#1163977 (C++17) No.3540 Arise

• 問題: No.3540 Arise
• ユーザー: i_am_noob
• 提出日時: 2026-05-08 23:15:17
• 言語: C++17 (gcc 15.2.0 + boost 1.89.0)
• 結果: AC
• 実行時間: 205 ms / 2,500 ms
• コード長: 9,172 bytes
• コンパイル時間: 2,627 ms
• コンパイル使用メモリ: 232,716 KB
• 実行使用メモリ: 6,400 KB
• 最終ジャッジ日時: 2026-05-08 23:15:29
• 合計ジャッジ時間: 6,723 ms
• ジャッジサーバーID （参考情報）: judge3_1 / judge1_1

サブタスク	配点	結果
サブタスク1	30 %	AC * 19
サブタスク2	70 %	AC * 22
合計	3.5 * 100% = 350 点

ソースコード

// BEGIN: main.cpp
#line 1 "main.cpp"
#include<bits/stdc++.h>
using namespace std;

#define all(a) a.begin(),a.end()
#define pb push_back
#define sz(a) ((int)a.size())

using ll=long long;
using u32=unsigned int;
using u64=unsigned long long;
using i128=__int128;
using u128=unsigned __int128;
using f128=__float128;

using pii=pair<int,int>;
using pll=pair<ll,ll>;

template<typename T> using vc=vector<T>;
template<typename T> using vvc=vc<vc<T>>;
template<typename T> using vvvc=vc<vvc<T>>;

using vi=vc<int>;
using vll=vc<ll>;
using vvi=vc<vi>;
using vvll=vc<vll>;

#define vv(type,name,n,...) \
    vector<vector<type>> name(n,vector<type>(__VA_ARGS__))
#define vvv(type,name,n,m,...) \
    vector<vector<vector<type>>> name(n,vector<vector<type>>(m,vector<type>(__VA_ARGS__)))

template<typename T> using min_heap=priority_queue<T,vector<T>,greater<T>>;
template<typename T> using max_heap=priority_queue<T>;

// https://trap.jp/post/1224/
#define rep1(n) for(ll i=0; i<(ll)(n); ++i)
#define rep2(i,n) for(ll i=0; i<(ll)(n); ++i)
#define rep3(i,a,b) for(ll i=(ll)(a); i<(ll)(b); ++i)
#define rep4(i,a,b,c) for(ll i=(ll)(a); i<(ll)(b); i+=(c))
#define cut4(a,b,c,d,e,...) e
#define rep(...) cut4(__VA_ARGS__,rep4,rep3,rep2,rep1)(__VA_ARGS__)
#define per1(n) for(ll i=((ll)n)-1; i>=0; --i)
#define per2(i,n) for(ll i=((ll)n)-1; i>=0; --i)
#define per3(i,a,b) for(ll i=((ll)a)-1; i>=(ll)(b); --i)
#define per4(i,a,b,c) for(ll i=((ll)a)-1; i>=(ll)(b); i-=(c))
#define per(...) cut4(__VA_ARGS__,per4,per3,per2,per1)(__VA_ARGS__)
#define rep_subset(i,s) for(ll i=(s); i>=0; i=(i==0?-1:(i-1)&(s)))

template<typename T, typename S> constexpr T ifloor(const T a, const S b){return a/b-(a%b&&(a^b)<0);}
template<typename T, typename S> constexpr T iceil(const T a, const S b){return ifloor(a+b-1,b);}

template<typename T>
void sort_unique(vector<T> &vec){
    sort(vec.begin(),vec.end());
    vec.resize(unique(vec.begin(),vec.end())-vec.begin());
}

template<typename T, typename S> constexpr bool chmin(T &a, const S b){if(a>b) return a=b,true; return false;}
template<typename T, typename S> constexpr bool chmax(T &a, const S b){if(a<b) return a=b,true; return false;}

template<typename T, typename S> istream& operator >> (istream& i, pair<T,S> &p){return i >> p.first >> p.second;}
template<typename T, typename S> ostream& operator << (ostream& o, const pair<T,S> &p){return o << p.first << ' ' << p.second;}

#ifdef i_am_noob
#define bug(...) cerr << "#" << __LINE__ << ' ' << #__VA_ARGS__ << "- ", _do(__VA_ARGS__)
template<typename T> void _do(vector<T> x){for(auto i: x) cerr << i << ' ';cerr << "\n";}
template<typename T> void _do(set<T> x){for(auto i: x) cerr << i << ' ';cerr << "\n";}
template<typename T> void _do(unordered_set<T> x){for(auto i: x) cerr << i << ' ';cerr << "\n";}
template<typename T> void _do(T && x) {cerr << x << endl;}
template<typename T, typename ...S> void _do(T && x, S&&...y) {cerr << x << ", "; _do(y...);}
#else
#define bug(...) 777771449
#endif

template<typename T> void print(vector<T> x){for(auto i: x) cout << i << ' ';cout << "\n";}
template<typename T> void print(set<T> x){for(auto i: x) cout << i << ' ';cout << "\n";}
template<typename T> void print(unordered_set<T> x){for(auto i: x) cout << i << ' ';cout << "\n";}
template<typename T> void print(T && x) {cout << x << "\n";}
template<typename T, typename... S> void print(T && x, S&&... y) {cout << x << ' ';print(y...);}

template<typename T> istream& operator >> (istream& i, vector<T> &vec){for(auto &x: vec) i >> x; return i;}

vvi read_graph(int n, int m, int base=1){
    vvi adj(n);
    for(int i=0,u,v; i<m; ++i){
        cin >> u >> v,u-=base,v-=base;
        adj[u].pb(v),adj[v].pb(u);
    }
    return adj;
}

vvi read_tree(int n, int base=1){return read_graph(n,n-1,base);}

template<typename T, typename S> pair<T,S> operator + (const pair<T,S> &a, const pair<T,S> &b){return {a.first+b.first,a.second+b.second};}

template<typename T> constexpr T inf=0;
template<> constexpr int inf<int> = 0x3f3f3f3f;
template<> constexpr ll inf<ll> = 0x3f3f3f3f3f3f3f3f;

template<typename T> vector<T> operator += (vector<T> &a, int val){for(auto &i: a) i+=val; return a;}

template<typename T> T isqrt(const T &x){T y=sqrt(x+2); while(y*y>x) y--; return y;}

#define ykh mt19937 rng(chrono::steady_clock::now().time_since_epoch().count())

// BEGIN: library/mod/modint.hpp
#line 1 "library/mod/modint.hpp"

// BEGIN: library/nt/extgcd.hpp
#line 1 "library/nt/extgcd.hpp"

// ax + by = gcd(a,b), {gcd(a,b),x,y}
template<typename T>
array<T,3> extgcd(T a, T b){
    T x1=1,y1=0,x2=0,y2=1;
    while(b!=0){
        T q=a/b;
        a%=b;
        swap(a,b);
        T x3=x1-x2*q,y3=y1-y2*q;
        x1=x2,y1=y2,x2=x3,y2=y3;
    }
    return {a,x1,y1};
}

template<typename T>
T modinv(T x, T m){
    auto [g,val1,val2]=extgcd<T>(x,m);
    assert(g==1);
    if(val1<0) val1+=m;
    return val1;
}// END: library/nt/extgcd.hpp
#line 4 "library/mod/modint.hpp"

template<int64_t m, bool is_prime, typename word, typename dword>
struct Modint{
    using mint=Modint;

    static constexpr word mod=m;

    static constexpr word get_mod(){
        return mod;
    }

    word x;
    constexpr Modint():x(0){}

    constexpr Modint(int _x):x((_x%m+m)%m){}
    constexpr Modint(ll _x):x((_x%m+m)%m){}
    constexpr Modint(__int128 _x):x((_x%m+m)%m){}
    constexpr Modint(uint32_t _x):x(_x%m){}
    constexpr Modint(uint64_t _x):x(_x%m){}
    constexpr Modint(unsigned __int128 _x):x(_x%m){}

    mint &operator += (const mint &o){
        if((x+=o.x)>=mod) x-=mod;
        return *this;
    }
    mint &operator -= (const mint &o){
        if((x-=o.x)<0) x+=mod;
        return *this;
    }
    mint &operator *= (const mint &o){
        x=((dword)x)*o.x%mod;
        return *this;
    }
    mint &operator /= (const mint &o){
        return (*this)*=o.inv();
    }
    mint operator + (const mint &o) const {return mint(*this)+=o;}
    mint operator - (const mint &o) const {return mint(*this)-=o;}
    mint operator * (const mint &o) const {return mint(*this)*=o;}
    mint operator / (const mint &o) const {return mint(*this)/=o;}
    mint operator - () const {return mint(0)-*this;}
    mint pow(int64_t n) const {
        assert(n>=0);
        mint res=1,b=*this;
        for(; n; n>>=1,b*=b) if(n&1) res*=b;
        return res;
    }
    inline mint inv1() const {
        return pow(m-2);
    }
    inline mint inv2() const {
        auto [g,val1,val2]=extgcd<word>(x,mod);
        assert(g==1);
        return mint(val1);
    }
    mint inv() const {
        if(is_prime) return inv1();
        return inv2();
    }

    bool operator == (const mint &o) const {
        return x==o.x;
    }
    bool operator != (const mint &o) const {
        return x!=o.x;
    }

    friend istream& operator >> (istream& is, mint &b){
        ll y;
        is >> y;
        b=mint(y);
        return is;
    }
    friend ostream& operator << (ostream& os, const mint &b){
        return os << b.x;
    }

    // v2(m-1), 2^(v2(m-1))-th root
    static constexpr pair<int,int> ntt_data(){
        if(m==998244353) return {23,31};
        if(m==167772161) return {25,17};
        if(m==469762049) return {26,30};
        if(m==754974721) return {24,362};
        return {-1,-1};
    }

    static constexpr bool can_ntt(){
        return ntt_data().first>=0;
    }
};

template<int64_t m, bool is_prime=true> using modint=Modint<m,is_prime,int32_t,int64_t>;
template<int64_t m, bool is_prime=true> using modint_64=Modint<m,is_prime,int64_t,__int128>;// END: library/mod/modint.hpp
#line 107 "main.cpp"
using mint=modint<998244353>;
//using mint=modint<1000000007>;

void mango(){
    int n; cin >> n;
    vi a(n); cin >> a;
    sort(all(a));
    int m=a[0];
    vc<mint> dp1(n+1);
    dp1[0]=1;
    vc<mint> ainv(n);
    rep(n) ainv[i]=mint(a[i]).inv();
    rep(n){
        vc<mint> ndp1(n+1);
        rep(j,n+1) if(dp1[j]!=mint(0)){
            mint nw=mint(m-j)*ainv[i];
            ndp1[j+1]+=dp1[j]*nw;
            ndp1[j]+=dp1[j]*(mint(1)-nw);
        }
        dp1=ndp1;
    }
    mint res1;
    rep(i,1,n+1){
        res1+=dp1[i]*(m+1)/(i+1);
    }
    vv(mint,dp2,n+1,2);
    dp2[0][0]=1;
    rep(n){
        vv(mint,ndp2,n+1,2);
        rep(j,n+1){
            mint nw=mint(m-j)*ainv[i];
            rep(t,2) if(dp2[j][t]!=mint(0)){
                ndp2[j+1][t]+=dp2[j][t]*nw;
                ndp2[j][t]+=dp2[j][t]*(mint(1)-nw-(t?ainv[i]:mint(0)));
            }
            if(dp2[j][0]!=mint(0)){
                mint p=mint(j)*ainv[i];
                ndp2[j][1]+=dp2[j][0]*p*mint(a[i]);
                ndp2[j+1][1]+=dp2[j][0]*nw*mint(a[i]);
            }
        }
        dp2=ndp2;
        rep(j,n+1) rep(t,2) if(dp2[j][t]!=mint(0)){
            //bug(i,j,t,dp2[j][t]);
        }
    }
    mint res2;
    rep(i,1,n+1){
        //bug(i,dp2[i][1]);
        res2+=dp2[i][1]/mint(i);
    }
    mint base;
    rep(n) base+=mint(a[i]+1)/mint(2);
    bug(base,res1,res2);
    print(base+res2-res1);
}

signed main(){
    ios_base::sync_with_stdio(0),cin.tie(0);
    cout << fixed << setprecision(20);
    int t=1;
    //cin >> t;
    while(t--) mango();
}
// END: main.cpp