#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; constexpr ll mod = 1012924417; const ll INF = mod * mod; typedef pairP; #define stop char nyaa;cin>>nyaa; #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; typedef long double ld; typedef pair LDP; const ld eps = 1e-12; const ld pi = acosl(-1.0); ll mod_pow(ll x, ll n, ll m=mod) { ll res = 1; while (n) { if (n & 1)res = res * x % m; x = x * x % m; n >>= 1; } return res; } struct modint { ll n; modint() :n(0) { ; } modint(ll m) :n(m) { if (n >= mod)n %= mod; else if (n < 0)n = (n % mod + mod) % mod; } operator int() { return 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 -= mod; return a; } modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += 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)); } const int max_n = 1 << 19; 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]; } int get_premitive_root() { int primitive_root = 0; if (!primitive_root) { primitive_root = [&]() { set fac; int v = mod - 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 < mod; g++) { bool ok = true; for (auto i : fac) if (mod_pow(g,(mod-1)/i)==1){ ok = false; break; } if (ok) return g; } return -1; }(); } return primitive_root; } const int proot = get_premitive_root(); typedef vector poly; void dft(poly& f, bool inverse = false) { int n = f.size(); if (n == 1)return; static poly w{ 1 }, iw{ 1 }; for (int m = w.size(); m < n / 2; m *= 2) { modint dw = mod_pow(proot, (mod - 1) / (4 * m)), dwinv = (modint)1 / dw; w.resize(m * 2); iw.resize(m * 2); for (int i = 0; i < m; i++)w[m + i] = w[i] * dw, iw[m + i] = iw[i] * dwinv; } 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++) { modint x = f[i], y = f[i + m] * w[k]; f[i] = x + y, f[i + m] = x - y; } } } } 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++) { modint x = f[i], y = f[i + m]; f[i] = x + y, f[i + m] = (x - y) * iw[k]; } } } modint n_inv = (modint)1 / (modint)n; for (modint& v : f)v *= n_inv; } } poly multiply(poly g, poly h) { 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); dft(g); dft(h); rep(i, n) { g[i] *= h[i]; } dft(g, true); return g; } struct FormalPowerSeries :vector { using vector::vector; using fps = FormalPowerSeries; void shrink() { while (this->size() && this->back() == (modint)0)this->pop_back(); } fps operator+(const fps& r)const { return fps(*this) += r; } fps operator+(const modint& v)const { return fps(*this) += v; } fps operator-(const fps& r)const { return fps(*this) -= r; } fps operator-(const modint& v)const { return fps(*this) -= v; } fps operator*(const fps& r)const { return fps(*this) *= r; } fps operator*(const modint& v)const { return fps(*this) *= v; } fps& operator+=(const fps& r) { if (r.size() > this->size())this->resize(r.size()); rep(i, r.size())(*this)[i] += r[i]; shrink(); return *this; } fps& operator+=(const modint& v) { if (this->empty())this->resize(1); (*this)[0] += v; shrink(); return *this; } fps& operator-=(const fps& r) { if (r.size() > this->size())this->resize(r.size()); rep(i, r.size())(*this)[i] -= r[i]; shrink(); return *this; } fps& operator-=(const modint& v) { if (this->empty())this->resize(1); (*this)[0] -= v; shrink(); return *this; } fps& operator*=(const fps& r) { if (this->empty() || r.empty())this->clear(); else { poly ret = multiply(*this, r); *this = fps(all(ret)); } return *this; } fps& operator*=(const modint& v) { for (auto& x : (*this))x *= v; shrink(); return *this; } fps operator-()const { fps ret = *this; for (auto& v : ret)v = -v; return ret; } fps pre(int sz)const { fps ret(this->begin(), this->begin() + min((int)this->size(), sz)); ret.shrink(); return ret; } fps inv(int deg) { const int n = this->size(); if (deg == -1)deg = n; fps ret({ (modint)1 / (*this)[0] }); for (int i = 1; i < deg; i <<= 1) { ret = (ret + ret - ret * ret * pre(i << 1)).pre(i << 1); } ret = ret.pre(deg); ret.shrink(); return ret; } }; using fps = FormalPowerSeries; void solve() { int n; cin >> n; fps s(n + 1); for (int t = 1; t <= n; t += 2) { modint x = factinv[t]; if ((t / 2) % 2)x *= -1; s[t] = x; } s[0] = 1; fps c(n + 1); for (int t = 0; t <= n; t += 2) { modint x = factinv[t]; if ((t / 2) % 2)x *= -1; c[t] = x; } fps x = s * c.inv(n + 1); modint ans = x[n]*fact[n]; ans = ans + ans; cout << ans << "\n"; } signed main() { ios::sync_with_stdio(false); cin.tie(0); //cout << fixed << setprecision(15); init_f(); //init(); //expr(); //int t; cin >> t; rep(i, t) solve(); return 0; }