/* preprocessor start */ #ifdef LOCAL //* #define _GLIBCXX_DEBUG // gcc /*/ #define _LIBCPP_DEBUG 0 // clang //*/ #define __clock__ // #define __buffer_check__ #else #pragma GCC optimize("Ofast") /* #define _GLIBCXX_DEBUG // gcc /*/ // #define _LIBCPP_DEBUG 0 // clang //*/ // #define __buffer_check__ // #define NDEBUG #endif #define __precision__ 10 #define iostream_untie true #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #define __all(v) std::begin(v), std::end(v) #define __rall(v) std::rbegin(v), std::rend(v) #define __popcount(n) __builtin_popcountll(n) #define __clz32(n) __builtin_clz(n) #define __clz64(n) __builtin_clzll(n) #define __ctz32(n) __builtin_ctz(n) #define __ctz64(n) __builtin_ctzll(n) /* preprocessor end */ namespace std { // hash template size_t hash_combine(size_t seed, T const &key) { return seed ^ (hash()(key) + 0x9e3779b9 + (seed << 6) + (seed >> 2)); } template struct hash> { size_t operator()(pair const &pr) const { return hash_combine(hash_combine(0, pr.first), pr.second); } }; template ::value - 1> struct tuple_hash_calc { static size_t apply(size_t seed, tuple_t const &t) { return hash_combine(tuple_hash_calc::apply(seed, t), get(t)); } }; template struct tuple_hash_calc { static size_t apply(size_t seed, tuple_t const &t) { return hash_combine(seed, get<0>(t)); } }; template struct hash> { size_t operator()(tuple const &t) const { return tuple_hash_calc>::apply(0, t); } }; // iostream template istream &operator>>(istream &is, pair &p) { return is >> p.first >> p.second; } template ostream &operator<<(ostream &os, const pair &p) { return os << p.first << ' ' << p.second; } template struct tupleis { static istream &apply(istream &is, tuple_t &t) { tupleis::apply(is, t); return is >> get(t); } }; template struct tupleis { static istream &apply(istream &is, tuple_t &t) { return is; } }; template istream &operator>>(istream &is, tuple &t) { return tupleis, tuple_size>::value - 1>::apply(is, t); } template <> istream &operator>>(istream &is, tuple<> &t) { return is; } template struct tupleos { static ostream &apply(ostream &os, const tuple_t &t) { tupleos::apply(os, t); return os << ' ' << get(t); } }; template struct tupleos { static ostream &apply(ostream &os, const tuple_t &t) { return os << get<0>(t); } }; template ostream &operator<<(ostream &os, const tuple &t) { return tupleos, tuple_size>::value - 1>::apply(os, t); } template <> ostream &operator<<(ostream &os, const tuple<> &t) { return os; } template , string>::value, nullptr_t> = nullptr> istream& operator>>(istream& is, Container &cont) { for(auto&& e : cont) is >> e; return is; } template , string>::value, nullptr_t> = nullptr> ostream& operator<<(ostream& os, const Container &cont) { bool flag = 1; for(auto&& e : cont) flag ? flag = 0 : (os << ' ', 0), os << e; return os; } } // namespace std namespace setting { using namespace std; using namespace chrono; system_clock::time_point start_time, end_time; long long get_elapsed_time() { end_time = system_clock::now(); return duration_cast(end_time - start_time).count(); } void print_elapsed_time() { cerr << "\n----- Exec time : " << get_elapsed_time() << " ms -----\n"; } void buffer_check() { char bufc; if(cin >> bufc) cerr << "\n\033[1;35mwarning\033[0m: buffer not empty.\n"; } struct setupper { setupper() { if(iostream_untie) ios::sync_with_stdio(false), cin.tie(nullptr); cout << fixed << setprecision(__precision__); #ifdef stderr_path if(freopen(stderr_path, "a", stderr)) cerr << fixed << setprecision(__precision__); #endif #ifdef LOCAL cerr << "\n----- stderr at LOCAL -----\n\n"; #endif #ifdef __buffer_check__ atexit(buffer_check); #endif #ifdef __clock__ start_time = system_clock::now(); atexit(print_elapsed_time); #endif } } __setupper; // struct setupper } // namespace setting #ifdef __clock__ #include "C:\Users\euler\OneDrive\Documents\Competitive_Programming\Library\local\Clock.hpp" #else #define build_clock() ((void)0) #define set_clock() ((void)0) #define get_clock() ((void)0) #endif #ifdef LOCAL #include "C:\Users\euler\OneDrive\Documents\Competitive_Programming\Library\local\Dump.hpp" #else #define dump(...) ((void)0) #endif /* function utility start */ template T read(types... args) noexcept { typename std::remove_const::type obj(args...); std::cin >> obj; return obj; } #define input(type, var, ...) type var{read(__VA_ARGS__)} // substitute y for x if x > y. template inline bool sbmin(T &x, const T &y) { return x > y ? x = y, true : false; } // substitute y for x if x < y. template inline bool sbmax(T &x, const T &y) { return x < y ? x = y, true : false; } // binary search on discrete range. template iter_type binary(iter_type __ok, iter_type __ng, pred_type pred) { std::ptrdiff_t dist(__ng - __ok); while(std::abs(dist) > 1) { iter_type mid(__ok + dist / 2); if(pred(mid)) __ok = mid, dist -= dist / 2; else __ng = mid, dist /= 2; } return __ok; } // binary search on real numbers. template long double binary(long double __ok, long double __ng, const long double eps, pred_type pred) { while(std::abs(__ok - __ng) > eps) { long double mid{(__ok + __ng) / 2}; (pred(mid) ? __ok : __ng) = mid; } return __ok; } // reset all bits. template void reset(A &array) { memset(array, 0, sizeof(array)); } // be careful that val is type-sensitive. template void init(A (&array)[N], const T &val) { std::fill((T*)array, (T*)(array + N), val); } /* functon utility end */ /* using alias start */ using namespace std; using i32 = int_least32_t; using i64 = int_least64_t; using u32 = uint_least32_t; using u64 = uint_least64_t; using pii = pair; using pll = pair; template > using heap = priority_queue, Comp>; template using hashset = unordered_set; template using hashmap = unordered_map; /* using alias end */ /* library start */ #ifndef Modint_hpp #define Modint_hpp #include #include template class modint { int val; public: constexpr modint() noexcept : val{0} {} constexpr modint(long long x) noexcept : val((x %= mod) < 0 ? mod + x : x) {} constexpr long long value() const noexcept { return val; } constexpr modint operator++(int) noexcept { modint t = *this; return ++val, t; } constexpr modint operator--(int) noexcept { modint t = *this; return --val, t; } constexpr modint &operator++() noexcept { return ++val, *this; } constexpr modint &operator--() noexcept { return --val, *this; } constexpr modint operator-() const noexcept { return modint(-val); } constexpr modint &operator+=(const modint &other) noexcept { return (val += other.val) < mod ? 0 : val -= mod, *this; } constexpr modint &operator-=(const modint &other) noexcept { return (val += mod - other.val) < mod ? 0 : val -= mod, *this; } constexpr modint &operator*=(const modint &other) noexcept { return val = (long long)val * other.val % mod, *this; } constexpr modint &operator/=(const modint &other) noexcept { return *this *= inverse(other); } constexpr modint operator+(const modint &other) const noexcept { return modint(*this) += other; } constexpr modint operator-(const modint &other) const noexcept { return modint(*this) -= other; } constexpr modint operator*(const modint &other) const noexcept { return modint(*this) *= other; } constexpr modint operator/(const modint &other) const noexcept { return modint(*this) /= other; } constexpr bool operator==(const modint &other) const noexcept { return val == other.val; } constexpr bool operator!=(const modint &other) const noexcept { return val != other.val; } constexpr bool operator!() const noexcept { return !val; } friend constexpr modint operator+(long long x, modint y) noexcept { return modint(x) + y; } friend constexpr modint operator-(long long x, modint y) noexcept { return modint(x) - y; } friend constexpr modint operator*(long long x, modint y) noexcept { return modint(x) * y; } friend constexpr modint operator/(long long x, modint y) noexcept { return modint(x) / y; } static constexpr modint inverse(const modint &other) noexcept { assert(other != 0); int a{mod}, b{other.val}, u{}, v{1}, t{}; while(b) t = a / b, a ^= b ^= (a -= t * b) ^= b, u ^= v ^= (u -= t * v) ^= v; return {u}; } static constexpr modint pow(modint other, long long e) noexcept { if(e < 0) e = e % (mod - 1) + mod - 1; modint res{1}; while(e) { if(e & 1) res *= other; other *= other, e >>= 1; } return res; } friend std::ostream &operator<<(std::ostream &os, const modint &other) noexcept { return os << other.val; } friend std::istream &operator>>(std::istream &is, modint &other) noexcept { long long val; other = {(is >> val, val)}; return is; } }; // class modint template <> class modint<2> { bool val; public: constexpr modint(bool x = false) noexcept : val{x} {} constexpr modint(int x) noexcept : val(x & 1) {} constexpr modint(long long x) noexcept : val(x & 1) {} constexpr operator bool() const noexcept { return val; } constexpr bool value() const noexcept { return val; } constexpr modint &operator+=(const modint &other) noexcept { return val ^= other.val, *this; } constexpr modint &operator-=(const modint &other) noexcept { return val ^= other.val, *this; } constexpr modint &operator*=(const modint &other) noexcept { return val &= other.val, *this; } constexpr modint &operator/=(const modint &other) noexcept { assert(other.val); return *this; } constexpr modint operator!() const noexcept { return !val; } constexpr modint operator-() const noexcept { return *this; } constexpr modint operator+(const modint &other) const noexcept { return val != other.val; } constexpr modint operator-(const modint &other) const noexcept { return val != other.val; } constexpr modint operator*(const modint &other) const noexcept { return val && other.val; } constexpr modint operator/(const modint &other) const noexcept { assert(other.val); return *this; } constexpr bool operator==(const modint &other) const noexcept { return val == other.val; } constexpr bool operator!=(const modint &other) const noexcept { return val != other.val; } friend constexpr modint operator+(long long x, modint y) noexcept { return x & 1 ? !y : y; } friend constexpr modint operator-(long long x, modint y) noexcept { return x & 1 ? !y : y; } friend constexpr modint operator*(long long x, modint y) noexcept { return x & 1 ? y : modint<2>{0}; } friend constexpr modint operator/(long long x, modint y) noexcept { assert(y.val); return x & 1 ? y : modint<2>{0}; } friend std::ostream &operator<<(std::ostream &os, const modint &other) noexcept { return os << other.val; } friend std::istream &operator>>(std::istream &is, modint &other) noexcept { long long val; other.val = (is >> val, val & 1); return is; } }; // class modint specialization #endif // Modint_hpp #ifndef Matrix_hpp #define Matrix_hpp #include #include #include template class matrix { size_t h, w; using row_type = std::valarray; using data_type = std::valarray>; data_type data; friend std::istream &operator>>(std::istream &is, matrix &x) { for(size_t i = 0; i != x.h; ++i) { for(size_t j = 0; j != x.w; ++j) is >> x.data[i][j]; } return is; } friend std::ostream &operator<<(std::ostream &os, const matrix &x) { for(size_t i = 0; i != x.h; ++i) { if(i) os << "\n"; for(size_t j = 0; j != x.w; ++j) os << (j ? " " : "") << x.data[i][j]; } return os; } friend matrix transpose(const matrix &x) { matrix res(x.w, x.h); for(size_t i = 0; i != x.w; ++i) for(size_t j = 0; j != x.h; ++j) res[i][j] = x.data[j][i]; return res; } friend matrix pow(matrix x, long long n) { assert(x.square()); if(n < 0) x = inverse(x), n = -n; matrix res{identity(x.h)}; while(n) { if(n & 1) res *= x; x *= x, n >>= 1; } return res; } friend matrix inverse(const matrix &x) { assert(x.square()); matrix ext_x(x.h, x.h * 2), res(x.h); for(size_t i = 0; i != x.h; ++i) ext_x.data[i][std::slice(0, x.h, 1)] = x.data[i], ext_x.data[i][i + x.h] = 1; if(ext_x.row_canonicalize().size() != x.h) return matrix{0}; for(size_t i = 0; i != x.h; ++i) res[i] = ext_x.data[i][std::slice(x.h, x.h, 1)]; return res; } public: explicit matrix(size_t _n = 0) : h(_n), w(_n) { resize(_n, _n);} matrix(size_t _h, size_t _w) : h(_h), w(_w) { resize(_h, _w); } matrix(const data_type &_data) : h(_data.size()), w(_data.size() ? _data[0].size() : 0), data(_data) {} operator data_type() const { return data; } size_t height() const noexcept { return h; } size_t width() const noexcept { return w; } bool square() const noexcept { return h == w; } row_type &operator[](const size_t i) noexcept { assert(i < data.size()); return data[i]; } void resize(size_t h, size_t w, const Field val = Field(0)) { data.resize(h, std::valarray(val, w)); } static matrix identity(const size_t n) noexcept { data_type data(row_type(n), n); for(size_t i = 0; i != n; ++i) data[i][i] = 1; return data; } matrix operator-() const noexcept { return {-data}; } matrix &operator+=(const matrix &other) noexcept { data += other.data; return *this; } matrix &operator-=(const matrix &other) { data -= other.data; return *this; } matrix &operator*=(matrix other) noexcept { other = transpose(other); for(size_t i = 0; i != h; ++i) { const row_type copied{data[i]}; for(size_t j = 0; j != other.h; ++j) data[i][j] = (copied * other.data[j]).sum(); } return *this; } matrix operator+(const matrix &x) const noexcept { return matrix(*this) += x; } matrix operator-(const matrix &x) const noexcept { return matrix(*this) -= x; } matrix operator*(const matrix &x) const noexcept { return matrix(*this) *= x; } // return the list of pivot columns std::vector row_canonicalize() { std::vector pivots; for(size_t j = 0, rank = 0; j != w; ++j) { row_type *row_ptr = nullptr; for(size_t i = rank; i != h; ++i) { if(data[i][j] != Field{0}) { const Field f = data[i][j]; if(row_ptr) data[i][std::slice(j, w - j, 1)] -= *row_ptr * f; else { swap(data[rank], data[i]); std::slice_array tmp{data[rank][std::slice(j, w - j, 1)]}; tmp = *(row_ptr = new row_type{tmp}) /= f; } } } if(row_ptr) { for(size_t k = 0; k != rank; ++k) { const Field f = data[k][j]; data[k][std::slice(j, w - j, 1)] -= *row_ptr * f; } ++rank; pivots.emplace_back(j); delete row_ptr; } } return pivots; } Field determinant() const { assert(square()); data_type copied{data}; Field res{1}; for(size_t j = 0; j != w; ++j) { row_type *row_ptr = nullptr; for(size_t i = j; i != h; ++i) { if(copied[i][j] != Field{0}) { const Field f = copied[i][j]; if(row_ptr) copied[i][std::slice(j, w - j, 1)] -= *row_ptr * f; else { swap(copied[i], copied[j]); if(i != j) res = -res; res *= f; std::slice_array tmp{copied[j][std::slice(j, w - j, 1)]}; tmp = *(row_ptr = new row_type{tmp}) /= f; } } } if(!row_ptr) return 0; } return res; } }; // class matrix #endif // Matrix_hpp /* library end */ /* The main code follows. */ using mint=modint<(int)1e9+7>; struct solver { solver() { input(int,n); int lis[3<<17]={}; while(n--) { input(int,a); int now=lis[1]+1; for(int d=2;d*d<=a;++d) { if(a%d) continue; sbmax(now,lis[d]+1); sbmax(now,lis[a/d]+1); } lis[a]=now; } cout << *max_element(__all(lis)) << "\n"; } }; // struct solver int main(int argc, char *argv[]) { u32 t; // loop count #ifdef LOCAL t = 1; #else t = 1; // single test case #endif // t = -1; // infinite loop // cin >> t; // case number given while(t--) { solver(); } }