
	for (int i = 0; i < n; i++)
		for (int j = 0; j <= (i >> 1); j++)
			for (int k = 0; j + k <= (i >> 1); k++)
				if (~g[i][j][k]) {
					if (s[i+1] == '0') upd(g[i+1][j+1][k], g[i][j][k] - 1);
					else upd(g[i+1][j][k+1], g[i][j][k] - 1);
					if (i + 2 <= n) {
						upd(g[i+2][j][k], g[i][j][k] + 1);
						if (s[i+1] == '0' || s[i+2] == '0')
							upd(g[i+2][j+1][k], g[i][j][k]);
						if (s[i+1] == '1' || s[i+2] == '1')
							upd(g[i+2][j][k+1], g[i][j][k]);
					}
				}
	for (int i = 0; i <= n; i++)
		for (int j = n; ~j; j--)
			for (int k = n; ~k; k--) {
				v[i][j][k] = ~g[i][j][k];
				if (i) v[i][j][k] |= v[i-1][j][k];
				v[i][j][k] |= v[i][j+1][k];
				v[i][j][k] |= v[i][j][k+1];
			}
	for (int i = 0; i <= n; i++)
		for (int j = 0; j <= i; j++)
			for (int k = 0; j + k <= i; k++)
				if (v[i][j][k]) ans += f[i][j][k];
	print(ans - 1);
	return 0;
}
### Prompt

Construct a Cpp code solution to the problem outlined:

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
//Author:xht37
#include <bits/stdc++.h>

#define ui unsigned int
#define ll long long
#define ul unsigned ll
#define ld long double

#define pi pair <int, int>
#define fi first
#define se second
#define mp make_pair

#define ls (p << 1)
#define rs (ls | 1)
#define md ((t[p].l + t[p].r) >> 1)

#define vi vector <int>
#define pb push_back
#define pq priority_queue

#define dbg(x) cerr << #x" = " << x << endl
#define debug(...) fprintf(stderr, __VA_ARGS__)

#define fl(x) freopen(x".in", "r", stdin), freopen(x".out", "w", stdout)

using namespace std;

namespace io {
	const int SI = 1 << 21 | 1;
	char IB[SI], *IS, *IT, OB[SI], *OS = OB, *OT = OS + SI - 1, c, ch[100];
	int f, t;
	#define gc() (IS == IT ? (IT = (IS = IB) + fread(IB, 1, SI, stdin), IS == IT ? EOF : *IS++) : *IS++)
	inline void flush() {
		fwrite(OB, 1, OS - OB, stdout), OS = OB;
	}
	inline void pc(char x) {
		*OS++ = x;
		if (OS == OT) flush();
	}

	template <class I>
	inline void rd(I &x) {
		for (f = 1, c = gc(); c < '0' || c > '9'; c = gc()) if (c == '-') f = -1;
		for (x = 0; c >= '0' && c <= '9'; x = (x << 3) + (x << 1) + (c & 15), c = gc());
		x *= f;
	}
	template <class I>
	inline void rd(I &x, I &y) {
		rd(x), rd(y);
	}
	template <class I>
	inline void rd(I &x, I &y, I &z) {
		rd(x), rd(y), rd(z);
	}
	template <class I>
	inline void rda(I *a, int n) {
		for (int i = 1; i <= n; i++) rd(a[i]);
	}
	inline void rdc(char &c) {
		for (c = gc(); c < 33 || c > 126; c = gc());
	}
	inline void rds(char *s, int &n) {
		for (c = gc(); c < 33 || c > 126; c = gc());
		for (n = 0; c >= 33 && c <= 126; s[++n] = c, c = gc());
		s[n+1] = '\0';
	}
	inline void rds(string &s) {
		for (c = gc(); c < 33 || c > 126; c = gc());
		for (s.clear(); c >= 33 && c <= 126; s.pb(c), c = gc());
	}

	template <class I>
	inline void print(I x, char k = '\n') {
		if (!x) pc('0');
		if (x < 0) pc('-'), x = -x;
		while (x) ch[++t] = x % 10 + '0', x /= 10;
		while (t) pc(ch[t--]);
		pc(k);
	}
	template <class I>
	inline void print(I x, I y) {
		print(x, ' '), print(y);
	}
	template <class I>
	inline void print(I x, I y, I z) {
		print(x, ' '), print(y, ' '), print(z);
	}
	template <class I>
	inline void printa(I *a, int n) {
		for (int i = 1; i <= n; i++) print(a[i], " \n"[i==n]);
	}
	inline void printc(char c) {
		pc(c);
	}
	inline void prints(char *s, int n) {
		for (int i = 1; i <= n; i++) pc(s[i]);
		pc('\n');
	}
	inline void prints(string s) {
		int n = s.length();
		while (t < n) pc(s[t++]);
		pc('\n'), t = 0;
	}
	struct Flush {
		~Flush() {
			flush();
		}
	} flusher;
}
using io::rd;
using io::rda;
using io::rdc;
using io::rds;
using io::print;
using io::printa;
using io::printc;
using io::prints;

const int P = 998244353;

struct modint {
    int x;
    inline modint(int x = 0) : x(x) {}
    inline modint &operator = (int o) { return x = o, *this; }
    inline modint &operator += (modint o) { return (x += o.x) >= P && (x -= P), *this; }
    inline modint &operator -= (modint o) { return (x -= o.x) < 0 && (x += P), *this; }
    inline modint &operator *= (modint o) { return x = 1ll * x * o.x % P, *this; }
    template <class I>
    inline modint &operator ^= (I b) {
        modint a = *this, c;
        if (!~b) b = P - 2;
        c.x = 1 % P;
        while (b) {
            if (b & 1) c *= a;
            a *= a, b >>= 1;
        }
        return x = c.x, *this;
    }
    inline modint &operator /= (modint o) { return *this *= o ^ -1; }
    inline modint &operator += (int o) { return (x += o) >= P && (x -= P), *this; }
    inline modint &operator -= (int o) { return (x -= o) < 0 && (x += P), *this; }
    inline modint &operator *= (int o) { return x = 1ll * x * o % P, *this; }
    inline modint &operator /= (int o) { return *this *= (modint)o ^ -1; }
    template <class I>
    inline friend modint operator + (modint a, I b) { return a += b; }
    template <class I>
    inline friend modint operator - (modint a, I b) { return a -= b; }
    template <class I>
    inline friend modint operator * (modint a, I b) { return a *= b; }
    template <class I>
    inline friend modint operator ^ (modint a, I b) { return a ^= b; }
    template <class I>
    inline friend modint operator / (modint a, I b) { return a /= b; }
    inline friend bool operator == (modint a, int b) { return a.x == b; }
    inline friend bool operator != (modint a, int b) { return a.x != b; }
    inline friend bool operator < (modint a, int b) { return a.x < b; }
    inline friend bool operator <= (modint a, int b) { return a.x <= b; }
    inline friend bool operator > (modint a, int b) { return a.x > b; }
    inline friend bool operator >= (modint a, int b) { return a.x >= b; }
    inline friend bool operator == (modint a, modint b) { return a.x == b.x; }
    inline friend bool operator != (modint a, modint b) { return a.x != b.x; }
    inline friend bool operator < (modint a, modint b) { return a.x < b.x; }
    inline friend bool operator <= (modint a, modint b) { return a.x <= b.x; }
    inline friend bool operator > (modint a, modint b) { return a.x > b.x; }
    inline friend bool operator >= (modint a, modint b) { return a.x >= b.x; }
    inline bool operator ! () { return !x; }
    inline modint operator - () { return x ? P - x : 0; }
};
inline void rd(modint &x) { rd(x.x); }
inline void print(modint x, char k = '\n') { print(x.x, k); }

//const int NP = 1e6 + 7;
//modint p[NP], v[NP], vp[NP];
//inline void init(int n) {
//  p[0] = v[0] = 1;
//  for (int i = 1; i <= n; i++) p[i] = p[i-1] * i;
//  vp[n] = 1 / p[n];
//  for (int i = n; i; i--) v[i] = vp[i] * p[i-1], vp[i-1] = vp[i] * i;
//}
//inline modint binom(int n, int m) {
//  return (m < 0 || n < m) ? 0 : p[n] * vp[m] * vp[n-m];
//}

const int N = 307;
int n;
char s[N];
modint f[N][N][N], ans;
int g[N][N][N];
bool v[N][N][N];

inline void upd(int &x, int y) {
	x = max(x, y);
} 

int main() {
	rds(s, n);
	f[n][0][0] = 1;
	for (int i = n; i; i--)
		for (int j = 0; j < i; j++)
			for (int k = 0; j + k < i; k++) {
				f[i-1][j][k] += f[i][j][k];
				if (s[i] == '0') f[i][j][k+1] += f[i][j][k];
				else f[i][j+1][k] += f[i][j][k];
			}
	for (int i = 0; i <= n; i++)
		for (int j = 0; j <= n; j++)
			for (int k = 0; k <= n; k++)
				g[i][j][k] = -1;
	g[0][0][0] = 0;
	for (int i = 0; i < n; i++)
		for (int j = 0; j <= (i >> 1); j++)
			for (int k = 0; j + k <= (i >> 1); k++)
				if (~g[i][j][k]) {
					if (s[i+1] == '0') upd(g[i+1][j+1][k], g[i][j][k] - 1);
					else upd(g[i+1][j][k+1], g[i][j][k] - 1);
					if (i + 2 <= n) {
						upd(g[i+2][j][k], g[i][j][k] + 1);
						if (s[i+1] == '0' || s[i+2] == '0')
							upd(g[i+2][j+1][k], g[i][j][k]);
						if (s[i+1] == '1' || s[i+2] == '1')
							upd(g[i+2][j][k+1], g[i][j][k]);
					}
				}
	for (int i = 0; i <= n; i++)
		for (int j = n; ~j; j--)
			for (int k = n; ~k; k--) {
				v[i][j][k] = ~g[i][j][k];
				if (i) v[i][j][k] |= v[i-1][j][k];
				v[i][j][k] |= v[i][j+1][k];
				v[i][j][k] |= v[i][j][k+1];
			}
	for (int i = 0; i <= n; i++)
		for (int j = 0; j <= i; j++)
			for (int k = 0; j + k <= i; k++)
				if (v[i][j][k]) ans += f[i][j][k];
	print(ans - 1);
	return 0;
}
```