#include "bits/stdc++.h" using namespace std; #define int long long #define REP(i, n) for (int i = 0; i < (int)n; ++i) #define RREP(i, n) for (int i = (int)n - 1; i >= 0; --i) #define FOR(i, s, n) for (int i = s; i < (int)n; ++i) #define RFOR(i, s, n) for (int i = (int)n - 1; i >= s; --i) #define ALL(a) a.begin(), a.end() #define IN(a, x, b) (a <= x && x < b) templateistream&operator >>(istream&is,vector&vec){for(T&x:vec)is>>x;return is;} templateinline void out(T t){cout << t << "\n";} templateinline void out(T t,Ts... ts){cout << t << " ";out(ts...);} templateinline bool CHMIN(T&a,T b){if(a > b){a = b;return true;}return false;} templateinline bool CHMAX(T&a,T b){if(a < b){a = b;return true;}return false;} constexpr int INF = 1e18; template struct Fp { long long val; constexpr Fp(long long v = 0) noexcept : val(v % MOD) { if (val < 0) val += MOD; } constexpr int getmod() { return MOD; } constexpr Fp operator - () const noexcept { return val ? MOD - val : 0; } constexpr Fp operator + (const Fp& r) const noexcept { return Fp(*this) += r; } constexpr Fp operator - (const Fp& r) const noexcept { return Fp(*this) -= r; } constexpr Fp operator * (const Fp& r) const noexcept { return Fp(*this) *= r; } constexpr Fp operator / (const Fp& r) const noexcept { return Fp(*this) /= r; } constexpr Fp& operator += (const Fp& r) noexcept { val += r.val; if (val >= MOD) val -= MOD; return *this; } constexpr Fp& operator -= (const Fp& r) noexcept { val -= r.val; if (val < 0) val += MOD; return *this; } constexpr Fp& operator *= (const Fp& r) noexcept { val = val * r.val % MOD; return *this; } constexpr Fp& operator /= (const Fp& r) noexcept { long long a = r.val, b = MOD, u = 1, v = 0; while (b) { long long t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } val = val * u % MOD; if (val < 0) val += MOD; return *this; } constexpr bool operator == (const Fp& r) const noexcept { return this->val == r.val; } constexpr bool operator != (const Fp& r) const noexcept { return this->val != r.val; } friend constexpr ostream& operator << (ostream &os, const Fp& x) noexcept { return os << x.val; } friend constexpr Fp modpow(const Fp &a, long long n) noexcept { if (n == 0) return 1; auto t = modpow(a, n / 2); t = t * t; if (n & 1) t = t * a; return t; } }; template struct BiCoef { vector fact_, inv_, finv_; constexpr BiCoef() {} constexpr BiCoef(int n) noexcept : fact_(n, 1), inv_(n, 1), finv_(n, 1) { init(n); } constexpr void init(int n) noexcept { fact_.assign(n, 1), inv_.assign(n, 1), finv_.assign(n, 1); int MOD = fact_[0].getmod(); for(int i = 2; i < n; i++){ fact_[i] = fact_[i-1] * i; inv_[i] = -inv_[MOD%i] * (MOD/i); finv_[i] = finv_[i-1] * inv_[i]; } } constexpr T com(int n, int k) const noexcept { if (n < k || n < 0 || k < 0) return 0; return fact_[n] * finv_[k] * finv_[n-k]; } constexpr T P(int n, int k) const noexcept { if (n < k || n < 0 || k < 0) return 0; return fact_[n] * finv_[n-k]; } constexpr T fact(int n) const noexcept { if (n < 0) return 0; return fact_[n]; } constexpr T inv(int n) const noexcept { if (n < 0) return 0; return inv_[n]; } constexpr T finv(int n) const noexcept { if (n < 0) return 0; return finv_[n]; } }; // const int MOD = 1000000007; const int MOD = 998244353; using mint = Fp; BiCoef bc; // bc.init(500050); template struct SegmentTree{ using F = function; int n; F f; T ti; vector dat; SegmentTree(){} SegmentTree(F f,T ti):f(f),ti(ti){} void init(int n_){ n=1; while(n &v){ int n_=v.size(); init(n_); for(int i=0;i>=1) dat[k]=f(dat[(k<<1)|0],dat[(k<<1)|1]); } T query(int a,int b){ if(a>=b) return ti; T vl=ti,vr=ti; for(int l=a+n,r=b+n;l>=1,r>>=1) { if(l&1) vl=f(vl,dat[l++]); if(r&1) vr=f(dat[--r],vr); } return f(vl,vr); } template int find(int st,C &check,T &acc,int k,int l,int r){ if(l+1==r){ acc=f(acc,dat[k]); return check(acc)?k-n:-1; } int m=(l+r)>>1; if(m<=st) return find(st,check,acc,(k<<1)|1,m,r); if(st<=l&&!check(f(acc,dat[k]))){ acc=f(acc,dat[k]); return -1; } int vl=find(st,check,acc,(k<<1)|0,l,m); if(~vl) return vl; return find(st,check,acc,(k<<1)|1,m,r); } template int find(int st,C &check){ T acc=ti; return find(st,check,acc,1,0,n); } //アウトの条件を渡す }; template< typename T > struct Compress { vector< T > xs; Compress() = default; Compress(const vector< T > &vs) { add(vs); } Compress(const initializer_list< vector< T > > &vs) { for(auto &p : vs) add(p); } void add(const vector< T > &vs) { copy(begin(vs), end(vs), back_inserter(xs)); } void add(const T &x) { xs.emplace_back(x); } void build() { sort(begin(xs), end(xs)); xs.erase(unique(begin(xs), end(xs)), end(xs)); } vector< int > get(const vector< T > &vs) const { vector< int > ret; transform(begin(vs), end(vs), back_inserter(ret), [&](const T &x) { return lower_bound(begin(xs), end(xs), x) - begin(xs); }); return ret; } int get(const T &x) const { return lower_bound(begin(xs), end(xs), x) - begin(xs); } const T &operator[](int k) const { return xs[k]; } }; signed main(){ bc.init(500050); int N; cin >> N; vectora(N); cin >> a; auto b = a; sort(ALL(b)); int mi = 0; REP(i, N) { mi += lower_bound(ALL(b), a[i]) - b.begin(); } Compress c(a); c.build(); a = c.get(a); SegmentTree seg([](int a, int b) {return a + b;}, 0ll); seg.build(vector(N)); int tentou = 0; REP(i, N) { tentou += seg.query(a[i] + 1, N); seg.set_val(a[i], seg.query(a[i], a[i] + 1) + 1); } mint sum = 1; mint ans = 0; { FOR(i, 1, N + 1) { sum *= bc.com(N, i); } } { mint tmp = 0; FOR(i, 1, N + 1) { tmp += sum / bc.com(N, i) * bc.com(N - 2, i - 2); } ans += tmp * tentou; } { sum = 1; vectordp(N + 1); FOR(i, 1, N + 1) { dp[i] = dp[i - 1] * bc.com(N, i) + sum * bc.com(N - 1, i - 1); sum *= bc.com(N, i); } FOR(i, 2, N + 1) { sum /= bc.com(N, i - 1); ans += dp[i - 1] * sum / bc.com(N, i) * bc.com(N - 1, i - 1) * mi; } } //out(mi); out(ans); }