D 宝石装箱

 

 

#include<bits/stdc++.h>
#define int long long
using namespace std;
const int N = 8e3 + 10;
const int mod = 998244353;
int a[N] , fac[N] , dp[N];
void init()
{
    fac[0] = 1;
    for(int i = 1 ; i <= N - 10 ; i ++) fac[i] = fac[i - 1] * i % mod;
}
signed main()
{
    ios::sync_with_stdio(false);
    init();
    int n , m = 0;
    cin >> n;
    for(int i = 1 ; i <= n ; i ++)
    {
        int x;
        cin >> x;
        a[x] ++ ;
    } 
    dp[0] = 1;
    for(int i = 1 ; i <= n ; i ++)
        for(int j = i ; j >= 1 ; j --)
            dp[j] += dp[j - 1] * a[i] , dp[j] %= mod;
    int ans = 0;
    for(int i = 0 ; i <= n ; i ++)
    {
        if(i & 1) ans -= dp[i] * fac[n - i] ; 
        else ans += dp[i] * fac[n - i];
        ans = (ans + mod) % mod;
    }
    cout << ans << '\n';
    return 0;
}