#include <bits/stdc++.h>
using namespace std;

using ll = long long;
using pii = pair<int, int>;
template <class T>
using V = vector<T>;
template <class T>
using VV = V<V<T>>;

#define pb push_back
#define eb emplace_back
#define mp make_pair
#define fi first
#define se second
#define rep(i, n) rep2(i, 0, n)
#define rep2(i, m, n) for (int i = m; i < (n); i++)
#define per(i, b) per2(i, 0, b)
#define per2(i, a, b) for (int i = int(b) - 1; i >= int(a); i--)
#define ALL(c) (c).begin(), (c).end()
#define SZ(x) ((int)(x).size())

constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n - 1); }

template <class T, class U>
void chmin(T& t, const U& u) {
    if (t > u) t = u;
}
template <class T, class U>
void chmax(T& t, const U& u) {
    if (t < u) t = u;
}

template <class T, class U>
ostream& operator<<(ostream& os, const pair<T, U>& p) {
    os << "(" << p.first << "," << p.second << ")";
    return os;
}

template <class T>
ostream& operator<<(ostream& os, const vector<T>& v) {
    os << "{";
    rep(i, v.size()) {
        if (i) os << ",";
        os << v[i];
    }
    os << "}";
    return os;
}

#ifdef LOCAL
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
    cerr << " " << H;
    debug_out(T...);
}
#define debug(...) \
    cerr << __LINE__ << " [" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#define dump(x) cerr << __LINE__ << " " << #x << " = " << (x) << endl
#else
#define debug(...) (void(0))
#define dump(x) (void(0))
#endif

template <unsigned int MOD>
struct ModInt {
    using uint = unsigned int;
    using ull = unsigned long long;
    using M = ModInt;

    uint v;

    ModInt(ll _v = 0) { set_norm(_v % MOD + MOD); }
    M& set_norm(uint _v) {  //[0, MOD * 2)->[0, MOD)
        v = (_v < MOD) ? _v : _v - MOD;
        return *this;
    }

    explicit operator bool() const { return v != 0; }
    M operator+(const M& a) const { return M().set_norm(v + a.v); }
    M operator-(const M& a) const { return M().set_norm(v + MOD - a.v); }
    M operator*(const M& a) const { return M().set_norm(ull(v) * a.v % MOD); }
    M operator/(const M& a) const { return *this * a.inv(); }
    M& operator+=(const M& a) { return *this = *this + a; }
    M& operator-=(const M& a) { return *this = *this - a; }
    M& operator*=(const M& a) { return *this = *this * a; }
    M& operator/=(const M& a) { return *this = *this / a; }
    M operator-() const { return M() - *this; }
    M& operator++(int) { return *this = *this + 1; }
    M& operator--(int) { return *this = *this - 1; }

    M pow(ll n) const {
        if (n < 0) return inv().pow(-n);
        M x = *this, res = 1;
        while (n) {
            if (n & 1) res *= x;
            x *= x;
            n >>= 1;
        }
        return res;
    }

    M inv() const {
        ll a = v, b = MOD, p = 1, q = 0, t;
        while (b != 0) {
            t = a / b;
            swap(a -= t * b, b);
            swap(p -= t * q, q);
        }
        return M(p);
    }

    bool operator==(const M& a) const { return v == a.v; }
    bool operator!=(const M& a) const { return v != a.v; }
    friend ostream& operator<<(ostream& os, const M& a) { return os << a.v; }
    static uint get_mod() { return MOD; }
};

using Mint = ModInt<998244353>;

bool sub[310][310][310];
Mint dp[310][310][310];
Mint comb[310][310];

int main() {
    rep(i, 310) {
        comb[i][0] = comb[i][i] = 1;
        for (int j = 1; j < i; ++j) {
            comb[i][j] = comb[i - 1][j] + comb[i - 1][j - 1];
        }
    }

    string S;
    cin >> S;

    int n = S.size();
    sub[0][0][0] = 1;

    rep(i, n) {
        rep(j, i + 1) {
            rep(k, i + 1 - j) {
                if (sub[i][j][k]) {
                    if (S[i] == '0') {
                        if (k) {
                            sub[i + 1][j + 1][k - 1] = 1;
                            sub[i + 1][j][k] = 1;
                        }
                        if (j) {
                            sub[i + 1][j][k] = 1;
                        }
                    } else {
                        if (j) {
                            sub[i + 1][j - 1][k + 1] = 1;
                            sub[i + 1][j][k] = 1;
                        }
                        if (k) {
                            sub[i + 1][j][k] = 1;
                        }
                    }

                    if (i + 2 <= n) {
                        int p = S[i] - '0', q = S[i + 1] - '0';
                        if (p > q) swap(p, q);
                        if (q == 0) {
                            sub[i + 2][j + 1][k] = 1;
                        } else if (p == 1) {
                            sub[i + 2][j][k + 1] = 1;
                        } else {
                            sub[i + 2][j + 1][k] = sub[i + 2][j][k + 1] = 1;
                        }
                    }
                }
            }
        }

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

    rep(i, n + 1) {
        rep(j, n + 1) {
            rep(k, n + 1) {
                if (sub[i][j][k]) {
                    // debug(i, j, k);
                }
            }
        }
    }

    // use S[i,n)
    rep(j, n + 1) {
        rep(k, n + 1 - j) { dp[n][j][k] = comb[j + k][j]; }
    }

    for (int i = n - 1; i >= 0; --i) {
        int c = S[i] - '0';
        rep(j, n + 1) {
            rep(k, n + 1 - j) {
                if (c == 0) {
                    for (int p = 0; p <= k; ++p) {
                        dp[i][j][k] += dp[i + 1][j][k - p];
                    }
                } else {
                    for (int q = 0; q <= j; ++q) {
                        dp[i][j][k] += dp[i + 1][j - q][k];
                    }
                }
            }
        }
    }

    Mint ans;
    rep(i, n + 1) {
        rep(j, n + 1) {
            rep(k, n + 1 - j) {
                if (sub[i][j][k]) {
                    Mint u = dp[i][j][k];
                    int nj = j, nk = k;
                    if (i > 0) {
                        if (S[i - 1] == '0') {
                            --nj;
                        } else {
                            --nk;
                        }

                        if (nj >= 0 && nk >= 0 && sub[i - 1][nj][nk]) {
                            u -= dp[i - 1][nj][nk];
                        }
                    }
                    ans += u;
                }
            }
        }
    }
    cout << ans << endl;

    return 0;
}
### Prompt

Your task is to create 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
#include <bits/stdc++.h>
using namespace std;

using ll = long long;
using pii = pair<int, int>;
template <class T>
using V = vector<T>;
template <class T>
using VV = V<V<T>>;

#define pb push_back
#define eb emplace_back
#define mp make_pair
#define fi first
#define se second
#define rep(i, n) rep2(i, 0, n)
#define rep2(i, m, n) for (int i = m; i < (n); i++)
#define per(i, b) per2(i, 0, b)
#define per2(i, a, b) for (int i = int(b) - 1; i >= int(a); i--)
#define ALL(c) (c).begin(), (c).end()
#define SZ(x) ((int)(x).size())

constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n - 1); }

template <class T, class U>
void chmin(T& t, const U& u) {
    if (t > u) t = u;
}
template <class T, class U>
void chmax(T& t, const U& u) {
    if (t < u) t = u;
}

template <class T, class U>
ostream& operator<<(ostream& os, const pair<T, U>& p) {
    os << "(" << p.first << "," << p.second << ")";
    return os;
}

template <class T>
ostream& operator<<(ostream& os, const vector<T>& v) {
    os << "{";
    rep(i, v.size()) {
        if (i) os << ",";
        os << v[i];
    }
    os << "}";
    return os;
}

#ifdef LOCAL
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
    cerr << " " << H;
    debug_out(T...);
}
#define debug(...) \
    cerr << __LINE__ << " [" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#define dump(x) cerr << __LINE__ << " " << #x << " = " << (x) << endl
#else
#define debug(...) (void(0))
#define dump(x) (void(0))
#endif

template <unsigned int MOD>
struct ModInt {
    using uint = unsigned int;
    using ull = unsigned long long;
    using M = ModInt;

    uint v;

    ModInt(ll _v = 0) { set_norm(_v % MOD + MOD); }
    M& set_norm(uint _v) {  //[0, MOD * 2)->[0, MOD)
        v = (_v < MOD) ? _v : _v - MOD;
        return *this;
    }

    explicit operator bool() const { return v != 0; }
    M operator+(const M& a) const { return M().set_norm(v + a.v); }
    M operator-(const M& a) const { return M().set_norm(v + MOD - a.v); }
    M operator*(const M& a) const { return M().set_norm(ull(v) * a.v % MOD); }
    M operator/(const M& a) const { return *this * a.inv(); }
    M& operator+=(const M& a) { return *this = *this + a; }
    M& operator-=(const M& a) { return *this = *this - a; }
    M& operator*=(const M& a) { return *this = *this * a; }
    M& operator/=(const M& a) { return *this = *this / a; }
    M operator-() const { return M() - *this; }
    M& operator++(int) { return *this = *this + 1; }
    M& operator--(int) { return *this = *this - 1; }

    M pow(ll n) const {
        if (n < 0) return inv().pow(-n);
        M x = *this, res = 1;
        while (n) {
            if (n & 1) res *= x;
            x *= x;
            n >>= 1;
        }
        return res;
    }

    M inv() const {
        ll a = v, b = MOD, p = 1, q = 0, t;
        while (b != 0) {
            t = a / b;
            swap(a -= t * b, b);
            swap(p -= t * q, q);
        }
        return M(p);
    }

    bool operator==(const M& a) const { return v == a.v; }
    bool operator!=(const M& a) const { return v != a.v; }
    friend ostream& operator<<(ostream& os, const M& a) { return os << a.v; }
    static uint get_mod() { return MOD; }
};

using Mint = ModInt<998244353>;

bool sub[310][310][310];
Mint dp[310][310][310];
Mint comb[310][310];

int main() {
    rep(i, 310) {
        comb[i][0] = comb[i][i] = 1;
        for (int j = 1; j < i; ++j) {
            comb[i][j] = comb[i - 1][j] + comb[i - 1][j - 1];
        }
    }

    string S;
    cin >> S;

    int n = S.size();
    sub[0][0][0] = 1;

    rep(i, n) {
        rep(j, i + 1) {
            rep(k, i + 1 - j) {
                if (sub[i][j][k]) {
                    if (S[i] == '0') {
                        if (k) {
                            sub[i + 1][j + 1][k - 1] = 1;
                            sub[i + 1][j][k] = 1;
                        }
                        if (j) {
                            sub[i + 1][j][k] = 1;
                        }
                    } else {
                        if (j) {
                            sub[i + 1][j - 1][k + 1] = 1;
                            sub[i + 1][j][k] = 1;
                        }
                        if (k) {
                            sub[i + 1][j][k] = 1;
                        }
                    }

                    if (i + 2 <= n) {
                        int p = S[i] - '0', q = S[i + 1] - '0';
                        if (p > q) swap(p, q);
                        if (q == 0) {
                            sub[i + 2][j + 1][k] = 1;
                        } else if (p == 1) {
                            sub[i + 2][j][k + 1] = 1;
                        } else {
                            sub[i + 2][j + 1][k] = sub[i + 2][j][k + 1] = 1;
                        }
                    }
                }
            }
        }

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

    rep(i, n + 1) {
        rep(j, n + 1) {
            rep(k, n + 1) {
                if (sub[i][j][k]) {
                    // debug(i, j, k);
                }
            }
        }
    }

    // use S[i,n)
    rep(j, n + 1) {
        rep(k, n + 1 - j) { dp[n][j][k] = comb[j + k][j]; }
    }

    for (int i = n - 1; i >= 0; --i) {
        int c = S[i] - '0';
        rep(j, n + 1) {
            rep(k, n + 1 - j) {
                if (c == 0) {
                    for (int p = 0; p <= k; ++p) {
                        dp[i][j][k] += dp[i + 1][j][k - p];
                    }
                } else {
                    for (int q = 0; q <= j; ++q) {
                        dp[i][j][k] += dp[i + 1][j - q][k];
                    }
                }
            }
        }
    }

    Mint ans;
    rep(i, n + 1) {
        rep(j, n + 1) {
            rep(k, n + 1 - j) {
                if (sub[i][j][k]) {
                    Mint u = dp[i][j][k];
                    int nj = j, nk = k;
                    if (i > 0) {
                        if (S[i - 1] == '0') {
                            --nj;
                        } else {
                            --nk;
                        }

                        if (nj >= 0 && nk >= 0 && sub[i - 1][nj][nk]) {
                            u -= dp[i - 1][nj][nk];
                        }
                    }
                    ans += u;
                }
            }
        }
    }
    cout << ans << endl;

    return 0;
}
```