#line 1 "a.cpp"
#line 1 "/home/nok0/documents/programming/library/atcoder/modint.hpp"


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

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

#line 1 "/home/nok0/documents/programming/library/atcoder/internal_math.hpp"


#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 < 2^31`
	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 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);

// @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


#line 1 "/home/nok0/documents/programming/library/atcoder/internal_type_traits.hpp"


#line 7 "/home/nok0/documents/programming/library/atcoder/internal_type_traits.hpp"

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


#line 14 "/home/nok0/documents/programming/library/atcoder/modint.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


#line 3 "/home/nok0/documents/programming/library/math/factorial.hpp"
#include <vector>

#line 6 "/home/nok0/documents/programming/library/math/factorial.hpp"

template <class T>
struct factorial {
   public:
	static int MAX;
	static std::vector<T> fac, finv, inv;

	factorial() {}

	T binom(int n, int r) {
		if(n < r or n < 0 or r < 0) return T(0);
		assert(n < MAX);
		return fac[n] * finv[r] * finv[n - r];
	}

	T large_binom(long long n, int r) {
		if(n < r or n < 0 or r < 0) return T(0);
		assert(r < MAX);
		T ret = finv[r];
		for(int i = 1; i <= r; ++i)
			ret *= (n + 1 - i);
		return ret;
	}

	static void set_size(int n = 3000000) {
		MAX = (n > 1 ? n : 1) + 1;
		if((int)fac.size() >= MAX) return;
		fac.resize(MAX);
		finv.resize(MAX);
		inv.resize(MAX);
		const int MOD = T::mod();
		fac[0] = fac[1] = 1;
		finv[0] = finv[1] = 1;
		inv[1] = 1;
		for(int i = 2; i < MAX; i++) {
			fac[i] = fac[i - 1] * i;
			inv[i] = (T)MOD - inv[MOD % i] * (MOD / i);
			finv[i] = finv[i - 1] * inv[i];
		}
	}
};
template <class T>
int factorial<T>::MAX = 0;
template <class T>
std::vector<T> factorial<T>::fac;
template <class T>
std::vector<T> factorial<T>::finv;
template <class T>
std::vector<T> factorial<T>::inv;
#line 2 "/home/nok0/documents/programming/library/math/modint_iostream.hpp"
#include <iostream>

#line 5 "/home/nok0/documents/programming/library/math/modint_iostream.hpp"
template <int m>
std::istream &std::operator>>(std::istream &is, atcoder::static_modint<m> &a) {
	long long v;
	is >> v;
	a = v;
	return is;
}
template <int m>
std::istream &std::operator>>(std::istream &is, atcoder::dynamic_modint<m> &a) {
	long long v;
	is >> v;
	a = v;
	return is;
}
template <int m>
std::ostream &std::operator<<(std::ostream &os, const atcoder::static_modint<m> &a) { return os << a.val(); }
template <int m>
std::ostream &std::operator<<(std::ostream &os, const atcoder::dynamic_modint<m> &a) { return os << a.val(); }
#line 2 "/home/nok0/documents/programming/library/template/header.hpp"
#include <bits/stdc++.h>
#line 3 "/home/nok0/documents/programming/library/template/def_const.hpp"

const int inf = 1000000000;
const long long INF = 1000000000000000000ll;
#line 4 "/home/nok0/documents/programming/library/template/debug.hpp"

namespace viewer {
void view(const long long &e) {
	if(e == INF)
		std::cerr << "INF";
	else if(e == -INF)
		std::cerr << "-INF";
	else
		std::cerr << e;
}

void view(const int &e) {
	if(e == inf)
		std::cerr << "inf";
	else if(e == -inf)
		std::cerr << "-inf";
	else
		std::cerr << e;
}

template <typename T>
void view(const T &e) {
	std::cerr << e;
}

template <typename T, typename U>
void view(const std::pair<T, U> &p) {
	std::cerr << "(";
	view(p.first);
	std::cerr << ", ";
	view(p.second);
	std::cerr << ")";
}

template <class T0, class T1, class T2>
void view(const std::tuple<T0, T1, T2> &p) {
	std::cerr << "(";
	view(std::get<0>(p));
	std::cerr << ", ";
	view(std::get<1>(p));
	std::cerr << ", ";
	view(std::get<2>(p));
	std::cerr << ")";
}

template <class T0, class T1, class T2, class T3>
void view(const std::tuple<T0, T1, T2, T3> &p) {
	std::cerr << "(";
	view(std::get<0>(p));
	std::cerr << ", ";
	view(std::get<1>(p));
	std::cerr << ", ";
	view(std::get<2>(p));
	std::cerr << ", ";
	view(std::get<3>(p));
	std::cerr << ")";
}

template <typename T>
void view(const std::set<T> &s) {
	if(s.empty()) {
		std::cerr << "{ }";
		return;
	}
	std::cerr << "{ ";
	for(auto &t : s) {
		view(t);
		std::cerr << ", ";
	}
	std::cerr << "\b\b }";
}

template <typename T>
void view(const std::unordered_set<T> &s) {
	if(s.empty()) {
		std::cerr << "{ }";
		return;
	}
	std::cerr << "{ ";
	for(auto &t : s) {
		view(t);
		std::cerr << ", ";
	}
	std::cerr << "\b\b }";
}

template <typename T>
void view(const std::multiset<T> &s) {
	if(s.empty()) {
		std::cerr << "{ }";
		return;
	}
	std::cerr << "{ ";
	for(auto &t : s) {
		view(t);
		std::cerr << ", ";
	}
	std::cerr << "\b\b }";
}

template <typename T>
void view(const std::unordered_multiset<T> &s) {
	if(s.empty()) {
		std::cerr << "{ }";
		return;
	}
	std::cerr << "{ ";
	for(auto &t : s) {
		view(t);
		std::cerr << ", ";
	}
	std::cerr << "\b\b }";
}

template <typename T>
void view(const std::vector<T> &v) {
	if(v.empty()) {
		std::cerr << "{ }";
		return;
	}
	std::cerr << "{ ";
	for(const auto &e : v) {
		view(e);
		std::cerr << ", ";
	}
	std::cerr << "\b\b }";
}

template <typename T, std::size_t ary_size>
void view(const std::array<T, ary_size> &v) {
	if(v.empty()) {
		std::cerr << "{ }";
		return;
	}
	std::cerr << "{ ";
	for(const auto &e : v) {
		view(e);
		std::cerr << ", ";
	}
	std::cerr << "\b\b }";
}

template <typename T>
void view(const std::vector<std::vector<T>> &vv) {
	std::cerr << "{\n";
	for(const auto &v : vv) {
		std::cerr << "\t";
		view(v);
		std::cerr << '\n';
	}
	std::cerr << "}";
}

template <typename T, typename U>
void view(const std::vector<std::pair<T, U>> &v) {
	std::cerr << "{\n";
	for(const auto &c : v) {
		std::cerr << "\t(";
		view(c.first);
		std::cerr << ", ";
		view(c.second);
		std::cerr << ")\n";
	}
	std::cerr << "}";
}

template <class T0, class T1, class T2>
void view(const std::vector<std::tuple<T0, T1, T2>> &v) {
	if(v.empty()) {
		std::cerr << "{ }";
		return;
	}
	std::cerr << '{';
	for(const auto &t : v) {
		std::cerr << "\n\t";
		view(t);
		std::cerr << ",";
	}
	std::cerr << "\n}";
}

template <class T0, class T1, class T2, class T3>
void view(const std::vector<std::tuple<T0, T1, T2, T3>> &v) {
	if(v.empty()) {
		std::cerr << "{ }";
		return;
	}
	std::cerr << '{';
	for(const auto &t : v) {
		std::cerr << "\n\t";
		view(t);
		std::cerr << ",";
	}
	std::cerr << "\n}";
}

template <typename T, typename U>
void view(const std::map<T, U> &m) {
	std::cerr << "{\n";
	for(const auto &t : m) {
		std::cerr << "\t[";
		view(t.first);
		std::cerr << "] : ";
		view(t.second);
		std::cerr << '\n';
	}
	std::cerr << "}";
}

template <typename T, typename U>
void view(const std::unordered_map<T, U> &m) {
	std::cerr << "{\n";
	for(const auto &t : m) {
		std::cerr << "\t[";
		view(t.first);
		std::cerr << "] : ";
		view(t.second);
		std::cerr << '\n';
	}
	std::cerr << "}";
}
}  // namespace viewer

// when compiling : g++ foo.cpp -DLOCAL
#ifdef LOCAL
void debug_out() {}
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
	viewer::view(H);
	std::cerr << ", ";
	debug_out(T...);
}
#define debug(...)                                                \
	do {                                                          \
		std::cerr << __LINE__ << " [" << #__VA_ARGS__ << "] : ["; \
		debug_out(__VA_ARGS__);                                   \
		std::cerr << "\b\b]\n";                                   \
	} while(0)
#define dump(x)                                      \
	do {                                             \
		std::cerr << __LINE__ << " " << #x << " : "; \
		viewer::view(x);                             \
		std::cerr << '\n';                           \
	} while(0)

#else
#define debug(...) (void(0))
#define dump(x)    (void(0))
#endif
#line 3 "/home/nok0/documents/programming/library/template/def_name.hpp"

#define pb        push_back
#define eb        emplace_back
#define fi        first
#define se        second
#define SZ(x)     ((int)(x).size())
#define all(x)    (x).begin(), (x).end()
#define rall(x)   (x).rbegin(), (x).rend()
#define popcnt(x) __builtin_popcountll(x)
template <class T = int>
using V = std::vector<T>;
template <class T = int>
using VV = std::vector<std::vector<T>>;
template <class T>
using pqup = std::priority_queue<T, std::vector<T>, std::greater<T>>;
using ll = long long;
using ld = long double;
using int128 = __int128_t;
using pii = std::pair<int, int>;
using pll = std::pair<long long, long long>;
#line 3 "/home/nok0/documents/programming/library/template/fast_io.hpp"

struct fast_io {
	fast_io() {
		std::ios::sync_with_stdio(false);
		std::cin.tie(nullptr);
		std::cout << std::fixed << std::setprecision(15);
	}
} fast_io_;
#line 3 "/home/nok0/documents/programming/library/template/input.hpp"

template <class T, class U>
std::istream &operator>>(std::istream &is, std::pair<T, U> &p) {
	is >> p.first >> p.second;
	return is;
}
template <class T>
std::istream &operator>>(std::istream &is, std::vector<T> &v) {
	for(T &i : v) is >> i;
	return is;
}
std::istream &operator>>(std::istream &is, __int128_t &a) {
	std::string s;
	is >> s;
	__int128_t ret = 0;
	for(int i = 0; i < (int)s.length(); i++)
		if('0' <= s[i] and s[i] <= '9')
			ret = 10 * ret + s[i] - '0';
	a = ret * (s[0] == '-' ? -1 : 1);
	return is;
}
namespace scanner {
void scan(int &a) { std::cin >> a; }
void scan(long long &a) { std::cin >> a; }
void scan(std::string &a) { std::cin >> a; }
void scan(char &a) { std::cin >> a; }
void scan(char a[]) { std::scanf("%s", a); }
void scan(double &a) { std::cin >> a; }
void scan(long double &a) { std::cin >> a; }
template <class T, class U>
void scan(std::pair<T, U> &p) { std::cin >> p; }
template <class T>
void scan(std::vector<T> &a) { std::cin >> a; }
void INPUT() {}
template <class Head, class... Tail>
void INPUT(Head &head, Tail &...tail) {
	scan(head);
	INPUT(tail...);
}
}  // namespace scanner
#define VEC(type, name, size)     \
	std::vector<type> name(size); \
	scanner::INPUT(name)
#define VVEC(type, name, h, w)                                    \
	std::vector<std::vector<type>> name(h, std::vector<type>(w)); \
	scanner::INPUT(name)
#define INT(...)     \
	int __VA_ARGS__; \
	scanner::INPUT(__VA_ARGS__)
#define LL(...)            \
	long long __VA_ARGS__; \
	scanner::INPUT(__VA_ARGS__)
#define STR(...)             \
	std::string __VA_ARGS__; \
	scanner::INPUT(__VA_ARGS__)
#define CHAR(...)     \
	char __VA_ARGS__; \
	scanner::INPUT(__VA_ARGS__)
#define DOUBLE(...)     \
	double __VA_ARGS__; \
	scanner::INPUT(__VA_ARGS__)
#define LD(...)              \
	long double __VA_ARGS__; \
	scanner::INPUT(__VA_ARGS__)
#line 3 "/home/nok0/documents/programming/library/template/math.hpp"

template <class T, class U>
inline bool chmin(T &a, const U &b) { return a > b ? a = b, true : false; }
template <class T, class U>
inline bool chmax(T &a, const U &b) { return a < b ? a = b, true : false; }
template <class T>
T divup(T x, T y) { return (x + y - 1) / y; }
template <class T>
T POW(T a, long long n) {
	T ret = 1;
	while(n) {
		if(n & 1) ret *= a;
		a *= a;
		n >>= 1;
	}
	return ret;
}
long long POW(long long a, long long n, const int mod) {
	long long ret = 1;
	a = (a % mod + mod) % mod;
	while(n) {
		if(n & 1) (ret *= a) %= mod;
		(a *= a) %= mod;
		n >>= 1;
	}
	return ret;
}
template <class T, class F>
T bin_search(T ok, T ng, const F &f) {
	while(abs(ok - ng) > 1) {
		T mid = (ok + ng) >> 1;
		(f(mid) ? ok : ng) = mid;
	}
	return ok;
}
template <class T, class F>
T bin_search(T ok, T ng, const F &f, int loop) {
	for(int i = 0; i < loop; i++) {
		T mid = (ok + ng) / 2;
		(f(mid) ? ok : ng) = mid;
	}
	return ok;
}
#line 3 "/home/nok0/documents/programming/library/template/output.hpp"


template <class T, class U>
std::ostream &operator<<(std::ostream &os, const std::pair<T, U> &p) {
	os << p.first << " " << p.second;
	return os;
}
template <class T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &a) {
	for(int i = 0; i < int(a.size()); ++i) {
		if(i) os << " ";
		os << a[i];
	}
	return os;
}
std::ostream &operator<<(std::ostream &dest, __int128_t &value) {
	std::ostream::sentry s(dest);
	if(s) {
		__uint128_t tmp = value < 0 ? -value : value;
		char buffer[128];
		char *d = std::end(buffer);
		do {
			--d;
			*d = "0123456789"[tmp % 10];
			tmp /= 10;
		} while(tmp != 0);
		if(value < 0) {
			--d;
			*d = '-';
		}
		int len = std::end(buffer) - d;
		if(dest.rdbuf()->sputn(d, len) != len) {
			dest.setstate(std::ios_base::badbit);
		}
	}
	return dest;
}
template <class T>
void print(const T a) { std::cout << a << '\n'; }
template <class Head, class... Tail>
void print(Head H, Tail... T) {
	std::cout << H << ' ';
	print(T...);
}
template <class T>
void println(const T a) { std::cout << a << '\n'; }
template <class T>
void println(const std::vector<T> &a) {
	for(const auto &v : a)
		std::cout << v << '\n';
}
template <class Head, class... Tail>
void println(Head H, Tail... T) {
	std::cout << H << '\n';
	println(T...);
}
void Yes(const bool b = true) { std::cout << (b ? "Yes\n" : "No\n"); }
void No() { std::cout << "No\n"; }
void YES(const bool b = true) { std::cout << (b ? "YES\n" : "NO\n"); }
void NO() { std::cout << "NO\n"; }
#line 2 "/home/nok0/documents/programming/library/template/rep.hpp"

#define foa(v, a)                   for(auto &v : a)
#define repname(a, b, c, d, e, ...) e
#define rep(...)                    repname(__VA_ARGS__, rep3, rep2, rep1, rep0)(__VA_ARGS__)
#define rep0(x)                     for(int rep_counter = 0; rep_counter < (x); ++rep_counter)
#define rep1(i, x)                  for(int i = 0; i < (x); ++i)
#define rep2(i, l, r)               for(int i = (l); i < (r); ++i)
#define rep3(i, l, r, c)            for(int i = (l); i < (r); i += (c))

#define repsname(a, b, c, ...) c
#define reps(...)              repsname(__VA_ARGS__, reps1, reps0)(__VA_ARGS__)
#define reps0(x)               for(int reps_counter = 1; reps_counter <= (x); ++reps_counter)
#define reps1(i, x)            for(int i = 1; i <= (x); ++i)

#define rrepname(a, b, c, ...) c
#define rrep(...)              rrepname(__VA_ARGS__, rrep1, rrep0)(__VA_ARGS__)
#define rrep0(x)               for(int rrep_counter = (x)-1; rrep_counter >= 0; --rrep_counter)
#define rrep1(i, x)            for(int i = (x)-1; i >= 0; --i)
#line 3 "/home/nok0/documents/programming/library/template/string_converter.hpp"

struct string_converter {
	char start = 0;
	char type(const char &c) const { return (islower(c) ? 'a' : isupper(c) ? 'A' :
		                                                    isdigit(c)     ? '0' :
		                                                                     0); }
	int convert(const char &c) {
		if(!start) start = type(c);
		return c - start;
	}
	int convert(const char &c, const std::string &chars) { return chars.find(c); }
	template <typename T>
	auto convert(const T &v) {
		std::vector<decltype(convert(v[0]))> ret;
		ret.reserve(size(v));
		for(auto &&e : v) ret.emplace_back(convert(e));
		return ret;
	}
	template <typename T>
	auto convert(const T &v, const std::string &chars) {
		std::vector<decltype(convert(v[0], chars))> ret;
		ret.reserve(size(v));
		for(auto &&e : v) ret.emplace_back(convert(e, chars));
		return ret;
	}
	int operator()(const char &v, char s = 0) {
		start = s;
		return convert(v);
	}
	int operator()(const char &v, const std::string &chars) { return convert(v, chars); }
	template <typename T>
	auto operator()(const T &v, char s = 0) {
		start = s;
		return convert(v);
	}
	template <typename T>
	auto operator()(const T &v, const std::string &chars) { return convert(v, chars); }
} toint;
#line 3 "/home/nok0/documents/programming/library/template/vector.hpp"

template <class T>
int lb(const std::vector<T> &a, const T x) { return std::distance((a).begin(), std::lower_bound((a).begin(), (a).end(), (x))); }
template <class T>
int ub(const std::vector<T> &a, const T x) { return std::distance((a).begin(), std::upper_bound((a).begin(), (a).end(), (x))); }
template <class T>
void UNIQUE(std::vector<T> &a) {
	std::sort(a.begin(), a.end());
	a.erase(std::unique(a.begin(), a.end()), a.end());
}
template <class T>
std::vector<T> press(std::vector<T> &a) {
	auto res = a;
	UNIQUE(res);
	for(auto &v : a)
		v = lb(res, v);
	return res;
}
#define SORTname(a, b, c, ...) c
#define SORT(...)              SORTname(__VA_ARGS__, SORT1, SORT0, ...)(__VA_ARGS__)
#define SORT0(a)               std::sort((a).begin(), (a).end())
#define SORT1(a, c)            std::sort((a).begin(), (a).end(), [](const auto x, const auto y) { return x c y; })
template <class T>
void ADD(std::vector<T> &a, const T x = 1) {
	for(auto &v : a) v += x;
}
template <class T>
void SUB(std::vector<T> &a, const T x = 1) {
	for(auto &v : a) v -= x;
}
template <class T>
struct cum_vector {
   public:
	cum_vector() = default;
	template <class U>
	cum_vector(const std::vector<U> &vec) : cum((int)vec.size() + 1) {
		for(int i = 0; i < (int)vec.size(); i++)
			cum[i + 1] = cum[i] + vec[i];
	}
	T prod(int l, int r) {
		return cum[r] - cum[l];
	}

   private:
	std::vector<T> cum;
};
std::vector<std::pair<char, int>> rle(const std::string &s) {
	const int n = s.size();
	std::vector<std::pair<char, int>> ret;
	ret.reserve(n);
	for(int l = 0; l < n;) {
		int r = l + 1;
		for(; r < n and s[l] == s[r]; r++) {}
		ret.emplace_back(s[l], r - l);
		l = r;
	}
	return ret;
}
template <class T>
std::vector<std::pair<T, int>> rle(const std::vector<T> &v) {
	const int n = v.size();
	std::vector<std::pair<T, int>> ret;
	ret.reserve(n);
	for(int l = 0; l < n;) {
		int r = l + 1;
		for(; r < n and v[l] == v[r]; r++) {}
		ret.emplace_back(v[l], r - l);
		l = r;
	}
	return ret;
}
std::vector<int> iota(int n) {
	std::vector<int> p(n);
	std::iota(p.begin(), p.end(), 0);
	return p;
}
#line 12 "/home/nok0/documents/programming/library/template/all"
using namespace std;
#line 4 "a.cpp"

void main_();
int main() {
	int t = 1;
	while(t--) main_();
}
using mint = atcoder::modint998244353;
factorial<mint> fac;

mint dp[4500][4500];

void naive(int n) {
	const mint tinv = mint(1) / 2;
	dp[0][0] = 1;
	rep(i, n * 2 + 2) {
		rep(j, n * 2 + 2) {
			dp[i + 2][j] += dp[i][j] * (i + 1) * i * tinv;
			dp[i][j + 2] += dp[i][j] * (j + 1) * j * tinv;
			dp[i + 1][j + 1] += dp[i][j] * (i * j + 1);
		}
	}
	rep(k, n * 2 + 1) {
		print(dp[k][n * 2 - k]);
	}
}


void main_() {
	factorial<mint>::set_size(5000);
	INT(n);
	naive(n);
	return;
}