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 = 5050;
const long long Mod = 998244353;
int n;
int inv[N], fac[N], ifac[N];
int f[N][N], ans[N];
int binom(int n, int m) {
  return 1LL * fac[n] * ifac[m] % Mod * ifac[n - m] % Mod;
}
int main() {
  scanf("%d", &n);
  inv[1] = fac[1] = ifac[1] = ifac[0] = fac[0] = 1;
  for (int i = 2; i <= n; ++i) {
    inv[i] = 1LL * (Mod - Mod / i) * inv[Mod % i] % Mod;
    fac[i] = 1LL * fac[i - 1] * i % Mod;
    ifac[i] = 1LL * ifac[i - 1] * inv[i] % Mod;
  }
  f[1][0] = 1;
  for (int i = 2; i <= n; ++i) {
    f[i][0] = 1;
    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)
    for (int j = 1; j <= i; ++j)
      ans[j] =
          (ans[j] + 1LL * binom(n, i) * f[i][j - 1] % Mod * fac[n - i] % Mod) %
          Mod;
  for (int i = 1; i <= n; ++i) printf("%d ", ans[i]);
  return 0;
}