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;
inline bool cmin(int &x, int y) { return x > y ? x = y, 1 : 0; }
inline bool cmax(int &x, int y) { return x < y ? x = y, 1 : 0; }
const int _ = 5055, mod = 998244353;
int N, fac[_], inv[_];
int f[_][_];
int ans[_];
inline int dec(int x) { return x >= mod ? x - mod : x; }
inline int Pow(int x, int y = mod - 2) {
  int ans(1);
  for (; y; y >>= 1, x = (long long)x * x % mod)
    if (y & 1) ans = (long long)ans * x % mod;
  return ans;
}
int main() {
  cin >> N;
  fac[0] = fac[1] = inv[0] = 1;
  for (int i = 2, I = N; i <= I; ++i) fac[i] = 1ll * fac[i - 1] * i % mod;
  inv[N] = Pow(fac[N]);
  for (int i = N, I = 2; i >= I; --i) inv[i - 1] = 1ll * inv[i] * i % mod;
  f[0][0] = 1;
  for (int i = 1, I = N; i <= I; ++i)
    for (int j = 1, I = i; j <= I; ++j)
      f[i][j] =
          (1ll * f[i - 1][j] * j + 1ll * f[i - 1][j - 1] * (i - j + 1)) % mod;
  for (int i = 1, I = N; i <= I; ++i)
    for (int j = 1, I = N; j <= I; ++j)
      ans[j] = (ans[j] + 1ll * f[i][j] * inv[i]) % mod;
  for (int i = 1, I = N; i <= I; ++i)
    cout << 1ll * ans[i] * fac[N] % mod << " ";
  return 0;
}