#include #include #include #include #include #include #include #include #include using namespace std; #pragma warning (disable: 4996) class BIT { public: int size_ = 1; vector bit; void init(int sz) { size_ = sz + 2; bit.resize(size_ + 2, 0); } void add(int pos, int x) { pos += 1; while (pos <= size_) { bit[pos] += x; pos += (pos & -pos); } } int sum(int pos) { pos += 1; int s = 0; while (pos >= 1) { s += bit[pos]; pos -= (pos & -pos); } return s; } }; long long modpow(long long a, long long b, long long m) { long long p = 1, q = a; for (int i = 0; i < 63; i++) { if ((b / (1LL << i)) % 2LL == 1) { p *= q; p %= m; } q *= q; q %= m; } return p; } long long Div(long long a, long long b, long long m) { return (a * modpow(b, m - 2, m)) % m; } long long mod = 998244353; long long N; long long A[1 << 18], cnt[1 << 18]; vector X; long long fact[1 << 19]; long long factinv[1 << 19]; void init() { fact[0] = 1; for (int i = 1; i <= 300000; i++) fact[i] = (1LL * i * fact[i - 1]) % mod; for (int i = 0; i <= 300000; i++) factinv[i] = Div(1, fact[i], mod); } long long ncr(long long n, long long r) { if (r < 0 || n < r) return 0; return (fact[n] * factinv[r] % mod) * factinv[n - r] % mod; } int main() { // Step #1. 入力 cin >> N; init(); for (int i = 1; i <= N; i++) cin >> A[i]; // Step #2. 座標圧縮 for (int i = 1; i <= N; i++) X.push_back(A[i]); sort(X.begin(), X.end()); X.erase(unique(X.begin(), X.end()), X.end()); for (int i = 1; i <= N; i++) A[i] = lower_bound(X.begin(), X.end(), A[i]) - X.begin(); // Step #3. 転倒数を求める long long ret1 = 0; BIT Z; Z.init(N + 2); for (int i = 1; i <= N; i++) { ret1 += Z.sum(N + 2) - Z.sum(A[i]); Z.add(A[i], 1); } ret1 %= mod; // Step #4. 同じペアの数を求める long long ret2 = 0; for (int i = 1; i <= N; i++) cnt[A[i]] += 1; for (int i = 0; i <= N; i++) ret2 += cnt[i] * cnt[i]; ret2 %= mod; // Step #5. 内側・外側のペア数を求める long long r1 = 0, r2 = 0; for (int i = 1; i <= N; i++) { r1 += 1LL * i * (i - 1LL) / 2LL; r1 %= mod; } for (int i = 1; i <= N; i++) { long long c1 = 1LL * i * (i - 1LL) / 2LL; long long c2 = i; r2 += c1 * c2; r2 %= mod; } // Step #6. 答えを求める long long s1 = Div(ret1 % mod, (N * (N - 1) / 2LL) % mod, mod); long long s2 = Div((N * N - ret2) % mod, (2LL * N * N) % mod, mod); long long Answer = r1 * s1 + r2 * s2; Answer %= mod; long long Patterns = 1; for (int i = 1; i <= N; i++) { Patterns *= ncr(N, i); Patterns %= mod; } cout << (Answer * Patterns) % mod << endl; return 0; }