#include <bits/stdc++.h>

namespace atcoder {

namespace internal {

constexpr long long safe_mod(long long x, long long m) {
    x %= m;
    if (x < 0) x += m;
    return x;
}

struct barrett {
    unsigned int _m;
    unsigned long long im;

    explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}

    unsigned int umod() const { return _m; }

    unsigned int mul(unsigned int a, unsigned int b) const {
        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));
    }
};

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;
}

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);

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};

    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

        auto tmp = s;
        s = t;
        t = tmp;
        tmp = m0;
        m0 = m1;
        m1 = tmp;
    }
    if (m0 < 0) m0 += b / s;
    return {s, m0};
}

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);

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;
        n = (unsigned long long)(y_max / m);
        b = (unsigned long long)(y_max % m);
        std::swap(m, a);
    }
    return ans;
}

}  // namespace internal

}  // namespace atcoder

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

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

// using Z = atcoder::modint1000000007;
using Z = atcoder::modint998244353;

int inv(int x) {
    return Z(x).inv().val();
}

implementer.cpp: In function ‘int main()’:
implementer.cpp:22:14: warning: ignoring return value of ‘int scanf(const char*, ...)’ declared with attribute ‘warn_unused_result’ [-Wunused-result]
   22 |         scanf("%d", &n);
      |         ~~~~~^~~~~~~~~~
/usr/bin/ld: /tmp/cc8MDCRB.o: in function `main':
implementer.cpp:(.text.startup+0x12b): undefined reference to `init(int)'
collect2: error: ld returned 1 exit status