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, e[5001][5001], ans;
int fac[5001], ifac[5001];
inline int add(int x, int y) { return x + y < mod ? x + y : x + y - mod; }
inline int power(int a, int n) {
  int tp = 1;
  while (n) {
    if (n & 1) tp = 1ll * tp * a % mod;
    a = 1ll * a * a % mod, n >>= 1;
  }
  return tp;
}
int main() {
  cin >> n;
  fac[0] = 1;
  for (int i = 1; i <= n; i++) {
    fac[i] = 1ll * fac[i - 1] * i % mod, e[i][0] = 1;
    for (int j = 1; j < i; j++)
      e[i][j] =
          (1ll * (i - j) * e[i - 1][j - 1] + 1ll * (j + 1) * e[i - 1][j]) % mod;
  }
  ifac[n] = power(fac[n], mod - 2);
  for (int i = n - 1; ~i; i--) ifac[i] = 1ll * ifac[i + 1] * (i + 1) % mod;
  for (int i = 1; i <= n; i++) {
    ans = 0;
    for (int j = i; j <= n; j++)
      ans = (ans + 1ll * e[j][i - 1] * ifac[j]) % mod;
    printf("%d ", 1ll * ans * fac[n] % mod);
  }
}