Problem: Note that the only differences between easy and hard versions are the constraints on n and the time limit. You can make hacks only if all versions are solved.

Slime is interested in sequences. He defined good positive integer sequences p of length n as follows:

  * For each k>1 that presents in p, there should be at least one pair of indices i,j, such that 1 ≤ i < j ≤ n, p_i = k - 1 and p_j = k.



For the given integer n, the set of all good sequences of length n is s_n. For the fixed integer k and the sequence p, let f_p(k) be the number of times that k appears in p. For each k from 1 to n, Slime wants to know the following value:

$$$\left(∑_{p∈ s_n} f_p(k)\right)\ mod\ 998 244 353$$$

Input

The first line contains one integer n\ (1≤ n≤ 5000).

Output

Print n integers, the i-th of them should be equal to \left(∑_{p∈ s_n} f_p(i)\right)\ mod\ 998 244 353.

Examples

Input


2


Output


3 1 


Input


3


Output


10 7 1 


Input


1


Output


1 

Note

In the first example, s=\{[1,1],[1,2]\}.

In the second example, s=\{[1,1,1],[1,1,2],[1,2,1],[1,2,2],[2,1,2],[1,2,3]\}.

In the third example, s=\{[1]\}.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int MOD = 998244353;
const int MX = 2e5 + 5;
const long long INF = 1e18;
const long double PI = acos((long double)-1);
const int xd[4] = {1, 0, -1, 0}, yd[4] = {0, 1, 0, -1};
template <class T>
bool ckmin(T& a, const T& b) {
  return b < a ? a = b, 1 : 0;
}
template <class T>
bool ckmax(T& a, const T& b) {
  return a < b ? a = b, 1 : 0;
}
int pct(int x) { return __builtin_popcount(x); }
int bit(int x) { return 31 - __builtin_clz(x); }
int cdiv(int a, int b) { return a / b + !(a < 0 || a % b == 0); }
template <class A>
void re(complex<A>& c);
template <class A, class B>
void re(pair<A, B>& p);
template <class A>
void re(vector<A>& v);
template <class A, size_t SZ>
void re(array<A, SZ>& a);
template <class T>
void re(T& x) {
  cin >> x;
}
void re(double& d) {
  string t;
  re(t);
  d = stod(t);
}
void re(long double& d) {
  string t;
  re(t);
  d = stold(t);
}
template <class H, class... T>
void re(H& h, T&... t) {
  re(h);
  re(t...);
}
template <class A>
void re(complex<A>& c) {
  A a, b;
  re(a, b);
  c = {a, b};
}
template <class A, class B>
void re(pair<A, B>& p) {
  re(p.first, p.second);
}
template <class A>
void re(vector<A>& x) {
  for (auto& a : x) re(a);
}
template <class A, size_t SZ>
void re(array<A, SZ>& x) {
  for (auto& a : x) re(a);
}
template <class A, class B>
string to_string(pair<A, B> p);
template <class A>
string to_string(complex<A> c) {
  return to_string(make_pair(c.real(), c.imag()));
}
string to_string(bool b) { return b ? "true" : "false"; }
string to_string(char c) {
  string second = "";
  second += c;
  return second;
}
string to_string(string second) { return second; }
string to_string(const char* second) { return (string)second; }
string to_string(vector<bool> v) {
  bool fst = 1;
  string res = "{";
  for (int i = (0); i < ((int)v.size()); ++i) {
    if (!fst) res += ", ";
    fst = 0;
    res += to_string(v[i]);
  }
  res += "}";
  return res;
}
template <size_t SZ>
string to_string(bitset<SZ> b) {
  string res = "";
  for (int i = (0); i < (SZ); ++i) res += char('0' + b[i]);
  return res;
}
template <class T>
string to_string(T v) {
  bool fst = 1;
  string res = "{";
  for (const auto& x : v) {
    if (!fst) res += ", ";
    fst = 0;
    res += to_string(x);
  }
  res += "}";
  return res;
}
template <class A, class B>
string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
template <class A>
void pr(A x) {
  cout << to_string(x);
}
template <class H, class... T>
void pr(const H& h, const T&... t) {
  pr(h);
  pr(t...);
}
void ps() { pr("\n"); }
template <class H, class... T>
void ps(const H& h, const T&... t) {
  pr(h);
  if (sizeof...(t)) pr(" ");
  ps(t...);
}
void DBG() { cerr << "]" << endl; }
template <class H, class... T>
void DBG(H h, T... t) {
  cerr << to_string(h);
  if (sizeof...(t)) cerr << ", ";
  DBG(t...);
}
void setIn(string second) { freopen(second.c_str(), "r", stdin); }
void setOut(string second) { freopen(second.c_str(), "w", stdout); }
void unsyncIO() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
}
void setIO(string second = "") {
  unsyncIO();
  if ((int)second.size()) {
    setIn(second + ".in"), setOut(second + ".out");
  }
}
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count());
struct mi {
  typedef decay<decltype(MOD)>::type T;
  T v;
  explicit operator T() const { return v; }
  mi() { v = 0; }
  mi(long long _v) {
    v = (-MOD < _v && _v < MOD) ? _v : _v % MOD;
    if (v < 0) v += MOD;
  }
  friend bool operator==(const mi& a, const mi& b) { return a.v == b.v; }
  friend bool operator!=(const mi& a, const mi& b) { return !(a == b); }
  friend bool operator<(const mi& a, const mi& b) { return a.v < b.v; }
  friend void re(mi& a) {
    long long x;
    re(x);
    a = mi(x);
  }
  friend string to_string(mi a) { return to_string(a.v); }
  mi& operator+=(const mi& m) {
    if ((v += m.v) >= MOD) v -= MOD;
    return *this;
  }
  mi& operator-=(const mi& m) {
    if ((v -= m.v) < 0) v += MOD;
    return *this;
  }
  mi& operator*=(const mi& m) {
    v = (long long)v * m.v % MOD;
    return *this;
  }
  mi& operator/=(const mi& m) { return (*this) *= inv(m); }
  friend mi pow(mi a, long long p) {
    mi ans = 1;
    assert(p >= 0);
    for (; p; p /= 2, a *= a)
      if (p & 1) ans *= a;
    return ans;
  }
  friend mi inv(const mi& a) {
    assert(a.v != 0);
    return pow(a, MOD - 2);
  }
  mi operator-() const { return mi(-v); }
  mi& operator++() { return *this += 1; }
  mi& operator--() { return *this -= 1; }
  friend mi operator+(mi a, const mi& b) { return a += b; }
  friend mi operator-(mi a, const mi& b) { return a -= b; }
  friend mi operator*(mi a, const mi& b) { return a *= b; }
  friend mi operator/(mi a, const mi& b) { return a /= b; }
};
vector<vector<mi> > comb;
void genComb(int SZ) {
  comb.assign(SZ, vector<mi>(SZ));
  comb[0][0] = 1;
  for (int i = (1); i < (SZ); ++i)
    for (int j = (0); j < (i + 1); ++j)
      comb[i][j] = comb[i - 1][j] + (j ? comb[i - 1][j - 1] : 0);
}
const int mx = 5005;
mi Eul[mx + 5][mx + 5];
mi ans[mx + 5];
mi fac[mx + 5];
int main() {
  setIO();
  int n;
  cin >> n;
  Eul[1][1] = 1;
  for (int i = 2; i <= mx; i++) {
    for (int j = 1; j <= mx; j++) {
      Eul[i][j] = mi(j) * Eul[i - 1][j] + mi(i - j + 1) * Eul[i - 1][j - 1];
    }
  }
  fac[0] = 1;
  for (int i = 1; i <= mx; i++) {
    fac[i] = mi(i) * fac[i - 1];
  }
  genComb(5005);
  int N = n + 1;
  for (int i = 1; i <= N; i++) {
    for (int j = i; j <= N - 1; j++) {
      ans[i] += Eul[j][i] * fac[N - 1 - j] * comb[N - 1][j];
    }
  }
  for (int i = 1; i <= n; i++) {
    cout << ans[i].v << " ";
  }
}