/* 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__ 15 #define iostream_untie true #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\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 freopen(stderr_path, "a", stderr); #endif #ifdef LOCAL cerr << fixed << setprecision(__precision__) << boolalpha << "\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 "clock.hpp" #else #define build_clock() ((void)0) #define set_clock() ((void)0) #define get_clock() ((void)0) #endif #ifdef LOCAL #include "dump.hpp" #else #define dump(...) ((void)0) #endif /* function utility start */ // lambda wrapper for recursive method. template class make_recursive { lambda_type func; public: make_recursive(lambda_type &&f) : func(std::move(f)) {} template auto operator()(Args &&... args) const { return func(*this, std::forward(args)...); } }; /* 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 chmin(T &x, const T &y) { return x > y ? x = y, true : false; } // substitute y for x if x < y. template inline bool chmax(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; } // size of array. template size_t size(A (&array)[N]) { return N; } // 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 p32 = pair; using p64 = pair; template > using heap = priority_queue, Comp>; template using hashset = unordered_set; template using hashmap = unordered_map; using namespace __gnu_cxx; /* using alias end */ /* library start */ #include #include template class segment_tree { using size_type = typename std::vector::size_type; class unique_queue { size_type *que, *begin, *end; bool *in; public: unique_queue() : que(), begin(), end(), in() {} unique_queue(size_type n) : que(new size_type[n]), begin(que), end(que), in(new bool[n]{}) {} ~unique_queue() { delete[] que; delete[] in; } void clear() { begin = end = que; } bool empty() const { return begin == end; } bool push(size_type index) { if(in[index]) return false; return in[*end++ = index] = true; } size_type pop() { return in[*begin] = false, *begin++; } }; // struct unique_queue size_type size_orig, height, size_ext; std::vector data; unique_queue que; void recalc(const size_type node) { data[node] = data[node << 1] + data[node << 1 | 1]; } void rebuild() { while(!que.empty()) { const size_type index = que.pop() >> 1; if(index && que.push(index)) recalc(index); } que.clear(); } template size_type left_search_subtree(size_type index, const pred_type pred, monoid mono) const { assert(index); while(index < size_ext) { const monoid tmp = data[(index <<= 1) | 1] + mono; if(pred(tmp)) mono = tmp; else ++index; } return ++index -= size_ext; } template size_type right_search_subtree(size_type index, const pred_type pred, monoid mono) const { assert(index); while(index < size_ext) { const monoid tmp = mono + data[index <<= 1]; if(pred(tmp)) ++index, mono = tmp; } return (index -= size_ext) < size_orig ? index : size_orig; } public: segment_tree(const size_type n = 0) : size_orig{n}, height(n > 1 ? 32 - __builtin_clz(n - 1) : 0), size_ext{1u << height}, data(size_ext << 1), que(size_ext << 1) {} segment_tree(const size_type n, const monoid &init) : segment_tree(n) { std::fill(std::next(std::begin(data), size_ext), std::end(data), init); for(size_type i{size_ext}; --i; ) recalc(i); } template ::value_type> segment_tree(iter_type first, iter_type last) : size_orig(std::distance(first, last)), height(size_orig > 1 ? 32 - __builtin_clz(size_orig - 1) : 0), size_ext{1u << height}, data(size_ext << 1), que(size_ext << 1) { static_assert(std::is_constructible::value, "monoid(iter_type::value_type) is not constructible."); for(auto iter{std::next(std::begin(data), size_ext)}; iter != std::end(data) && first != last; ++iter, ++first) *iter = monoid{*first}; for(size_type i{size_ext}; --i; ) recalc(i); } template segment_tree(const container_type &cont) : segment_tree(std::begin(cont), std::end(cont)) {} size_type size() const { return size_orig; } size_type capacity() const { return size_ext; } // reference to the element at the index. typename decltype(data)::reference operator[](size_type index) { assert(index < size_orig); que.push(index |= size_ext); return data[index]; } // const reference to the element at the index. typename decltype(data)::const_reference operator[](size_type index) const { assert(index < size_orig); return data[index |= size_orig]; } monoid fold(size_type first, size_type last) { assert(last <= size_orig); rebuild(); monoid leftval{}, rightval{}; first += size_ext, last += size_ext; while(first < last) { if(first & 1) leftval = leftval + data[first++]; if(last & 1) rightval = data[--last] + rightval; first >>= 1, last >>= 1; } return leftval + rightval; } monoid fold() { return fold(0, size_orig); } template size_type left_search(size_type right, const pred_type pred) { assert(right <= size_orig); rebuild(); right += size_ext; monoid mono{}; for(size_type left{size_ext}; left != right; left >>= 1, right >>= 1) { if((left & 1) != (right & 1)) { const monoid tmp = data[--right] + mono; if(!pred(tmp)) return left_search_subtree(right, pred, mono); mono = tmp; } } return 0; } template size_type right_search(size_type left, const pred_type pred) { assert(left <= size_orig); rebuild(); left += size_ext; monoid mono{}; for(size_type right{size_ext << 1}; left != right; left >>= 1, right >>= 1) { if((left & 1) != (right & 1)) { const monoid tmp = mono + data[left]; if(!pred(tmp)) return right_search_subtree(left, pred, mono); mono = tmp; ++left; } } return size_orig; } }; // class segment_tree #include #include template class deque_aggregation { template class stack_aggregation { friend deque_aggregation; struct data { monoid value, acc; }; size_t capacity; data *stack, *end, *itr; bool top_referred; void recalc() { if(top_referred) { assert(itr != stack); top_referred = false; monoid top_val{top().value}; pop(); push(top_val); } } public: stack_aggregation() : capacity(1), stack(new data[1]), end(std::next(stack)), itr(stack), top_referred() {} ~stack_aggregation() { delete[] stack; } bool empty() const { return stack == itr; } size_t size() const { return itr - stack; } // copy of the element at the index. data operator[](size_t index) const { assert(index < size()); recalc(); return stack[index]; } // reference to the last element data &top() { assert(itr != stack); top_referred = true; return *std::prev(itr); } void pop() { assert(itr != stack); --itr; top_referred = false; } void push(const monoid &mono) { recalc(); if(itr == end) { data *tmp = new data[capacity << 1]; std::swap(stack, tmp); end = (itr = std::copy(tmp, tmp + capacity, stack)) + capacity; capacity <<= 1; delete[] tmp; } if(left_operand_added) *itr = data{mono, mono + fold()}; else *itr = data{mono, fold() + mono}; ++itr; } monoid fold() { if(itr == stack) return monoid(); recalc(); return std::prev(itr)->acc; } }; // class stack_aggregation stack_aggregation left; stack_aggregation right; void balance_to_left() { if(!left.empty() || right.empty()) return; left.recalc(); right.recalc(); size_t mid = (right.size() + 1) >> 1; auto *itr = right.stack + mid; do { left.push((--itr)->value); } while(itr != right.stack); monoid acc; for(auto *p = right.stack + mid; p != right.itr; ++p, ++itr) { *itr = {p->value, acc = acc + p->value}; } right.itr = itr; } void balance_to_right() { if(!right.empty() || left.empty()) return; left.recalc(); right.recalc(); size_t mid = (left.size() + 1) >> 1; auto *itr = left.stack + mid; do { right.push((--itr)->value); } while(itr != left.stack); monoid acc; for(auto *p = left.stack + mid; p != left.itr; ++p, ++itr) { *itr = {p->value, acc = p->value + acc}; } left.itr = itr; } public: bool empty() const { return left.empty() && right.empty(); } size_t size() const { return left.size() + right.size(); } // reference to the first element. monoid &front() { assert(!empty()); return balance_to_left(), left.top().value; } // reference to the last element. monoid &back() { assert(!empty()); return balance_to_right(), right.top().value; } // copy of the element at the index. monoid operator[](size_t index) const { assert(index < left.size() + right.size()); return index < left.size() ? left[index].value : right[index - left.size()].value; } void push_front(const monoid &mono) { left.push(mono); } void push_back(const monoid &mono) { right.push(mono); } void pop_front() { assert(!empty()); balance_to_left(); left.pop(); } void pop_back() { assert(!empty()); balance_to_right(); right.pop(); } monoid fold() { return left.fold() + right.fold(); } }; // class deque_aggregation /* library end */ /* The main code follows. */ struct solver; template void _main(); int main() { _main<>(); } template void _main() { unsigned t = 1; #ifdef LOCAL t = 1; #endif // t = -1; // infinite loop // cin >> t; // case number given while(t--) solver(); } struct mono_type { i64 val; mono_type(i64 v=0) : val(v) {} // binary operation mono_type operator+(const mono_type& rhs) const { return mono_type{*this} += rhs; } // operation assignment mono_type &operator+=(const mono_type &rhs) { val=gcd(val,rhs.val); return *this; } }; struct solver { solver() { int n; cin>>n; deque_aggregation qu; i64 ans=0; for(int i=0,now=0; i>a; qu.push_back(a); while(qu.fold().val==1) { now++; qu.pop_front(); } ans+=now; } cout << ans << "\n"; } };