记录编号	610011	评测结果	AAAAAAAAAA
题目名称	分组游戏	最终得分	100
用户昵称	梦那边的美好TE	是否通过	通过
代码语言	C++	运行时间	2.420 s
提交时间	2025-12-06 14:56:57	内存使用	18.02 MiB

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <vector>
using namespace std;
const int mod = 998244353;
const int G = 3;
const int Gi = 332748118;
int qpow(int a, int b) {
    int res = 1;
    while (b) {
        if (b & 1) res = 1ll * res * a % mod;
        a = 1ll * a * a % mod;
        b >>= 1;
    }
    return res;
}
void ntt(vector<int>& a, int len, int type) {
    for (int i = 1, j = len >> 1; i < len - 1; i++) {
        if (i < j) swap(a[i], a[j]);
        int k = len >> 1;
        while (j >= k) {
            j -= k;
            k >>= 1;
        }
        if (j < k) j += k;
    }
    for (int h = 2; h <= len; h <<= 1) {
        int wn = qpow(type == 1 ? G : Gi, (mod - 1) / h);
        for (int j = 0; j < len; j += h) {
            int w = 1;
            for (int k = j; k < j + h / 2; k++) {
                int u = a[k];
                int t = 1ll * w * a[k + h / 2] % mod;
                a[k] = (u + t) % mod;
                a[k + h / 2] = (u - t + mod) % mod;
                w = 1ll * w * wn % mod;
            }
        }
    }
    if (type == -1) {
        int inv = qpow(len, mod - 2);
        for (int i = 0; i < len; i++) {
            a[i] = 1ll * a[i] * inv % mod;
        }
    }
}
vector<int> multiply(const vector<int>& a, const vector<int>& b) {
    int len = 1;
    int n = a.size(), m = b.size();
    while (len < n + m) len <<= 1;
    vector<int> A(len, 0), B(len, 0);
    for (int i = 0; i < n; i++) A[i] = a[i];
    for (int i = 0; i < m; i++) B[i] = b[i];
    ntt(A, len, 1);
    ntt(B, len, 1);
    for (int i = 0; i < len; i++) {
        A[i] = 1ll * A[i] * B[i] % mod;
    }
    ntt(A, len, -1);
    A.resize(n + m - 1);
    return A;
}
const int N = 2005;
int n, a[N];
int fac[N], invfac[N];
int dp[N][N], f[N][N];
void init() {
    fac[0] = 1;
    for (int i = 1; i <= n; i++) {
        fac[i] = 1ll * fac[i-1] * i % mod;
    }
    invfac[n] = qpow(fac[n], mod - 2);
    for (int i = n-1; i >= 0; i--) {
        invfac[i] = 1ll * invfac[i+1] * (i+1) % mod;
    }
}
int main() {
    freopen("gamem.in", "r", stdin);
    freopen("gamem.out", "w", stdout);
    scanf("%d", &n);
    for (int i = 1; i <= n; i++) {
        scanf("%d", a+i);
    }
    sort(a+1, a+1+n, greater<int>());
    init();
    dp[1][0] = 1;
    f[1][0] = dp[1][0];
    for (int i = 1; i <= n; i++) {
        for (int j = 0; j < i; j++) {
            f[i+1][j+1] = (f[i+1][j+1] + 1ll * f[i][j] * (j+1) % mod) % mod;
        }
        int limit = min(a[i] - 1, i - 1);
        if (limit >= 0) {
            vector<int> A(i, 0);
            for (int j = 0; j < i; j++) {
                A[j] = f[i][j];
            }
            vector<int> B(limit + 1, 0);
            for (int k = 0; k <= limit; k++) {
                B[limit - k] = invfac[k];
            }
            vector<int> C = multiply(A, B);
            for (int j = 0; j < i; j++) {
                if (j + limit < (int)C.size()) {
                    f[i+1][j] = (f[i+1][j] + C[j + limit]) % mod;
                }
            }
        }
        for (int j = 0; j <= i; j++) {
            dp[i+1][j] = 1ll * f[i+1][j] * invfac[j] % mod;
        }
    }
    printf("%d\n", dp[n+1][0]);
    return 0;
}