#537917 (C++17) No.1193 Penguin Sequence

• 問題: No.1193 Penguin Sequence
• ユーザー: haruki_K
• 提出日時: 2020-08-22 15:49:20
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 401 ms / 2,000 ms
• コード長: 10,304 bytes
• コンパイル時間: 2,865 ms
• コンパイル使用メモリ: 213,304 KB
• 最終ジャッジ日時: 2025-01-13 09:51:52
• ジャッジサーバーID （参考情報）: judge1 / judge2

ファイルパターン	結果
sample	AC * 3
other	AC * 38

ソースコード

// >>> TEMPLATES
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
using i32 = int32_t;
using i64 = int64_t;
using u32 = uint32_t;
using u64 = uint64_t;
#define int ll
#define double ld
#define rep(i,n) for (int i = 0; i < (int)(n); i++)
#define rep1(i,n) for (int i = 1; i <= (int)(n); i++)
#define repR(i,n) for (int i = (int)(n)-1; i >= 0; i--)
#define rep1R(i,n) for (int i = (int)(n); i >= 1; i--)
#define loop(i,a,B) for (int i = a; i B; i++)
#define loopR(i,a,B) for (int i = a; i B; i--)
#define all(x) (x).begin(), (x).end()
#define allR(x) (x).rbegin(), (x).rend()
#define pb push_back
#define eb emplace_back
#define mp make_pair
#define fst first
#define snd second
template <class Int> auto constexpr inf = numeric_limits<Int>::max()/2-1;
auto constexpr INF32 = inf<int32_t>;
auto constexpr INF64 = inf<int64_t>;
auto constexpr INF   = inf<int>;
#ifdef LOCAL
#include "debug.hpp"
#else
#define dump(...) (void)(0)
#define say(x) (void)(0)
#define debug if (0)
#endif
template <class T> using pque_max = priority_queue<T>;
template <class T> using pque_min = priority_queue<T, vector<T>, greater<T> >;
template <class T, class = typename T::iterator, class = typename enable_if<!is_same<T, string>::value>::type>
ostream& operator<<(ostream& os, T const& v) { bool f = true; for (auto const& x : v) os << (f ? "" : " ") << x, f = false; return os; }
template <class T, class = typename T::iterator, class = typename enable_if<!is_same<T, string>::value>::type>
istream& operator>>(istream& is, T &v) { for (auto& x : v) is >> x; return is; }
template <class T, class S> ostream& operator<<(ostream& os, pair<T,S> const& p) { return os << "(" << p.first << ", " << p.second << ")"; }
template <class T, class S> istream& operator>>(istream& is, pair<T,S>& p) { return is >> p.first >> p.second; }
struct IOSetup { IOSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } iosetup;
template <class F> struct FixPoint : private F {
    constexpr FixPoint(F&& f) : F(forward<F>(f)) {}
    template <class... T> constexpr auto operator()(T&&... x) const { return F::operator()(*this, forward<T>(x)...); }
};
struct MakeFixPoint {
    template <class F> constexpr auto operator|(F&& f) const { return FixPoint<F>(forward<F>(f)); }
};
#define MFP MakeFixPoint()|
#define def(name, ...) auto name = MFP [&](auto &&name, __VA_ARGS__)
template <class T, size_t d> struct vec_impl {
    using type = vector<typename vec_impl<T,d-1>::type>;
    template <class... U> static type make_v(size_t n, U&&... x) { return type(n, vec_impl<T,d-1>::make_v(forward<U>(x)...)); }
};
template <class T> struct vec_impl<T,0> { using type = T; static type make_v(T const& x = {}) { return x; } };
template <class T, size_t d = 1> using vec = typename vec_impl<T,d>::type;
template <class T, size_t d = 1, class... Args> auto make_v(Args&&... args) { return vec_impl<T,d>::make_v(forward<Args>(args)...); }
template <class T> void quit(T const& x) { cout << x << endl; exit(0); }
template <class T, class U> constexpr bool chmin(T& x, U const& y) { if (x > y) { x = y; return true; } return false; }
template <class T, class U> constexpr bool chmax(T& x, U const& y) { if (x < y) { x = y; return true; } return false; }
template <class It> constexpr auto sumof(It b, It e) { return accumulate(b,e,typename iterator_traits<It>::value_type{}); }
template <class T> int sz(T const& x) { return x.size(); }
template <class C, class T> int lbd(C const& v, T const& x) {
    return lower_bound(v.begin(), v.end(), x)-v.begin();
}
template <class C, class T> int ubd(C const& v, T const& x) {
    return upper_bound(v.begin(), v.end(), x)-v.begin();
}
const int dx[] = { 1,0,-1,0 };
const int dy[] = { 0,1,0,-1 };
constexpr int popcnt(ll x) { return __builtin_popcountll(x); }
template <class Int> struct Random {
    mt19937_64 mt{random_device{}()};
    //mt19937_64 mt{(unsigned)time(0)};
    Int a,b; // [a,b]
    Random(Int a, Int b) : a(a), b(b) {}
    Int operator()() { return uniform_int_distribution<Int>(a,b)(mt); }
};
template <class Int> Int rand(Int a, Int b) { // [a,b]
    static mt19937_64 mt{random_device{}()};
    return uniform_int_distribution<Int>(a,b)(mt);
}
// <<<
// >>> BIT

struct BIT {
    int n;
    vector<int> v; // use v[1..n]
    BIT(int n = 0) : n(n), v(n+1) {}
    int size() const { return n; }
    int get(int i) const { return sum(i+1)-sum(i); }
    void set(int i, int x) { add(i,x-get(i)); }
    void add(int i, int x) {
        assert(0 <= i); assert(i < n);
        for (i++; i <= n; i += i&(-i)) v[i] += x;
    }
    int sum(int r) const { // [0,r)
        assert(0 <= r); assert(r <= n);
        int s = 0;
        for (int i = r; i > 0; i -= i&(-i)) s += v[i];
        return s;
    }
    int sum(int l, int r) const { // [l,r)
        return sum(r)-sum(l);
    }
    // lower_bound({sum(0),sum(1),...,sum(n)}, x)
    int lower_bound(int x) const {
        if (x <= 0) return 0;
        int s = 0, i = 0, w = 1;
        while (2*w <= n) w *= 2;
        for ( ; w; w >>= 1) {
            if (i+w <= n && s+v[i+w] < x) {
                s += v[i+w];
                i += w;
            }
        }
        return i+1;
    }
    int upper_bound(int x) const {
        int s = 0, i = 0, w = 1;
        while (2*w <= n) w *= 2;
        for ( ; w; w >>= 1) {
            if (i+w <= n && s+v[i+w] <= x) {
                s += v[i+w];
                i += w;
            }
        }
        return i+1;
    }
};

// <<<
// >>> modint
template <uint32_t md>
class modint {
    static_assert(md < (1u<<31), "");
    using M = modint;
    using i64 = int64_t;
    uint32_t x;
public:
    static constexpr uint32_t mod = md;
    constexpr modint(i64 x = 0) : x((x%=md) < 0 ? x+md : x) { }
    constexpr i64 val() const { return x; }
    constexpr explicit operator i64() const { return x; }
    constexpr bool operator==(M r) const { return x == r.x; }
    constexpr bool operator!=(M r) const { return x != r.x; }
    constexpr M operator+() const { return *this; }
    constexpr M operator-() const { return M()-*this; }
    constexpr M& operator+=(M r) { x += r.x; x = (x < md ? x : x-md); return *this; }
    constexpr M& operator-=(M r) { x += md-r.x; x = (x < md ? x : x-md); return *this; }
    constexpr M& operator*=(M r) { x = (uint64_t(x)*r.x)%md; return *this; }
    constexpr M& operator/=(M r) { return *this *= r.inv(); }
    constexpr M operator+(M r) const { return M(*this) += r; }
    constexpr M operator-(M r) const { return M(*this) -= r; }
    constexpr M operator*(M r) const { return M(*this) *= r; }
    constexpr M operator/(M r) const { return M(*this) /= r; }
    friend constexpr M operator+(i64 x, M y) { return M(x)+y; }
    friend constexpr M operator-(i64 x, M y) { return M(x)-y; }
    friend constexpr M operator*(i64 x, M y) { return M(x)*y; }
    friend constexpr M operator/(i64 x, M y) { return M(x)/y; }
    constexpr M inv() const { assert(x > 0); return pow(md-2); }
    constexpr M pow(i64 n) const {
        assert(not (x == 0 && n == 0));
        if (n < 0) return inv().pow(-n);
        M v = *this, r = 1;
        for (; n > 0; n >>= 1, v *= v) if (n&1) r *= v;
        return r;
    }
#ifdef LOCAL
    friend string to_s(M r) { return to_s(r.val(), mod); }
#endif
    friend ostream& operator<<(ostream& os, M r) { return os << r.val(); }
    friend istream& operator>>(istream& is, M &r) { i64 x; is >> x; r = x; return is; }
};
// <<<
constexpr int64_t MOD = 998244353;
//constexpr int64_t MOD = 1e9+7;
using mint = modint<MOD>;
mint sgn(int n) { return n%2 == 0 ? +1 : -1; }
// >>> mod table
template <uint32_t mod>
struct ModTable {
    vector<uint32_t> fact = {1,1}, finv = {1,1}, inv = {0,1};
    void calc(int n) {
        int old = fact.size();
        if (n < old) return;
        fact.resize(n+1);
        finv.resize(n+1);
        inv.resize(n+1);
        for (int i = old; i <= n; i++) {
            fact[i] = uint64_t(fact[i-1])*i % mod;
            inv[i] = mod - uint64_t(inv[mod%i])*(mod/i) % mod;
            finv[i] = uint64_t(finv[i-1])*inv[i] % mod;
        }
    }
};
ModTable<MOD> mod_tab;

modint<MOD> fact(int n) {
    assert(0 <= n);
    return mod_tab.calc(n), mod_tab.fact[n];
}
modint<MOD> finv(int n) {
    assert(0 <= n);
    return mod_tab.calc(n), mod_tab.finv[n];
}
modint<MOD> C(int n, int k) {
    if (n < 0 || k < 0 || n < k) return 0;
    return fact(n)*finv(k)*finv(n-k);
}
modint<MOD> P(int n, int k) {
    assert(k >= 0); assert(n >= k);
    return fact(n)*finv(n-k);
}
// <<<
// >>> coordinate compression
template <class T>
struct Compress {
    vector<T> v;
    bool ok = false;
    void add(T const& x) { ok = false; v.push_back(x); }
    template <class V>
    void add(V const& u) { ok = false; copy(all(u), back_inserter(v)); }
    template <class... Ts>
    void add(Ts const&... xs) { (int[]){(add(xs),0)...}; }
    void init() { sort(all(v)); v.erase(unique(all(v)), v.end()); ok = true; }
    int size() const { return v.size(); }
    T operator[](int i) const { assert(ok); return v[i]; }
    int find(T const& x) const { assert(ok); auto it = lower_bound(all(v),x); assert(*it == x); return it-v.begin(); }
    void set(T& x) const { x = find(x); }
    template <class V>
    void set(V& u) const { for (auto &x : u) x = find(x); }
    template <class... Ts>
    void set(Ts&... xs) const { (int[]){(set(xs),0)...}; }
};
// <<<

int calc(vector<int> a) {
    Compress<int> Z;
    Z.add(a); Z.init(); Z.set(a);
    dump(a);

    BIT bit(Z.size());
    int ans = 0;
    for (int x : a) {
        ans += bit.sum(x+1,Z.size());
        bit.add(x,1);
    }

    return ans;
}

int32_t main() {
    int n; cin >> n;
    vector<int> a(n); cin >> a;
    dump(n,a);

    mint ans = 0;

    mint total = 1;
    rep1 (i,n) total *= C(n,i);
    dump(total);

    const int inv = calc(a);
    dump(inv);

    rep1 (i,n) ans += total * C(n-2,i-2)/C(n,i) * inv;
    dump(ans);

    mint s1 = 0, s2 = 0;
    rep1 (i,n) {
        mint x = C(n-1,i-1)/C(n,i);
        s1 += x;
        s2 += x*x;
    }
    mint A = total * (s1*s1-s2)/2;

    mint B = 0;
    map<int,int> cnt;
    rep (i,n) cnt[a[i]]++;
    B += C(n,2);
    for (auto [_,num] : cnt) B -= C(num,2);

    dump(A,B);
    ans += A * B;

    cout << ans << endl;

}