#pragma GCC optimize("O3") #include using namespace std; using ll = long long int; #define all(v) (v).begin(), (v).end() #define repeat(cnt, l) \ for (typename remove_const< \ typename remove_reference::type>::type cnt = {}; \ (cnt) < (l); ++(cnt)) #define rrepeat(cnt, l) for (auto cnt = (l)-1; 0 <= (cnt); --(cnt)) #define iterate(cnt, b, e) for (auto cnt = (b); (cnt) != (e); ++(cnt)) #define increase(cnt, b, e) for (auto cnt = (b); (cnt) < (e); ++(cnt)) #define decrease(cnt, b, e) for (auto cnt = (b); (e) <= (cnt); --(cnt)) const long long MD = 1000000007ll; const long double PI = 3.1415926535897932384626433832795L; template inline ostream &operator<<(ostream &o, const pair p) { o << '(' << p.first << ':' << p.second << ')'; return o; } template inline T &chmax(T &to, const T &val) { return to = max(to, val); } template inline T &chmin(T &to, const T &val) { return to = min(to, val); } void bye(string s, int code = 0) { cout << s << endl; exit(code); } mt19937_64 randdev(8901016); template ::value>::type * = nullptr> inline T rand(T l, T h, Random &rand = randdev) { return uniform_int_distribution(l, h)(rand); } template ::value>::type * = nullptr> inline T rand(T l, T h, Random &rand = randdev) { return uniform_real_distribution(l, h)(rand); } template static ostream &operator<<(ostream &o, const std::vector &v) { o << "[ "; for (const auto &e : v) o << e << ' '; return o << ']'; } template struct MyRangeFormat { I b, e; MyRangeFormat(I _b, I _e) : b(_b), e(_e) {} }; template static ostream &operator<<(ostream &o, const MyRangeFormat &f) { o << "[ "; iterate(i, f.b, f.e) o << *i << ' '; return o << ']'; } template struct MyMatrixFormat { const I &p; long long n, m; MyMatrixFormat(const I &_p, long long _n, long long _m) : p(_p), n(_n), m(_m) {} }; template static ostream &operator<<(ostream &o, const MyMatrixFormat &f) { o << '\n'; repeat(i, (f.n)) { repeat(j, f.m) o << f.p[i][j] << ' '; o << '\n'; } return o; } struct LOG_t { ~LOG_t() { cout << endl; } }; #define LOG (LOG_t(), cout << 'L' << __LINE__ << ": ") #define FMTA(m, w) (MyRangeFormat(m, m + w)) #define FMTR(b, e) (MyRangeFormat(b, e)) #define FMTV(v) FMTR(v.begin(), v.end()) #define FMTM(m, h, w) (MyMatrixFormat(m, h, w)) #if defined(_WIN32) || defined(_WIN64) #define getc_x _getc_nolock #define putc_x _putc_nolock #elif defined(__GNUC__) #define getc_x getc_unlocked #define putc_x putc_unlocked #else #define getc_x getc #define putc_x putc #endif class MaiScanner { FILE *fp_; constexpr bool isvisiblechar(char c) noexcept { return (0x21 <= (c) && (c) <= 0x7E); } public: inline MaiScanner(FILE *fp) : fp_(fp) {} template void input_integer(T &var) noexcept { var = 0; T sign = 1; int cc = getc_x(fp_); for (; cc < '0' || '9' < cc; cc = getc_x(fp_)) if (cc == '-') sign = -1; for (; '0' <= cc && cc <= '9'; cc = getc_x(fp_)) var = (var << 3) + (var << 1) + cc - '0'; var = var * sign; } inline int c() noexcept { return getc_x(fp_); } template ::value, nullptr_t>::type = nullptr> inline MaiScanner &operator>>(T &var) noexcept { input_integer(var); return *this; } inline MaiScanner &operator>>(string &var) { int cc = getc_x(fp_); for (; !isvisiblechar(cc); cc = getc_x(fp_)) ; for (; isvisiblechar(cc); cc = getc_x(fp_)) var.push_back(cc); return *this; } template inline void in(IT begin, IT end) { for (auto it = begin; it != end; ++it) *this >> *it; } }; class MaiPrinter { FILE *fp_; public: inline MaiPrinter(FILE *fp) : fp_(fp) {} template void output_integer(T var) noexcept { if (var == 0) { putc_x('0', fp_); return; } if (var < 0) putc_x('-', fp_), var = -var; char stack[32]; int stack_p = 0; while (var) stack[stack_p++] = '0' + (var % 10), var /= 10; while (stack_p) putc_x(stack[--stack_p], fp_); } inline MaiPrinter &operator<<(char c) noexcept { putc_x(c, fp_); return *this; } template ::value, nullptr_t>::type = nullptr> inline MaiPrinter &operator<<(T var) noexcept { output_integer(var); return *this; } inline MaiPrinter &operator<<(char *str_p) noexcept { while (*str_p) putc_x(*(str_p++), fp_); return *this; } inline MaiPrinter &operator<<(const string &str) { const char *p = str.c_str(); const char *l = p + str.size(); while (p < l) putc_x(*p++, fp_); return *this; } template void join(IT begin, IT end, char sep = ' ') { for (bool b = 0; begin != end; ++begin, b = 1) b ? *this << sep << *begin : *this << *begin; } }; MaiScanner scanner(stdin); MaiPrinter printer(stdout); // class SquareRootDecomposition { struct Node { int add_; shared_ptr> data_; int get(int i) const { return data_->operator[](i) + add_; } int set(int i, int x) { apply(); return data_->operator[](i) = x; } void apply() { // データが複数のNodeから参照されているならば if (data_.use_count() > 1) { // O(M)時間で複製する data_ = make_shared>(*data_); } // add_を適用する。 if (add_ == 0) return; for (auto &e : *data_) e += add_; add_ = 0; } void copyNode(Node &src) { add_ = src.add_; // note: 参照をコピーするのでO(1)時間で完了する data_ = src.data_; } }; int M_; vector nodes_; public: SquareRootDecomposition(int sqrtN) : M_(sqrtN), nodes_(sqrtN) {} void fill(int x) { for (Node &node : nodes_) { node.add_ = 0; node.data_ = make_shared>(M_, x); } } int getValue(int i) const { const auto &node = nodes_[i / M_]; int x = node.get(i % M_); return x; } void addValueRange(int be, int en, int x) { if (be >= en) return; while (be / M_ * M_ != be) { auto &node = nodes_[be / M_]; node.set(be % M_, node.get(be % M_) + x); if (++be >= en) return; } while (be / M_ != en / M_) { auto &node = nodes_[be / M_]; node.add_ += x; if ((be += M_) >= en) return; } while (be < en) { auto &node = nodes_[be / M_]; node.set(be % M_, node.get(be % M_) + x); ++be; } } void copyValueRange(int be, int en, SquareRootDecomposition &src) { if (be >= en) return; while (be / M_ * M_ != be) { auto &node = nodes_[be / M_]; auto &src_node = src.nodes_[be / M_]; node.set(be % M_, src_node.get(be % M_)); if (++be >= en) return; } while (be / M_ != en / M_) { auto &node = nodes_[be / M_]; auto &src_node = src.nodes_[be / M_]; node.copyNode(src_node); if ((be += M_) >= en) return; } while (be < en) { auto &node = nodes_[be / M_]; auto &src_node = src.nodes_[be / M_]; node.set(be % M_, src_node.get(be % M_)); ++be; } } }; // struct Problem { int N; vector A; void set(const Problem &p) { N = p.N; A = p.A; } void scan() { scanner >> N; A.resize(N); A.shrink_to_fit(); scanner.in(all(A)); } void generate(int n) { N = n; A.resize(N); A.shrink_to_fit(); iota(all(A), 1); shuffle(all(A), randdev); } virtual int solve() { return -1; }; }; // struct ProblemSolverExp : public Problem { int solve() override { if (N > 24) return -1; int best_len = 1; // 全列挙 for (int b = 1; b < (1 << N); ++b) { // ビット列から部分列を生成 vector aa; repeat(i, N) if (b & (1 << i)) aa.push_back(A[i]); if (aa.size() <= 1) continue; // 評価 int even_min = numeric_limits::max(); int odd_max = 0; int even_max = 0; int odd_min = numeric_limits::max(); repeat(j, int(aa.size())) { if (j & 1) { chmin(odd_min, aa[j]); chmax(odd_max, aa[j]); } else { chmin(even_min, aa[j]); chmax(even_max, aa[j]); } } if (even_max < odd_min || odd_max < even_min) chmax(best_len, aa.size()); } return best_len; } }; // struct ProblemSolverN2 : public Problem { private: int greedy(int t) { // 偶数/奇数要素がt+0.5未満/以上となるように貪欲で選ぶ // この貪欲な選び方はtを固定した上では最適 int best_len = 0; repeat(updown, 2) { int len = 0; bool odd = updown; repeat(i, N) { if (odd) { if (t < A[i]) { odd = !odd; len += 1; } } else { if (t >= A[i]) { odd = !odd; len += 1; } } } chmax(best_len, len); } return best_len; } public: int solve() override { if (N > 6000) return -1; int best_len = 1; repeat(i, N - 1) { // 境界値をi+1.5として選ぶ // 境界値を元に貪欲に決定 int l = greedy(i + 1); chmax(best_len, l); } return best_len; } }; // struct ProblemSolverN2a : public Problem { int solve() override { if (N > 6000) return -1; vector vec_down(N); // i+0.5 を境界としている vector vec_up(N); repeat(i, N) { int a = A[i] - 1; for (int x = 0; x <= a; ++x) { // chmax(vec_up[x], vec_down[x] + 1); vec_up[x] = vec_down[x] + 1; } for (int x = a + 1; x < N; ++x) { vec_down[x] = vec_up[x] + 1; } // 区間のコピーが必要!! // 区間の位置が変わらないコピーなので、平方分割が使える。 } int best_len = 1; repeat(i, N) chmax(best_len, vec_up[i]); repeat(i, N) chmax(best_len, vec_down[i]); return best_len; } }; struct ProblemSolverNq : public Problem { int solve() override { int m = max(3, int(sqrt(N)) + 1); SquareRootDecomposition vec_down(m); // i+0.5 を境界としている SquareRootDecomposition vec_up(m); vec_down.fill(0); vec_up.fill(0); repeat(i, N) { int a = A[i] - 1; { vec_up.copyValueRange(0, a + 1, vec_down); vec_up.addValueRange(0, a + 1, 1); } { vec_down.copyValueRange(a + 1, N, vec_up); vec_down.addValueRange(a + 1, N, 1); } } int best_len = 1; repeat(i, N) chmax(best_len, vec_up.getValue(i)); repeat(i, N) chmax(best_len, vec_down.getValue(i)); return best_len; } }; // // void test1() { Problem p; p.N = 8; p.A.resize(p.N); iota(all(p.A), 1); do { ProblemSolverExp p1; ProblemSolverN2 p2; ProblemSolverN2a p3; ProblemSolverNq p4; p1.set(p); p2.set(p); p3.set(p); p4.set(p); int a1 = p1.solve(); int a2 = p2.solve(); int a3 = p3.solve(); int a4 = p4.solve(); if (a1 != a2 || a2 != a3 || a3 != a4) { LOG << p.A; LOG << a1 << " " << a2 << " " << a3 << " " << a4; break; } } while (next_permutation(all(p.A))); LOG << "done"; } void test2() { Problem p; p.N = 100; p.A.resize(p.N); iota(all(p.A), 1); repeat(_, 1000) { shuffle(all(p.A), randdev); ProblemSolverN2 p2; ProblemSolverNq p4; p2.set(p); p4.set(p); int a2 = p2.solve(); int a4 = p4.solve(); if (a2 != a4) { LOG << p.A; LOG << a2 << " " << a4; break; } } LOG << "done"; } void single() { // ProblemSolverN2a p; ProblemSolverExp p; int T; scanner >> T; repeat(i, T) { p.scan(); printer << p.solve() << '\n'; } } int main() { single(); // test2(); return 0; }