#include <bits/stdc++.h>
#pragma GCC optimize("unroll-loops")
using namespace std;
using std::cout;
using std::cin;
using std::endl;
using ll=long long;
using ld=long double;
const ll ILL=2167167167167167167;
const int INF=2100000000;
const int mod=998244353;
#define rep(i,a,b) for (int i=(int)(a);i<(int)(b);i++)
#define all(p) p.begin(),p.end()
template<class T> using _pq = priority_queue<T, vector<T>, greater<T>>;
template<class T> ll LB(vector<T> &v,T a){return lower_bound(v.begin(),v.end(),a)-v.begin();}
template<class T> ll UB(vector<T> &v,T a){return upper_bound(v.begin(),v.end(),a)-v.begin();}
template<class T> bool chmin(T &a,const T &b){if(a>b){a=b;return 1;}else return 0;}
template<class T> bool chmax(T &a,const T &b){if(a<b){a=b;return 1;}else return 0;}
template<class T> void So(vector<T> &v) {sort(v.begin(),v.end());}
template<class T> void Sore(vector<T> &v) {sort(v.begin(),v.end(),[](T x,T y){return x>y;});}
void yneos(bool a,bool upp=0){if(a) cout<<(upp?"YES\n":"Yes\n"); else cout<<(upp?"NO\n":"No\n");}
template<class T> void vec_out(vector<T> &p,int ty=0){
if(ty==2){cout<<'{';for(int i=0;i<(int)p.size();i++){if(i){cout<<",";}cout<<'"'<<p[i]<<'"';}cout<<"}\n";}
else{if(ty==1){cout<<p.size()<<"\n";}for(int i=0;i<(int)(p.size());i++){if(i) cout<<" ";cout<<p[i];}cout<<"\n";}}
template<class T> T vec_min(vector<T> &a){assert(!a.empty());T ans=a[0];for(auto &x:a) chmin(ans,x);return ans;}
template<class T> T vec_max(vector<T> &a){assert(!a.empty());T ans=a[0];for(auto &x:a) chmax(ans,x);return ans;}
template<class T> T vec_sum(vector<T> &a){assert(!a.empty());T ans=a[0]-a[0];for(auto &x:a) ans+=x;return ans;}
int pop_count(long long a){int res=0;while(a){res+=(a&1),a>>=1;}return res;}

namespace atcoder {

namespace internal {

// @param n `0 <= n`
// @return minimum non-negative `x` s.t. `n <= 2**x`
int ceil_pow2(int n) {
    int x = 0;
    while ((1U << x) < (unsigned int)(n)) x++;
    return x;
}

// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
int bsf(unsigned int n) {
#ifdef _MSC_VER
    unsigned long index;
    _BitScanForward(&index, n);
    return index;
#else
    return __builtin_ctz(n);
#endif
}

}  // namespace internal

namespace internal {

// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m) {
    x %= m;
    if (x < 0) x += m;
    return x;
}

// Fast modular multiplication by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
    unsigned int _m;
    unsigned long long im;

    // @param m `1 <= m < 2^31`
    barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}

    // @return m
    unsigned int umod() const { return _m; }

    // @param a `0 <= a < m`
    // @param b `0 <= b < m`
    // @return `a * b % m`
    unsigned int mul(unsigned int a, unsigned int b) const {
        // [1] m = 1
        // a = b = im = 0, so okay

        // [2] m >= 2
        // im = ceil(2^64 / m)
        // -> im * m = 2^64 + r (0 <= r < m)
        // let z = a*b = c*m + d (0 <= c, d < m)
        // a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
        // c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2
        // ((ab * im) >> 64) == c or c + 1
        unsigned long long z = a;
        z *= b;
#ifdef _MSC_VER
        unsigned long long x;
        _umul128(z, im, &x);
#else
        unsigned long long x =
            (unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
        unsigned int v = (unsigned int)(z - x * _m);
        if (_m <= v) v += _m;
        return v;
    }
};

// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
    if (m == 1) return 0;
    unsigned int _m = (unsigned int)(m);
    unsigned long long r = 1;
    unsigned long long y = safe_mod(x, m);
    while (n) {
        if (n & 1) r = (r * y) % _m;
        y = (y * y) % _m;
        n >>= 1;
    }
    return r;
}

// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
constexpr bool is_prime_constexpr(int n) {
    if (n <= 1) return false;
    if (n == 2 || n == 7 || n == 61) return true;
    if (n % 2 == 0) return false;
    long long d = n - 1;
    while (d % 2 == 0) d /= 2;
    constexpr long long bases[3] = {2, 7, 61};
    for (long long a : bases) {
        long long t = d;
        long long y = pow_mod_constexpr(a, t, n);
        while (t != n - 1 && y != 1 && y != n - 1) {
            y = y * y % n;
            t <<= 1;
        }
        if (y != n - 1 && t % 2 == 0) {
            return false;
        }
    }
    return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);

// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
    a = safe_mod(a, b);
    if (a == 0) return {b, 0};

    // Contracts:
    // [1] s - m0 * a = 0 (mod b)
    // [2] t - m1 * a = 0 (mod b)
    // [3] s * |m1| + t * |m0| <= b
    long long s = b, t = a;
    long long m0 = 0, m1 = 1;

    while (t) {
        long long u = s / t;
        s -= t * u;
        m0 -= m1 * u;  // |m1 * u| <= |m1| * s <= b

        // [3]:
        // (s - t * u) * |m1| + t * |m0 - m1 * u|
        // <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
        // = s * |m1| + t * |m0| <= b

        auto tmp = s;
        s = t;
        t = tmp;
        tmp = m0;
        m0 = m1;
        m1 = tmp;
    }
    // by [3]: |m0| <= b/g
    // by g != b: |m0| < b/g
    if (m0 < 0) m0 += b / s;
    return {s, m0};
}

// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
constexpr int primitive_root_constexpr(int m) {
    if (m == 2) return 1;
    if (m == 167772161) return 3;
    if (m == 469762049) return 3;
    if (m == 754974721) return 11;
    if (m == 998244353) return 3;
    int divs[20] = {};
    divs[0] = 2;
    int cnt = 1;
    int x = (m - 1) / 2;
    while (x % 2 == 0) x /= 2;
    for (int i = 3; (long long)(i)*i <= x; i += 2) {
        if (x % i == 0) {
            divs[cnt++] = i;
            while (x % i == 0) {
                x /= i;
            }
        }
    }
    if (x > 1) {
        divs[cnt++] = x;
    }
    for (int g = 2;; g++) {
        bool ok = true;
        for (int i = 0; i < cnt; i++) {
            if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
                ok = false;
                break;
            }
        }
        if (ok) return g;
    }
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);

}  // namespace internal

namespace internal {

#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value ||
                                  std::is_same<T, __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_unsigned_int128 =
    typename std::conditional<std::is_same<T, __uint128_t>::value ||
                                  std::is_same<T, unsigned __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using make_unsigned_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value,
                              __uint128_t,
                              unsigned __int128>;

template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
                                                  is_signed_int128<T>::value ||
                                                  is_unsigned_int128<T>::value,
                                              std::true_type,
                                              std::false_type>::type;

template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
                                                 std::is_signed<T>::value) ||
                                                    is_signed_int128<T>::value,
                                                std::true_type,
                                                std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<(is_integral<T>::value &&
                               std::is_unsigned<T>::value) ||
                                  is_unsigned_int128<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<
    is_signed_int128<T>::value,
    make_unsigned_int128<T>,
    typename std::conditional<std::is_signed<T>::value,
                              std::make_unsigned<T>,
                              std::common_type<T>>::type>::type;

#else

template <class T> using is_integral = typename std::is_integral<T>;

template <class T>
using is_signed_int =
    typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<is_integral<T>::value &&
                                  std::is_unsigned<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
                                              std::make_unsigned<T>,
                                              std::common_type<T>>::type;

#endif

template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;

template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;

template <class T> using to_unsigned_t = typename to_unsigned<T>::type;

}  // namespace internal



namespace internal {

struct modint_base {};
struct static_modint_base : modint_base {};

template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;

}  // namespace internal

template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : internal::static_modint_base {
    using mint = static_modint;

  public:
    static constexpr int mod() { return m; }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }

    static_modint() : _v(0) {}
    template <class T, internal::is_signed_int_t<T>* = nullptr>
    static_modint(T v) {
        long long x = (long long)(v % (long long)(umod()));
        if (x < 0) x += umod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T>* = nullptr>
    static_modint(T v) {
        _v = (unsigned int)(v % umod());
    }
    static_modint(bool v) { _v = ((unsigned int)(v) % umod()); }

    unsigned int val() const { return _v; }

    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }

    mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v -= rhs._v;
        if (_v >= umod()) _v += umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        unsigned long long z = _v;
        z *= rhs._v;
        _v = (unsigned int)(z % umod());
        return *this;
    }
    mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }

    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }

    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        if (prime) {
            assert(_v);
            return pow(umod() - 2);
        } else {
            auto eg = internal::inv_gcd(_v, m);
            assert(eg.first == 1);
            return eg.second;
        }
    }

    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }

  private:
    unsigned int _v;
    static constexpr unsigned int umod() { return m; }
    static constexpr bool prime = internal::is_prime<m>;
};

template <int id> struct dynamic_modint : internal::modint_base {
    using mint = dynamic_modint;

  public:
    static int mod() { return (int)(bt.umod()); }
    static void set_mod(int m) {
        assert(1 <= m);
        bt = internal::barrett(m);
    }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }

    dynamic_modint() : _v(0) {}
    template <class T, internal::is_signed_int_t<T>* = nullptr>
    dynamic_modint(T v) {
        long long x = (long long)(v % (long long)(mod()));
        if (x < 0) x += mod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T>* = nullptr>
    dynamic_modint(T v) {
        _v = (unsigned int)(v % mod());
    }
    dynamic_modint(bool v) { _v = ((unsigned int)(v) % mod()); }

    unsigned int val() const { return _v; }

    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }

    mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v += mod() - rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        _v = bt.mul(_v, rhs._v);
        return *this;
    }
    mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }

    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }

    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        auto eg = internal::inv_gcd(_v, mod());
        assert(eg.first == 1);
        return eg.second;
    }

    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }

  private:
    unsigned int _v;
    static internal::barrett bt;
    static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt = 998244353;

using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;

namespace internal {

template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;

template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;

template <class> struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};

template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;

}  // namespace internal

namespace internal {

template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly(std::vector<mint>& a) {
    static constexpr int g = internal::primitive_root<mint::mod()>;
    int n = int(a.size());
    int h = internal::ceil_pow2(n);

    static bool first = true;
    static mint sum_e[30];  // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i]
    if (first) {
        first = false;
        mint es[30], ies[30];  // es[i]^(2^(2+i)) == 1
        int cnt2 = bsf(mint::mod() - 1);
        mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
        for (int i = cnt2; i >= 2; i--) {
            // e^(2^i) == 1
            es[i - 2] = e;
            ies[i - 2] = ie;
            e *= e;
            ie *= ie;
        }
        mint now = 1;
        for (int i = 0; i <= cnt2 - 2; i++) {
            sum_e[i] = es[i] * now;
            now *= ies[i];
        }
    }
    for (int ph = 1; ph <= h; ph++) {
        int w = 1 << (ph - 1), p = 1 << (h - ph);
        mint now = 1;
        for (int s = 0; s < w; s++) {
            int offset = s << (h - ph + 1);
            for (int i = 0; i < p; i++) {
                auto l = a[i + offset];
                auto r = a[i + offset + p] * now;
                a[i + offset] = l + r;
                a[i + offset + p] = l - r;
            }
            now *= sum_e[bsf(~(unsigned int)(s))];
        }
    }
}

template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly_inv(std::vector<mint>& a) {
    static constexpr int g = internal::primitive_root<mint::mod()>;
    int n = int(a.size());
    int h = internal::ceil_pow2(n);

    static bool first = true;
    static mint sum_ie[30];  // sum_ie[i] = es[0] * ... * es[i - 1] * ies[i]
    if (first) {
        first = false;
        mint es[30], ies[30];  // es[i]^(2^(2+i)) == 1
        int cnt2 = bsf(mint::mod() - 1);
        mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
        for (int i = cnt2; i >= 2; i--) {
            // e^(2^i) == 1
            es[i - 2] = e;
            ies[i - 2] = ie;
            e *= e;
            ie *= ie;
        }
        mint now = 1;
        for (int i = 0; i <= cnt2 - 2; i++) {
            sum_ie[i] = ies[i] * now;
            now *= es[i];
        }
    }

    for (int ph = h; ph >= 1; ph--) {
        int w = 1 << (ph - 1), p = 1 << (h - ph);
        mint inow = 1;
        for (int s = 0; s < w; s++) {
            int offset = s << (h - ph + 1);
            for (int i = 0; i < p; i++) {
                auto l = a[i + offset];
                auto r = a[i + offset + p];
                a[i + offset] = l + r;
                a[i + offset + p] =
                    (unsigned long long)(mint::mod() + l.val() - r.val()) *
                    inow.val();
            }
            inow *= sum_ie[bsf(~(unsigned int)(s))];
        }
    }
}

}  // namespace internal

template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution(std::vector<mint> a, std::vector<mint> b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};
    if (std::min(n, m) <= 60) {
        if (n < m) {
            std::swap(n, m);
            std::swap(a, b);
        }
        std::vector<mint> ans(n + m - 1);
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                ans[i + j] += a[i] * b[j];
            }
        }
        return ans;
    }
    int z = 1 << internal::ceil_pow2(n + m - 1);
    a.resize(z);
    internal::butterfly(a);
    b.resize(z);
    internal::butterfly(b);
    for (int i = 0; i < z; i++) {
        a[i] *= b[i];
    }
    internal::butterfly_inv(a);
    a.resize(n + m - 1);
    mint iz = mint(z).inv();
    for (int i = 0; i < n + m - 1; i++) a[i] *= iz;
    return a;
}

template <unsigned int mod = 998244353,
          class T,
          std::enable_if_t<internal::is_integral<T>::value>* = nullptr>
std::vector<T> convolution(const std::vector<T>& a, const std::vector<T>& b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};

    using mint = static_modint<mod>;
    std::vector<mint> a2(n), b2(m);
    for (int i = 0; i < n; i++) {
        a2[i] = mint(a[i]);
    }
    for (int i = 0; i < m; i++) {
        b2[i] = mint(b[i]);
    }
    auto c2 = convolution(move(a2), move(b2));
    std::vector<T> c(n + m - 1);
    for (int i = 0; i < n + m - 1; i++) {
        c[i] = c2[i].val();
    }
    return c;
}

std::vector<long long> convolution_ll(const std::vector<long long>& a,
                                      const std::vector<long long>& b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m) return {};

    static constexpr unsigned long long MOD1 = 754974721;  // 2^24
    static constexpr unsigned long long MOD2 = 167772161;  // 2^25
    static constexpr unsigned long long MOD3 = 469762049;  // 2^26
    static constexpr unsigned long long M2M3 = MOD2 * MOD3;
    static constexpr unsigned long long M1M3 = MOD1 * MOD3;
    static constexpr unsigned long long M1M2 = MOD1 * MOD2;
    static constexpr unsigned long long M1M2M3 = MOD1 * MOD2 * MOD3;

    static constexpr unsigned long long i1 =
        internal::inv_gcd(MOD2 * MOD3, MOD1).second;
    static constexpr unsigned long long i2 =
        internal::inv_gcd(MOD1 * MOD3, MOD2).second;
    static constexpr unsigned long long i3 =
        internal::inv_gcd(MOD1 * MOD2, MOD3).second;

    auto c1 = convolution<MOD1>(a, b);
    auto c2 = convolution<MOD2>(a, b);
    auto c3 = convolution<MOD3>(a, b);

    std::vector<long long> c(n + m - 1);
    for (int i = 0; i < n + m - 1; i++) {
        unsigned long long x = 0;
        x += (c1[i] * i1) % MOD1 * M2M3;
        x += (c2[i] * i2) % MOD2 * M1M3;
        x += (c3[i] * i3) % MOD3 * M1M2;
        // B = 2^63, -B <= x, r(real value) < B
        // (x, x - M, x - 2M, or x - 3M) = r (mod 2B)
        // r = c1[i] (mod MOD1)
        // focus on MOD1
        // r = x, x - M', x - 2M', x - 3M' (M' = M % 2^64) (mod 2B)
        // r = x,
        //     x - M' + (0 or 2B),
        //     x - 2M' + (0, 2B or 4B),
        //     x - 3M' + (0, 2B, 4B or 6B) (without mod!)
        // (r - x) = 0, (0)
        //           - M' + (0 or 2B), (1)
        //           -2M' + (0 or 2B or 4B), (2)
        //           -3M' + (0 or 2B or 4B or 6B) (3) (mod MOD1)
        // we checked that
        //   ((1) mod MOD1) mod 5 = 2
        //   ((2) mod MOD1) mod 5 = 3
        //   ((3) mod MOD1) mod 5 = 4
        long long diff =
            c1[i] - internal::safe_mod((long long)(x), (long long)(MOD1));
        if (diff < 0) diff += MOD1;
        static constexpr unsigned long long offset[5] = {
            0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3};
        x -= offset[diff % 5];
        c[i] = x;
    }

    return c;
}

}  // namespace atcoder
using namespace atcoder;


const int DIGIT = 6;
const int BASE = 1000000;
struct positive_bigint{
  std::vector<int> d;
  positive_bigint(){
  }
  positive_bigint(long long X){
    while (X > 0){
      d.push_back(X % BASE);
      X /= BASE;
    }
  }
  positive_bigint(std::string S){
    if (S == "0"){
      S = "";
    }
    int L = S.size();
    d.resize((L + DIGIT - 1) / DIGIT, 0);
    for (int i = L - 1; i >= 0; i -= 6){
      for (int j = std::max(i - 5, 0); j <= i; j++){
        d[i / DIGIT] *= 10;
        d[i / DIGIT] += S[j] - '0';
      }
    }
    std::reverse(d.begin(), d.end());
  }
  bool empty() const {
    return d.empty();
  }
  int size() const {
    return d.size();
  }
  int& operator [](int i){
    return d[i];
  }
  int operator [](int i) const {
    return d[i];
  }
};
std::string to_string(const positive_bigint &A){
  int N = A.size();
  std::string ans;
  for (int i = N - 1; i >= 0; i--){
    std::string tmp = std::to_string(A[i]);
    if (i < N - 1){
      ans += std::string(DIGIT - tmp.size(), '0');
    }
    ans += tmp;
  }
  if (ans.empty()){
    ans = "0";
  }
  return ans;
}
std::istream& operator >>(std::istream &is, positive_bigint &A){
  std::string S;
  is >> S;
  A = positive_bigint(S);
  return is;
}
std::ostream& operator <<(std::ostream &os, positive_bigint &A){
  os << to_string(A);
  return os;
}
int cmp(const positive_bigint &A, const positive_bigint &B){
  int N = A.size();
  int M = B.size();
  if (N < M){
    return -1;
  } else if (N > M){
    return 1;
  } else {
    for (int i = N - 1; i >= 0; i--){
      if (A[i] < B[i]){
        return -1;
      }
      if (A[i] > B[i]){
        return 1;
      }
    }
    return 0;
  }
}
bool operator ==(const positive_bigint &A, const positive_bigint &B){
  return cmp(A, B) == 0;
}
bool operator !=(const positive_bigint &A, const positive_bigint &B){
  return cmp(A, B) != 0;
}
bool operator <(const positive_bigint &A, const positive_bigint &B){
  return cmp(A, B) < 0;
}
bool operator >(const positive_bigint &A, const positive_bigint &B){
  return cmp(A, B) > 0;
}
bool operator <=(const positive_bigint &A, const positive_bigint &B){
  return cmp(A, B) <= 0;
}
bool operator >=(const positive_bigint &A, const positive_bigint &B){
  return cmp(A, B) >= 0;
}
positive_bigint& operator +=(positive_bigint &A, const positive_bigint &B){
  int N = A.size();
  int M = B.size();
  while (N < M){
    A.d.push_back(0);
    N++;
  }
  for (int i = 0; i < M; i++){
    A[i] += B[i];
  }
  for (int i = 0; i < N - 1; i++){
    if (A[i] >= BASE){
      A[i] -= BASE;
      A[i + 1]++;
    }
    else if(i >= M) break;
  }
  if (N > 0){
    if (A[N - 1] >= BASE){
      A.d.push_back(1);
      A[N - 1] -= BASE;
    }
  }
  return A;
}
positive_bigint operator +(const positive_bigint &A, const positive_bigint &B){
  positive_bigint A2 = A;
  A2 += B;
  return A2;
}
positive_bigint& operator -=(positive_bigint &A, const positive_bigint &B){
  int N = A.size();
  int M = B.size();
  for (int i = 0; i < M; i++){
    A[i] -= B[i];
  }
  for (int i = 0; i < N - 1; i++){
    if (A[i] < 0){
      A[i] += BASE;
      A[i + 1]--;
    }
  }
  while (!A.empty()){
    if (A.d.back() == 0){
      A.d.pop_back();
    } else {
      break;
    }
  }
  return A;
}
positive_bigint operator -(const positive_bigint &A, const positive_bigint &B){
  positive_bigint A2 = A;
  A2 -= B;
  return A2;
}
positive_bigint operator *(const positive_bigint &A, const positive_bigint &B){
  if (A.empty() || B.empty()){
    return 0;
  }
  int N = A.size();
  int M = B.size();
  std::vector<long long> a(N);
  for (int i=  0; i < N; i++){
    a[i] = A[i];
  }
  std::vector<long long> b(M);
  for (int i = 0; i < M; i++){
    b[i] = B[i];
  }
  std::vector<long long> C = atcoder::convolution_ll(a, b);
  for (int i = 0; i < N + M - 2; i++){
    C[i + 1] += C[i] / BASE;
    C[i] %= BASE;
  }
  if (C[N + M - 2] >= BASE){
    C.resize(N + M);
    C[N + M - 1] += C[N + M - 2] / BASE;
    C[N + M - 2] %= BASE;
  }
  positive_bigint ans;
  ans.d.resize(C.size());
  for (int i = 0; i < (int) C.size(); i++){
    ans[i] = C[i];
  }
  return ans;
}
positive_bigint operator *=(positive_bigint &A, const positive_bigint &B){
  A = A * B;
  return A;
}
struct bigint{
  bool neg = false;
  positive_bigint a;
  bigint(){
  }
  bigint(long long X): neg(X < 0), a(abs(X)){
  }
  bigint(const positive_bigint &X, bool neg = false): neg(neg), a(X){
  }
  bigint(const std::string &s){
    if (!s.empty()){
      if (s[0] == '-'){
        neg = true;
        a = positive_bigint(s.substr(1, s.size() - 1));
      } else {
        a = positive_bigint(s);
      }
    }
  }
  bool empty() const {
    return a.empty();
  }
  int size() const {
    return a.size();
  }
  int& operator [](int i){
    return a[i];
  }
};
std::string to_string(const bigint &A){
  std::string ans;
  if (A.neg){
    ans += '-';
  }
  ans += to_string(A.a);
  return ans;
}
std::istream& operator >>(std::istream &is, bigint &A){
  std::string S;
  is >> S;
  if (S != "0"){
    A = bigint(S);
  }
  return is;
}
std::ostream& operator <<(std::ostream &os, bigint A){
  os << to_string(A);
  return os;
}
positive_bigint abs(const bigint &A){
  return A.a;
}
int cmp(const bigint &A, const bigint &B){
  if (!A.neg){
    if (!B.neg){
      return cmp(A.a, B.a);
    } else {
      return 1;
    }
  } else {
    if (!B.neg){
      return -1;
    } else {
      return cmp(B.a, A.a);
    }
  }
}
bool operator ==(const bigint &A, const bigint &B){
  return cmp(A, B) == 0;
}
bool operator !=(const bigint &A, const bigint &B){
  return cmp(A, B) != 0;
}
bool operator <(const bigint &A, const bigint &B){
  return cmp(A, B) < 0;
}
bool operator >(const bigint &A, const bigint &B){
  return cmp(A, B) > 0;
}
bool operator <=(const bigint &A, const bigint &B){
  return cmp(A, B) <= 0;
}
bool operator >=(const bigint &A, const bigint &B){
  return cmp(A, B) >= 0;
}
bigint operator +(const bigint &A){
  return A;
}
bigint operator -(const bigint &A){
  bigint A2 = A;
  if (!A2.empty()){
    A2.neg = !A2.neg;
  }
  return A2;
}
bigint& operator +=(bigint &A, const bigint &B){
  if (A.neg == B.neg){
    A.a += B.a;
  } else {
    int c = cmp(A.a, B.a);
    if (c > 0){
      A.a -= B.a;
    } else if (c < 0){
      A.a = B.a - A.a;
      A.neg = !A.neg;
    } else {
      A = 0;
    }
  }
  return A;
}
bigint operator +(const bigint &A, const bigint &B){
  bigint A2 = A;
  A2 += B;
  return A2;
}
bigint& operator -=(bigint &A, const bigint &B){
  if (A.neg != B.neg){
    A.a += B.a;
  } else {
    int c = cmp(A.a, B.a);
    if (c > 0){
      A.a -= B.a;
    } else if (c < 0){
      A.a = B.a - A.a;
      A.neg = !A.neg;
    } else {
      A = 0;
    }
  }
  return A;
}
bigint operator -(const bigint &A, const bigint &B){
  bigint A2 = A;
  A2 -= B;
  return A2;
}
bigint operator *=(bigint &A, const bigint &B){
  if (A.empty() || B.empty()){
    A = 0;
  } else {
    if (B.neg){
      A.neg = !A.neg;
    }
    A.a *= B.a;
  }
  return A;
}
bigint operator *(const bigint &A, const bigint &B){
  bigint A2 = A;
  A2 *= B;
  return A2;
}
void solve();
// oddloop
int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    
    int t=1;
    //cin>>t;
    rep(i,0,t) solve();
}

void solve(){
    int N;
    string S;
    cin>>N>>S;
    // A*X+B
    struct F{
        bigint A;
        bigint B;
        bigint X;
    };
    vector<F> mem(N);
    int mem_ind=0;
    auto fix_F=[&](F &a) -> bigint {
        return a.X*a.A+a.B;
    };
    auto size_F=[&](F &a) -> int {
        return (int)max(a.A.size()+a.X.size(),a.B.size());
    };
    auto che_F=[&](F &a) -> void {
        if(size_F(a)!=(int)(a.X.size())){
            a.X=fix_F(a);
            a.A=1;
            a.B=0;
        }
    };
    auto ins = [&] (bigint n) -> int {
        mem[mem_ind]={1,0,n};
        return mem_ind++;
    };
    auto mul_F=[&](F &a,F &b) -> void {
        if(size_F(a)<size_F(b)) swap(a,b);
        auto tmp=fix_F(b);
        a.A*=tmp;
        a.B*=tmp;
        che_F(a);
    };
    auto add_F=[&](F &a,F &b) -> void {
        if(size_F(a)<size_F(b)) swap(a,b);
        a.B+=fix_F(b);
        che_F(a);
    };
    const int MUL=-1;
    const int ADD=-2;
    const int DEL=-3;
    int l=0;
    auto add_all=[&](vector<int> p) -> int {
        while((int)p.size()!=1){
            vector<int> n_p;
            rep(i,0,p.size()){
                if(i&1) continue;
                if(i+1==(int)(p.size())) n_p.push_back(p[i]);
                else{
                    n_p.push_back(p[i]);
                    add_F(mem[p[i]],mem[p[i+1]]);
                    mem[p[i+1]]={0,0,0};
                }
            }
            swap(n_p,p);
        }
        return p[0];
    };
    auto mul_all=[&](vector<int> p) -> int {
        while((int)p.size()!=1){
            vector<int> n_p;
            rep(i,0,p.size()){
                if(i&1) continue;
                if(i+1==(int)p.size()) n_p.push_back(p[i]);
                else{
                    n_p.push_back(p[i]);
                    mul_F(mem[p[i]],mem[p[i+1]]);
                    mem[p[i+1]]={0,0,0};
                }
            }
            swap(n_p,p);
        }
        return p[0];
    };
    auto f=[&](auto self) -> int {
        stack<int> st;
        st.push(ADD);
        while(l<N){
            if(S[l]=='('){
                l++;
                st.push(self(self));
            }
            else if(S[l]==')'){
                l++;
                break;
            }
            else if(S[l]=='-'){
                st.push(DEL);
                l++;
            }
            else if(S[l]=='+'){
                st.push(ADD);
                l++;
            }
            else if(S[l]=='*'){
                st.push(MUL);
                l++;
            }
            else{
                string tmp;
                while(l!=N&&'0'<=S[l]&&S[l]<='9') tmp+=S[l],l++;
                st.push(ins(bigint(tmp)));
            }
        }
        vector<vector<int>> G(1);
        int ind=0;
        bool ok=1;
        while(!st.empty()){
            int tmp=st.top();
            st.pop();
            if(tmp==MUL) ok=1;
            else if(tmp==ADD){
                // nop
            }
            else if(tmp==DEL){
                mem[G[ind].back()].A.neg^=true;
                mem[G[ind].back()].B.neg^=true;
            }
            else{
                if(!ok){
                    ind++;
                    G.push_back({});
                }
                ok=0;
                G[ind].push_back(tmp);
            }
        }
        vector<int> q;
        for(auto x:G) q.push_back(mul_all(x));
        return add_all(q);
    };
    int ans=f(f);
    cout<<fix_F(mem[ans])<<"\n";
}