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 N = 5005, mod = 998244353;
int n, s, c[N][N], fc[N], iv[N], p[N][N];
int qp(int a, int b) {
  int ans = 1;
  while (b) {
    if (b & 1) ans = 1ll * ans * a % mod;
    a = 1ll * a * a % mod;
    b >>= 1;
  }
  return ans;
}
int main() {
  scanf("%d", &n);
  for (int i = 0; i <= n; i++) {
    c[i][0] = 1;
    for (int j = 1; j <= i; j++)
      c[i][j] = (c[i - 1][j] + c[i - 1][j - 1]) % mod;
  }
  fc[0] = iv[0] = 1;
  for (int i = 1; i <= n; i++)
    fc[i] = 1ll * fc[i - 1] * i % mod, iv[i] = qp(fc[i], mod - 2);
  for (int i = 0; i <= n; i++) p[i][0] = 1;
  for (int i = 1; i <= n; i++)
    for (int j = 1; j <= i; j++)
      p[i][j] = (1ll * (i - j) * p[i - 1][j - 1] % mod +
                 1ll * (j + 1) * p[i - 1][j] % mod) %
                mod;
  for (int k = 0; k < n; k++) {
    s = 0;
    for (int i = max(k, 1); i <= n; i++)
      s = (s + 1ll * c[n][i] * p[i][k] % mod * fc[n - i] % mod) % mod;
    printf("%d ", s);
  }
  return 0;
}