#line 1 "sol.cpp"
#line 1 "library/Template/template.hpp"
#include <bits/stdc++.h>
using namespace std;

#define rep(i, a, b) for (int i = (int)(a); i < (int)(b); i++)
#define ALL(v) (v).begin(), (v).end()
#define UNIQUE(v) sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end())
#define SZ(v) (int)v.size()
#define MIN(v) *min_element(ALL(v))
#define MAX(v) *max_element(ALL(v))
#define LB(v, x) int(lower_bound(ALL(v), (x)) - (v).begin())
#define UB(v, x) int(upper_bound(ALL(v), (x)) - (v).begin())

using ll = long long int;
using ull = unsigned long long;
const int inf = 0x3fffffff;
const ll INF = 0x1fffffffffffffff;

template <typename T> inline bool chmax(T &a, T b) {
    if (a < b) {
        a = b;
        return 1;
    }
    return 0;
}
template <typename T> inline bool chmin(T &a, T b) {
    if (a > b) {
        a = b;
        return 1;
    }
    return 0;
}
template <typename T, typename U> T ceil(T x, U y) {
    assert(y != 0);
    if (y < 0)
        x = -x, y = -y;
    return (x > 0 ? (x + y - 1) / y : x / y);
}
template <typename T, typename U> T floor(T x, U y) {
    assert(y != 0);
    if (y < 0)
        x = -x, y = -y;
    return (x > 0 ? x / y : (x - y + 1) / y);
}
template <typename T> int popcnt(T x) { return __builtin_popcountll(x); }
template <typename T> int topbit(T x) {
    return (x == 0 ? -1 : 63 - __builtin_clzll(x));
}
template <typename T> int lowbit(T x) {
    return (x == 0 ? -1 : __builtin_ctzll(x));
}
#line 2 "library/Utility/fastio.hpp"
#include <unistd.h>

class FastIO {
    static constexpr int L = 1 << 16;
    char rdbuf[L];
    int rdLeft = 0, rdRight = 0;
    inline void reload() {
        int len = rdRight - rdLeft;
        memmove(rdbuf, rdbuf + rdLeft, len);
        rdLeft = 0, rdRight = len;
        rdRight += fread(rdbuf + len, 1, L - len, stdin);
    }
    inline bool skip() {
        for (;;) {
            while (rdLeft != rdRight and rdbuf[rdLeft] <= ' ')
                rdLeft++;
            if (rdLeft == rdRight) {
                reload();
                if (rdLeft == rdRight)
                    return false;
            } else
                break;
        }
        return true;
    }
    template <typename T, enable_if_t<is_integral<T>::value, int> = 0>
    inline bool _read(T &x) {
        if (!skip())
            return false;
        if (rdLeft + 20 >= rdRight)
            reload();
        bool neg = false;
        if (rdbuf[rdLeft] == '-') {
            neg = true;
            rdLeft++;
        }
        x = 0;
        while (rdbuf[rdLeft] >= '0' and rdLeft < rdRight) {
            x = x * 10 +
                (neg ? -(rdbuf[rdLeft++] ^ 48) : (rdbuf[rdLeft++] ^ 48));
        }
        return true;
    }
    inline bool _read(__int128_t &x) {
        if (!skip())
            return false;
        if (rdLeft + 40 >= rdRight)
            reload();
        bool neg = false;
        if (rdbuf[rdLeft] == '-') {
            neg = true;
            rdLeft++;
        }
        x = 0;
        while (rdbuf[rdLeft] >= '0' and rdLeft < rdRight) {
            x = x * 10 +
                (neg ? -(rdbuf[rdLeft++] ^ 48) : (rdbuf[rdLeft++] ^ 48));
        }
        return true;
    }
    inline bool _read(__uint128_t &x) {
        if (!skip())
            return false;
        if (rdLeft + 40 >= rdRight)
            reload();
        x = 0;
        while (rdbuf[rdLeft] >= '0' and rdLeft < rdRight) {
            x = x * 10 + (rdbuf[rdLeft++] ^ 48);
        }
        return true;
    }
    template <typename T, enable_if_t<is_floating_point<T>::value, int> = 0>
    inline bool _read(T &x) {
        if (!skip())
            return false;
        if (rdLeft + 20 >= rdRight)
            reload();
        bool neg = false;
        if (rdbuf[rdLeft] == '-') {
            neg = true;
            rdLeft++;
        }
        x = 0;
        while (rdbuf[rdLeft] >= '0' and rdbuf[rdLeft] <= '9' and
               rdLeft < rdRight) {
            x = x * 10 + (rdbuf[rdLeft++] ^ 48);
        }
        if (rdbuf[rdLeft] != '.')
            return true;
        rdLeft++;
        T base = .1;
        while (rdbuf[rdLeft] >= '0' and rdbuf[rdLeft] <= '9' and
               rdLeft < rdRight) {
            x += base * (rdbuf[rdLeft++] ^ 48);
            base *= .1;
        }
        if (neg)
            x = -x;
        return true;
    }
    inline bool _read(char &x) {
        if (!skip())
            return false;
        if (rdLeft + 1 >= rdRight)
            reload();
        x = rdbuf[rdLeft++];
        return true;
    }
    inline bool _read(string &x) {
        if (!skip())
            return false;
        for (;;) {
            int pos = rdLeft;
            while (pos < rdRight and rdbuf[pos] > ' ')
                pos++;
            x.append(rdbuf + rdLeft, pos - rdLeft);
            if (rdLeft == pos)
                break;
            rdLeft = pos;
            if (rdLeft == rdRight)
                reload();
            else
                break;
        }
        return true;
    }
    template <typename T> inline bool _read(vector<T> &v) {
        for (auto &x : v) {
            if (!_read(x))
                return false;
        }
        return true;
    }

    char wtbuf[L], tmp[50];
    int wtRight = 0;
    inline void _write(const char &x) {
        if (wtRight > L - 32)
            flush();
        wtbuf[wtRight++] = x;
    }
    inline void _write(const string &x) {
        for (auto &c : x)
            _write(c);
    }
    template <typename T, enable_if_t<is_integral<T>::value, int> = 0>
    inline void _write(T x) {
        if (wtRight > L - 32)
            flush();
        if (x == 0) {
            _write('0');
            return;
        } else if (x < 0) {
            _write('-');
            if (__builtin_expect(x == std::numeric_limits<T>::min(), 0)) {
                switch (sizeof(x)) {
                case 2:
                    _write("32768");
                    return;
                case 4:
                    _write("2147483648");
                    return;
                case 8:
                    _write("9223372036854775808");
                    return;
                }
            }
            x = -x;
        }
        int pos = 0;
        while (x != 0) {
            tmp[pos++] = char((x % 10) | 48);
            x /= 10;
        }
        rep(i, 0, pos) wtbuf[wtRight + i] = tmp[pos - 1 - i];
        wtRight += pos;
    }
    inline void _write(__int128_t x) {
        if (wtRight > L - 40)
            flush();
        if (x == 0) {
            _write('0');
            return;
        } else if (x < 0) {
            _write('-');
            x = -x;
        }
        int pos = 0;
        while (x != 0) {
            tmp[pos++] = char((x % 10) | 48);
            x /= 10;
        }
        rep(i, 0, pos) wtbuf[wtRight + i] = tmp[pos - 1 - i];
        wtRight += pos;
    }
    inline void _write(__uint128_t x) {
        if (wtRight > L - 40)
            flush();
        if (x == 0) {
            _write('0');
            return;
        }
        int pos = 0;
        while (x != 0) {
            tmp[pos++] = char((x % 10) | 48);
            x /= 10;
        }
        rep(i, 0, pos) wtbuf[wtRight + i] = tmp[pos - 1 - i];
        wtRight += pos;
    }
    inline void _write(double x) {
        ostringstream oss;
        oss << fixed << setprecision(15) << double(x);
        string s = oss.str();
        _write(s);
    }
    template <typename T> inline void _write(const vector<T> &v) {
        rep(i, 0, v.size()) {
            if (i)
                _write(' ');
            _write(v[i]);
        }
    }

  public:
    FastIO() {}
    ~FastIO() { flush(); }
    inline void read() {}
    template <typename Head, typename... Tail>
    inline void read(Head &head, Tail &...tail) {
        assert(_read(head));
        read(tail...);
    }
    template <bool ln = true, bool space = false> inline void write() {
        if (ln)
            _write('\n');
    }
    template <bool ln = true, bool space = false, typename Head,
              typename... Tail>
    inline void write(const Head &head, const Tail &...tail) {
        _write(head);
        write<ln, true>(tail...);
        if (space)
            _write(' ');
    }
    inline void flush() {
        fwrite(wtbuf, 1, wtRight, stdout);
        wtRight = 0;
    }
};

/**
 * @brief Fast IO
 */
#line 310 "sol.cpp"
#ifndef ATCODER_CONVOLUTION_HPP
#define ATCODER_CONVOLUTION_HPP 1

#include <algorithm>
#include <array>
#include <cassert>
#include <type_traits>
#include <vector>
#ifndef ATCODER_INTERNAL_BITOP_HPP
#define ATCODER_INTERNAL_BITOP_HPP 1

#ifdef _MSC_VER
#include <intrin.h>
#endif

#if __cplusplus >= 202002L
#include <bit>
#endif

namespace atcoder {

namespace internal {

#if __cplusplus >= 202002L

using std::bit_ceil;

#else

// @return same with std::bit::bit_ceil
unsigned int bit_ceil(unsigned int n) {
    unsigned int x = 1;
    while (x < (unsigned int)(n))
        x *= 2;
    return x;
}

#endif

// @param n `1 <= n`
// @return same with std::bit::countr_zero
int countr_zero(unsigned int n) {
#ifdef _MSC_VER
    unsigned long index;
    _BitScanForward(&index, n);
    return index;
#else
    return __builtin_ctz(n);
#endif
}

// @param n `1 <= n`
// @return same with std::bit::countr_zero
constexpr int countr_zero_constexpr(unsigned int n) {
    int x = 0;
    while (!(n & (1 << x)))
        x++;
    return x;
}

} // namespace internal

} // namespace atcoder

#endif // ATCODER_INTERNAL_BITOP_HPP#ifndef ATCODER_MODINT_HPP
#define ATCODER_MODINT_HPP 1

#include <cassert>
#include <numeric>
#include <type_traits>

#ifdef _MSC_VER
#include <intrin.h>
#endif
#ifndef ATCODER_INTERNAL_MATH_HPP
#define ATCODER_INTERNAL_MATH_HPP 1

#include <utility>

#ifdef _MSC_VER
#include <intrin.h>
#endif

namespace atcoder {

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`
    explicit 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 long long y = x * _m;
        return (unsigned int)(z - y + (z < y ? _m : 0));
    }
};

// @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);

// @param n `n < 2^32`
// @param m `1 <= m < 2^32`
// @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)
unsigned long long floor_sum_unsigned(unsigned long long n,
                                      unsigned long long m,
                                      unsigned long long a,
                                      unsigned long long b) {
    unsigned long long ans = 0;
    while (true) {
        if (a >= m) {
            ans += n * (n - 1) / 2 * (a / m);
            a %= m;
        }
        if (b >= m) {
            ans += n * (b / m);
            b %= m;
        }

        unsigned long long y_max = a * n + b;
        if (y_max < m)
            break;
        // y_max < m * (n + 1)
        // floor(y_max / m) <= n
        n = (unsigned long long)(y_max / m);
        b = (unsigned long long)(y_max % m);
        std::swap(m, a);
    }
    return ans;
}

} // namespace internal

} // namespace atcoder

#endif // ATCODER_INTERNAL_MATH_HPP#ifndef ATCODER_INTERNAL_TYPE_TRAITS_HPP
#define ATCODER_INTERNAL_TYPE_TRAITS_HPP 1

#include <cassert>
#include <numeric>
#include <type_traits>

namespace atcoder {

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 atcoder

#endif // ATCODER_INTERNAL_TYPE_TRAITS_HPP

namespace atcoder {

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());
    }

    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());
    }

    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 atcoder

namespace atcoder {

namespace internal {

template <class mint, int g = internal::primitive_root<mint::mod()>,
          internal::is_static_modint_t<mint> * = nullptr>
struct fft_info {
    static constexpr int rank2 = countr_zero_constexpr(mint::mod() - 1);
    std::array<mint, rank2 + 1> root;  // root[i]^(2^i) == 1
    std::array<mint, rank2 + 1> iroot; // root[i] * iroot[i] == 1

    std::array<mint, std::max(0, rank2 - 2 + 1)> rate2;
    std::array<mint, std::max(0, rank2 - 2 + 1)> irate2;

    std::array<mint, std::max(0, rank2 - 3 + 1)> rate3;
    std::array<mint, std::max(0, rank2 - 3 + 1)> irate3;

    fft_info() {
        root[rank2] = mint(g).pow((mint::mod() - 1) >> rank2);
        iroot[rank2] = root[rank2].inv();
        for (int i = rank2 - 1; i >= 0; i--) {
            root[i] = root[i + 1] * root[i + 1];
            iroot[i] = iroot[i + 1] * iroot[i + 1];
        }

        {
            mint prod = 1, iprod = 1;
            for (int i = 0; i <= rank2 - 2; i++) {
                rate2[i] = root[i + 2] * prod;
                irate2[i] = iroot[i + 2] * iprod;
                prod *= iroot[i + 2];
                iprod *= root[i + 2];
            }
        }
        {
            mint prod = 1, iprod = 1;
            for (int i = 0; i <= rank2 - 3; i++) {
                rate3[i] = root[i + 3] * prod;
                irate3[i] = iroot[i + 3] * iprod;
                prod *= iroot[i + 3];
                iprod *= root[i + 3];
            }
        }
    }
};

template <class mint, internal::is_static_modint_t<mint> * = nullptr>
void butterfly(std::vector<mint> &a) {
    int n = int(a.size());
    int h = internal::countr_zero((unsigned int)n);

    static const fft_info<mint> info;

    int len = 0; // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed
    while (len < h) {
        if (h - len == 1) {
            int p = 1 << (h - len - 1);
            mint rot = 1;
            for (int s = 0; s < (1 << len); s++) {
                int offset = s << (h - len);
                for (int i = 0; i < p; i++) {
                    auto l = a[i + offset];
                    auto r = a[i + offset + p] * rot;
                    a[i + offset] = l + r;
                    a[i + offset + p] = l - r;
                }
                if (s + 1 != (1 << len))
                    rot *= info.rate2[countr_zero(~(unsigned int)(s))];
            }
            len++;
        } else {
            // 4-base
            int p = 1 << (h - len - 2);
            mint rot = 1, imag = info.root[2];
            for (int s = 0; s < (1 << len); s++) {
                mint rot2 = rot * rot;
                mint rot3 = rot2 * rot;
                int offset = s << (h - len);
                for (int i = 0; i < p; i++) {
                    auto mod2 = 1ULL * mint::mod() * mint::mod();
                    auto a0 = 1ULL * a[i + offset].val();
                    auto a1 = 1ULL * a[i + offset + p].val() * rot.val();
                    auto a2 = 1ULL * a[i + offset + 2 * p].val() * rot2.val();
                    auto a3 = 1ULL * a[i + offset + 3 * p].val() * rot3.val();
                    auto a1na3imag =
                        1ULL * mint(a1 + mod2 - a3).val() * imag.val();
                    auto na2 = mod2 - a2;
                    a[i + offset] = a0 + a2 + a1 + a3;
                    a[i + offset + 1 * p] = a0 + a2 + (2 * mod2 - (a1 + a3));
                    a[i + offset + 2 * p] = a0 + na2 + a1na3imag;
                    a[i + offset + 3 * p] = a0 + na2 + (mod2 - a1na3imag);
                }
                if (s + 1 != (1 << len))
                    rot *= info.rate3[countr_zero(~(unsigned int)(s))];
            }
            len += 2;
        }
    }
}

template <class mint, internal::is_static_modint_t<mint> * = nullptr>
void butterfly_inv(std::vector<mint> &a) {
    int n = int(a.size());
    int h = internal::countr_zero((unsigned int)n);

    static const fft_info<mint> info;

    int len = h; // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed
    while (len) {
        if (len == 1) {
            int p = 1 << (h - len);
            mint irot = 1;
            for (int s = 0; s < (1 << (len - 1)); s++) {
                int offset = s << (h - len + 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()) *
                        irot.val();
                    ;
                }
                if (s + 1 != (1 << (len - 1)))
                    irot *= info.irate2[countr_zero(~(unsigned int)(s))];
            }
            len--;
        } else {
            // 4-base
            int p = 1 << (h - len);
            mint irot = 1, iimag = info.iroot[2];
            for (int s = 0; s < (1 << (len - 2)); s++) {
                mint irot2 = irot * irot;
                mint irot3 = irot2 * irot;
                int offset = s << (h - len + 2);
                for (int i = 0; i < p; i++) {
                    auto a0 = 1ULL * a[i + offset + 0 * p].val();
                    auto a1 = 1ULL * a[i + offset + 1 * p].val();
                    auto a2 = 1ULL * a[i + offset + 2 * p].val();
                    auto a3 = 1ULL * a[i + offset + 3 * p].val();

                    auto a2na3iimag =
                        1ULL *
                        mint((mint::mod() + a2 - a3) * iimag.val()).val();

                    a[i + offset] = a0 + a1 + a2 + a3;
                    a[i + offset + 1 * p] =
                        (a0 + (mint::mod() - a1) + a2na3iimag) * irot.val();
                    a[i + offset + 2 * p] =
                        (a0 + a1 + (mint::mod() - a2) + (mint::mod() - a3)) *
                        irot2.val();
                    a[i + offset + 3 * p] =
                        (a0 + (mint::mod() - a1) + (mint::mod() - a2na3iimag)) *
                        irot3.val();
                }
                if (s + 1 != (1 << (len - 2)))
                    irot *= info.irate3[countr_zero(~(unsigned int)(s))];
            }
            len -= 2;
        }
    }
}

template <class mint, internal::is_static_modint_t<mint> * = nullptr>
std::vector<mint> convolution_naive(const std::vector<mint> &a,
                                    const std::vector<mint> &b) {
    int n = int(a.size()), m = int(b.size());
    std::vector<mint> ans(n + m - 1);
    if (n < m) {
        for (int j = 0; j < m; j++) {
            for (int i = 0; i < n; i++) {
                ans[i + j] += a[i] * b[j];
            }
        }
    } else {
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                ans[i + j] += a[i] * b[j];
            }
        }
    }
    return ans;
}

template <class mint, internal::is_static_modint_t<mint> * = nullptr>
std::vector<mint> convolution_fft(std::vector<mint> a, std::vector<mint> b) {
    int n = int(a.size()), m = int(b.size());
    int z = (int)internal::bit_ceil((unsigned int)(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;
}

} // 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 {};

    int z = (int)internal::bit_ceil((unsigned int)(n + m - 1));
    assert((mint::mod() - 1) % z == 0);

    if (std::min(n, m) <= 60)
        return convolution_naive(a, b);
    return internal::convolution_fft(a, b);
}
template <class mint, internal::is_static_modint_t<mint> * = nullptr>
std::vector<mint> convolution(const std::vector<mint> &a,
                              const std::vector<mint> &b) {
    int n = int(a.size()), m = int(b.size());
    if (!n || !m)
        return {};

    int z = (int)internal::bit_ceil((unsigned int)(n + m - 1));
    assert((mint::mod() - 1) % z == 0);

    if (std::min(n, m) <= 60)
        return convolution_naive(a, b);
    return internal::convolution_fft(a, b);
}

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>;

    int z = (int)internal::bit_ceil((unsigned int)(n + m - 1));
    assert((mint::mod() - 1) % z == 0);

    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(std::move(a2), std::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;

    static constexpr int MAX_AB_BIT = 24;
    static_assert(MOD1 % (1ull << MAX_AB_BIT) == 1,
                  "MOD1 isn't enough to support an array length of 2^24.");
    static_assert(MOD2 % (1ull << MAX_AB_BIT) == 1,
                  "MOD2 isn't enough to support an array length of 2^24.");
    static_assert(MOD3 % (1ull << MAX_AB_BIT) == 1,
                  "MOD3 isn't enough to support an array length of 2^24.");
    assert(n + m - 1 <= (1 << MAX_AB_BIT));

    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

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]++;
        }
    }
    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 < 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;
}

typedef string::const_iterator State;

bigint expr(State &beg);
bigint term(State &beg);
bigint factor(State &beg);
bigint num(State &beg);

bigint expr(State &beg) {
    auto ret = term(beg);
    for (;;) {
        if ((*beg) == '+') {
            beg++;
            ret += term(beg);
        } else if ((*beg) == '-') {
            beg++;
            ret -= term(beg);
        } else
            break;
    }
    return ret;
}

bigint term(State &beg) {
    deque<bigint> deq;
    deq.push_back(factor(beg));
    while ((*beg) == '*') {
        beg++;
        deq.push_back(factor(beg));
    }
    while (deq.size() > 1) {
        auto x = deq[0];
        deq.pop_front();
        auto y = deq[0];
        deq.pop_front();
        deq.push_back(x * y);
    }
    return deq[0];
}

bigint factor(State &beg) {
    if ((*beg) == '(') {
        beg++;
        auto ret = expr(beg);
        beg++;
        return ret;
    } else
        return num(beg);
}

bigint num(State &beg) {
    bool neg = 0;
    while ((*beg) == '-') {
        neg ^= 1;
        beg++;
    }
    string buf;
    while (isdigit(*beg)) {
        buf += (*beg);
        beg++;
    }
    bigint ret(buf);
    if (neg)
        ret = -ret;
    return ret;
}

FastIO io;
int main() {
    int n = 1000000;
    string s;
    io.read(n, s);

    State it = s.begin();
    auto ret = expr(it);
    cout << ret << '\n';
    return 0;
}