#include #include #include #include template struct Matrix { std::vector> a; Matrix(int n, int m) : a(n, std::vector(m, 0)) {} Matrix(int n) : a(n, std::vector(n, 0)) {} int height() const { return a.size(); } int width() const { return a[0].size(); } inline const std::vector &operator[](int i) const { return a[i]; } inline std::vector &operator[](int i) { return a[i]; } static Matrix id(int n) { Matrix res(n); for (int i = 0; i < n; i++) res[i][i] = 1; return res; } Matrix &operator*=(const Matrix &b) { assert(width() == b.height()); std::vector> c(height(), std::vector(b.width())); for (int i = 0; i < height(); ++i) { for (int k = 0; k < b.height(); ++k) { for (int j = 0; j < b.width(); ++j) { c[i][j] += a[i][k] * b[k][j]; } } } a.swap(c); return *this; } Matrix pow(long long n) const { auto x = (*this), res = id(height()); while (n) { if (n & 1) { res *= x; --n; } else { x *= x; n >>= 1; } } return res; } Matrix operator*(const Matrix &b) const { return Matrix(*this) *= b; } std::vector operator*(const std::vector &v) { assert(width() == (int)v.size()); std::vector res(height(), 0); for (int i = 0; i < height(); ++i) { for (int j = 0; j < width(); ++j) { res[i] += a[i][j] * v[j]; } } return res; } }; template std::pair gauss_jordan(Matrix &a) { int rnk = 0; bool swp = false; for (int j = 0; j < a.width(); ++j) { int pivot = -1; for (int i = rnk; i < a.height(); ++i) { if (a[i][j] != 0) { pivot = i; break; } } if (pivot < 0) continue; swap(a[pivot], a[rnk]); if (pivot != rnk) swp ^= true; for (int i = 0; i < a.height(); ++i) { if (i != rnk && a[i][j] != 0) { auto coef = a[i][j] / a[rnk][j]; for (int k = j; k < a.width(); ++k) { a[i][k] -= a[rnk][k] * coef; } } } ++rnk; } return {rnk, swp}; } template T determinant(Matrix a) { auto [rnk, swp] = gauss_jordan(a); if (rnk < a.height()) return 0; T res = 1; for (int i = 0; i < a.height(); ++i) res *= a[i][i]; if (swp) res = -res; return res; } template std::pair, std::vector>> system_of_linear_equations(Matrix a, const std::vector &b) { assert(a.height() == (int)b.size()); Matrix aug(a.height(), a.width() + 1); for (int i = 0; i < a.height(); ++i) { for (int j = 0; j < a.width(); ++j) { aug[i][j] = a[i][j]; } aug[i][a.width()] = b[i]; } auto rnk = gauss_jordan(a).first, rnk_aug = gauss_jordan(aug).first; std::vector solution; std::vector> kernel; if (rnk < rnk_aug) return {solution, kernel}; solution.resize(a.width(), 0); std::vector used(a.width(), false); std::vector pos(rnk); for (int i = 0; i < rnk; ++i) { for (int j = 0; j < a.width(); ++j) { if (aug[i][j] != 0) { solution[j] = aug[i][a.width()] / aug[i][j]; used[j] = true; pos[i] = j; break; } } } for (int j = 0; j < a.width(); ++j) { if (!used[j]) { std::vector v(a.width(), 0); v[j] = 1; for (int i = 0; i < rnk; ++i) { v[pos[i]] = -aug[i][j] / aug[i][pos[i]]; } kernel.push_back(v); } } return {solution, kernel}; } #include #include #include template bool chmax(T &a, const T &b) { if (a < b) { a = b; return true; } return false; } template bool chmin(T &a, const T &b) { if (a > b) { a = b; return true; } return false; } template T div_floor(T a, T b) { if (b < 0) a *= -1, b *= -1; return a >= 0 ? a / b : (a + 1) / b - 1; } template T div_ceil(T a, T b) { if (b < 0) a *= -1, b *= -1; return a > 0 ? (a - 1) / b + 1 : a / b; } template struct CoordComp { std::vector v; bool sorted; CoordComp() : sorted(false) {} int size() { return v.size(); } void add(T x) { v.push_back(x); } void build() { std::sort(v.begin(), v.end()); v.erase(std::unique(v.begin(), v.end()), v.end()); sorted = true; } int get_idx(T x) { assert(sorted); return lower_bound(v.begin(), v.end(), x) - v.begin(); } T &operator[](int i) { return v[i]; } }; #define For(i, a, b) for (int i = (int)(a); (i) < (int)(b); ++(i)) #define rFor(i, a, b) for (int i = (int)(a)-1; (i) >= (int)(b); --(i)) #define rep(i, n) For(i, 0, n) #define rrep(i, n) rFor(i, n, 0) #define fi first #define se second using namespace std; using lint = long long; using pii = pair; using pll = pair; using mint = atcoder::modint998244353; void solve() { int n; scanf("%d", &n); Matrix a(2); a[0][0] = a[1][0] = 2; a[0][1] = a[1][1] = 1; a = a.pow(n); printf("%u\n", a[0][0].val()); } int main() { int t; scanf("%d", &t); rep(tt, t) solve(); }