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;
int n, f[5005][5005], jc[5005] = {1}, ny[5005] = {1};
int Power(int x, int y) {
  int ret = 1;
  while (y) {
    if (y & 1) ret = 1ll * ret * x % mod;
    x = 1ll * x * x % mod, y >>= 1;
  }
  return ret;
}
int main() {
  cin >> n, f[1][0] = jc[1] = ny[1] = 1;
  for (int i = 2; i <= n; i++) {
    f[i][0] = f[i - 1][0], jc[i] = 1ll * jc[i - 1] * i % mod,
    ny[i] = Power(jc[i], mod - 2);
    for (int j = 1; j < i; j++)
      f[i][j] =
          (1ll * (j + 1) * f[i - 1][j] + 1ll * (i - j) * f[i - 1][j - 1]) % mod;
  }
  for (int i = 1; i <= n; i++) {
    int ans = 0;
    for (int j = i; j <= n; j++)
      ans = (ans + 1ll * f[j][i - 1] * jc[n] % mod * ny[j]) % mod;
    cout << ans << ' ';
  }
  return 0;
}