#pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; //#define int long long typedef long long ll; typedef unsigned long long ul; typedef unsigned int ui; //ll mod = 1; constexpr ll mod = 998244353; //constexpr ll mod = 1000000007; const ll INF = mod * mod; typedef pairP; #define rep(i,n) for(int i=0;i=0;i--) #define Rep(i,sta,n) for(int i=sta;i=1;i--) #define Rep1(i,sta,n) for(int i=sta;i<=n;i++) #define all(v) (v).begin(),(v).end() typedef pair LP; using ld = long double; typedef pair LDP; const ld eps = 1e-10; const ld pi = acosl(-1.0); template void chmin(T& a, T b) { a = min(a, b); } template void chmax(T& a, T b) { a = max(a, b); } template vector vmerge(vector& a, vector& b) { vector res; int ida = 0, idb = 0; while (ida < a.size() || idb < b.size()) { if (idb == b.size()) { res.push_back(a[ida]); ida++; } else if (ida == a.size()) { res.push_back(b[idb]); idb++; } else { if (a[ida] < b[idb]) { res.push_back(a[ida]); ida++; } else { res.push_back(b[idb]); idb++; } } } return res; } template void cinarray(vector& v) { rep(i, v.size())cin >> v[i]; } template void coutarray(vector& v) { rep(i, v.size()) { if (i > 0)cout << " "; cout << v[i]; } cout << "\n"; } ll mod_pow(ll x, ll n, ll m = mod) { if (n < 0) { ll res = mod_pow(x, -n, m); return mod_pow(res, m - 2, m); } if (abs(x) >= m)x %= m; if (x < 0)x += m; //if (x == 0)return 0; ll res = 1; while (n) { if (n & 1)res = res * x % m; x = x * x % m; n >>= 1; } return res; } //mod should be <2^31 struct modint { int n; modint() :n(0) { ; } modint(ll m) { if (m < 0 || mod <= m) { m %= mod; if (m < 0)m += mod; } n = m; } operator int() { return n; } }; bool operator==(modint a, modint b) { return a.n == b.n; } bool operator<(modint a, modint b) { return a.n < b.n; } modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= (int)mod; return a; } modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += (int)mod; return a; } modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; } modint operator+(modint a, modint b) { return a += b; } modint operator-(modint a, modint b) { return a -= b; } modint operator*(modint a, modint b) { return a *= b; } modint operator^(modint a, ll n) { if (n == 0)return modint(1); modint res = (a * a) ^ (n / 2); if (n % 2)res = res * a; return res; } ll inv(ll a, ll p) { return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p); } modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); } modint operator/=(modint& a, modint b) { a = a / b; return a; } const int max_n = 1 << 20; modint fact[max_n], factinv[max_n]; void init_f() { fact[0] = modint(1); for (int i = 0; i < max_n - 1; i++) { fact[i + 1] = fact[i] * modint(i + 1); } factinv[max_n - 1] = modint(1) / fact[max_n - 1]; for (int i = max_n - 2; i >= 0; i--) { factinv[i] = factinv[i + 1] * modint(i + 1); } } modint comb(int a, int b) { if (a < 0 || b < 0 || a < b)return 0; return fact[a] * factinv[b] * factinv[a - b]; } modint combP(int a, int b) { if (a < 0 || b < 0 || a < b)return 0; return fact[a] * factinv[a - b]; } ll gcd(ll a, ll b) { a = abs(a); b = abs(b); if (a < b)swap(a, b); while (b) { ll r = a % b; a = b; b = r; } return a; } template void addv(vector& v, int loc, T val) { if (loc >= v.size())v.resize(loc + 1, 0); v[loc] += val; } /*const int mn = 2000005; bool isp[mn]; vector ps; void init() { fill(isp + 2, isp + mn, true); for (int i = 2; i < mn; i++) { if (!isp[i])continue; ps.push_back(i); for (int j = 2 * i; j < mn; j += i) { isp[j] = false; } } }*/ //[,val) template auto prev_itr(set& st, T val) { auto res = st.lower_bound(val); if (res == st.begin())return st.end(); res--; return res; } //[val,) template auto next_itr(set& st, T val) { auto res = st.lower_bound(val); return res; } using mP = pair; mP operator+(mP a, mP b) { return { a.first + b.first,a.second + b.second }; } mP operator+=(mP& a, mP b) { a = a + b; return a; } mP operator-(mP a, mP b) { return { a.first - b.first,a.second - b.second }; } mP operator-=(mP& a, mP b) { a = a - b; return a; } LP operator+(LP a, LP b) { return { a.first + b.first,a.second + b.second }; } LP operator+=(LP& a, LP b) { a = a + b; return a; } LP operator-(LP a, LP b) { return { a.first - b.first,a.second - b.second }; } LP operator-=(LP& a, LP b) { a = a - b; return a; } mt19937 mt(time(0)); const string drul = "DRUL"; string senw = "SENW"; //DRUL,or SENW //int dx[4] = { 1,0,-1,0 }; //int dy[4] = { 0,1,0,-1 }; //----------------------------------------- template struct BIT { private: vector node; int n; public: BIT(int n_) { n = n_; node.resize(n, 0); } //0-indexed void add(int a, T w) { for (int i = a; i < n; i |= i + 1)node[i] += w; } //[0,a) T sum(int a) { T ret = 0; for (int i = a - 1; i >= 0; i = (i & (i + 1)) - 1)ret += node[i]; return ret; } //[a,b) T sum(int a, int b) { return sum(b) - sum(a); } }; int get_premitive_root(const ll& p) { int primitive_root = 0; if (!primitive_root) { primitive_root = [&]() { set fac; int v = p - 1; for (ll i = 2; i * i <= v; i++) while (v % i == 0) fac.insert(i), v /= i; if (v > 1) fac.insert(v); for (int g = 1; g < p; g++) { bool ok = true; for (auto i : fac) if (mod_pow(g, (p - 1) / i, p) == 1) { ok = false; break; } if (ok) return g; } return -1; }(); } return primitive_root; } typedef vector poly; void dft(poly& f, const ll& p, const int& proot, bool inverse = false) { int n = f.size(); if (n == 1)return; poly w{ 1 }, iw{ 1 }; for (int m = w.size(); m < n / 2; m *= 2) { ll dw = mod_pow(proot, (p - 1) / (4 * m), p), dwinv = mod_pow(dw, p - 2, p); w.resize(m * 2); iw.resize(m * 2); for (int i = 0; i < m; i++)w[m + i] = w[i] * dw % p, iw[m + i] = iw[i] * dwinv % p; } if (!inverse) { for (int m = n; m >>= 1;) { for (int s = 0, k = 0; s < n; s += 2 * m, k++) { for (int i = s; i < s + m; i++) { ll x = f[i], y = f[i + m] * w[k] % p; f[i] = x + y, f[i + m] = x - y; if (f[i] >= p)f[i] -= p; if (f[i + m] < 0)f[i + m] += p; } } } } else { for (int m = 1; m < n; m *= 2) { for (int s = 0, k = 0; s < n; s += 2 * m, k++) { for (int i = s; i < s + m; i++) { ll x = f[i], y = f[i + m]; f[i] = x + y, f[i + m] = (x - y) * iw[k] % p; if (f[i] >= p)f[i] -= p; if (f[i + m] < 0)f[i + m] += p; } } } ll n_inv = mod_pow(n, p - 2, p); for (ll& v : f)(v *= n_inv) %= p; } } poly multi(poly g, poly h, const ll& p, int n) { const int proot = get_premitive_root(p); dft(g, p, proot, false); dft(h, p, proot, false); poly f(n); rep(i, n) { f[i] = g[i] * h[i] % p; } dft(f, p, proot, true); return f; } constexpr ll m0 = 1107296257; constexpr ll m1 = 1224736769; const ll inv01 = mod_pow(m0, m1 - 2, m1); ll calc(ll& a, ll& b) { ll res = 0; ll x1 = a; ll x2 = (b - x1) * inv01; x2 %= m1; if (x2 < 0)x2 += m1; res = x1 + x2 * m0; return res; } poly multiply(poly g, poly h) { if (min(g.size(), h.size()) <= 60) { poly res; rep(i, g.size())rep(j, h.size()) { addv(res, i + j, g[i] * h[j]); } return res; } int resz = g.size() + h.size() - 1; int n = 1; int pi = 0, qi = 0; rep(i, g.size())if (g[i])pi = i; rep(i, h.size())if (h[i])qi = i; int sz = pi + qi + 2; while (n < sz)n *= 2; g.resize(n); h.resize(n); poly vp[2]; vp[0] = multi(g, h, m0, n); vp[1] = multi(g, h, m1, n); poly res(resz); rep(i, res.size()) { ll a, b, c; if (i < vp[0].size())a = vp[0][i]; else a = 0; if (i < vp[1].size())b = vp[1][i]; else b = 0; res[i] = calc(a, b); } return res; } const ll mm = 1000000; struct Data { poly v0, v1; void init(P p) { v0.push_back(p.first); v1.push_back(p.second); } }; void normalize(poly &v) { rep(i, v.size()) { ll d = v[i] / mm; v[i] %= mm; if (d > 0) { if (i + 1 == v.size()) { v.push_back(d); } else { v[i + 1] += d; } } } while(v.size()&&v.back()==0)v.pop_back(); } poly operator+(poly& a, poly b) { poly res(max(a.size(), b.size())); rep(i, a.size())res[i] += a[i]; rep(i, b.size())res[i] += b[i]; normalize(res); return res; } poly operator*(poly& a, poly& b) { poly res = multiply(a, b); normalize(res); return res; } Data operator*(Data a, Data b) { Data res; res.v0 = a.v0 + (b.v0 * a.v1); res.v1 = a.v1 * b.v1; return res; } void solve() { int n; cin >> n; vector p(n); rep(i, n)cin >> p[i]; vector c(n); BIT bt(n + 1); per(i, n) { c[i] = bt.sum(p[i]); bt.add(p[i], 1); } vector vd; for (int i = 1; i <= n; i++) { Data cur; cur.init({ c[n - i],i }); vd.push_back(cur); } while (vd.size() > 1) { vector nvd; for (int i = 0; i + 1 < vd.size(); i += 2) { Data cur = vd[i] * vd[i + 1]; nvd.push_back(cur); } if (vd.size() % 2)nvd.push_back(vd.back()); swap(vd, nvd); } poly res = vd[0].v0; res[0]++; normalize(res); string ans; rep(i, res.size()) { int v = res[i]; assert(v < mm); rep(j, 6) { int r = v % 10; ans.push_back('0' + r); v /= 10; } } while (ans.back() == '0')ans.pop_back(); reverse(all(ans)); cout << ans << "\n"; } signed main() { ios::sync_with_stdio(false); cin.tie(0); //cout << fixed << setprecision(12); //init_f(); //init(); //while(true) //expr(); //int t; cin >> t; rep(i, t) solve(); return 0; }