#pragma region preprocessor #ifdef LOCAL //* #define _GLIBCXX_DEBUG // gcc /*/ #define _LIBCPP_DEBUG 0 // clang //*/ // #define __buffer_check__ #else #pragma GCC optimize("Ofast") // #define NDEBUG #endif #define __precision__ 15 #define __iostream_untie__ true #include #include #ifdef LOCAL #include "dump.hpp" #define mesg(str) std::cerr << "[ " << __LINE__ << " : " << __FUNCTION__ << " ] " << str << "\n" #else #define dump(...) ((void)0) #define mesg(str) ((void)0) #endif #pragma endregion #pragma region std-overload 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 #pragma endregion #pragma region config namespace config { const auto start_time{std::chrono::system_clock::now()}; int64_t elapsed_time() { using namespace std::chrono; const auto end_time{std::chrono::system_clock::now()}; return duration_cast(end_time - start_time).count(); } __attribute__((constructor)) void setup() { using namespace std; 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"; atexit([]{ cerr << "\n----- Exec time : " << elapsed_time() << " ms -----\n\n"; }); #endif #ifdef __buffer_check__ atexit([]{ ofstream cnsl("CON"); char bufc; if(cin >> bufc) cnsl << "\n\033[1;35mwarning\033[0m: buffer not empty.\n\n"; }); #endif } } // namespace config #pragma endregion #pragma region utility // 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) { assert(__ok != __ng); 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) { assert(__ok != __ng); while(std::abs(__ok - __ng) > eps) { long double mid{(__ok + __ng) / 2}; (pred(mid) ? __ok : __ng) = mid; } return __ok; } // trinary search on discrete range. template iter_type trinary(iter_type __first, iter_type __last, comp_type comp) { assert(__first < __last); std::ptrdiff_t dist(__last - __first); while(dist > 2) { iter_type __left(__first + dist / 3), __right = (__first + dist * 2 / 3); if(comp(__left, __right)) __last = __right, dist = dist * 2 / 3; else __first = __left, dist -= dist / 3; } if(dist > 1 && comp(next(__first), __first)) ++__first; return __first; } // trinary search on real numbers. template long double trinary(long double __first, long double __last, const long double eps, comp_type comp) { assert(__first < __last); while(__last - __first > eps) { long double __left{(__first * 2 + __last) / 3}, __right{(__first + __last * 2) / 3}; if(comp(__left, __right)) __last = __right; else __first = __left; } return __first; } // 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); } #pragma endregion #pragma region alias 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; #pragma endregion #pragma region library #include #include template class lazy_segment_tree { using size_type = typename std::vector::size_type; size_type size_orig, height, size_ext; std::vector data; std::vector lazy; void recalc(const size_type node) { data[node] = data[node << 1] + data[node << 1 | 1]; } void apply(size_type index, const homomorphism &homo) { homo.apply(data[index]); if(index < size_ext) lazy[index] *= homo; } void push(size_type index) { if(index >= size_ext) return; apply(index << 1, lazy[index]); apply(index << 1 | 1, lazy[index]); lazy[index] = homomorphism{}; } template size_type left_search_subtree(size_type index, const pred_type pred, monoid mono) { assert(index); while(index < size_ext) { push(index); 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) { assert(index); while(index < size_ext) { push(index); const monoid tmp = mono + data[index <<= 1]; if(pred(tmp)) ++index, mono = tmp; } return (index -= size_ext) < size_orig ? index : size_orig; } public: lazy_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), lazy(size_ext) {} lazy_segment_tree(const size_type n, const monoid &init) : lazy_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> lazy_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), lazy(size_ext) { 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 lazy_segment_tree(const container_type &cont) : lazy_segment_tree(std::begin(cont), std::end(cont)) {} size_type size() const { return size_orig; } size_type capacity() const { return size_ext; } monoid operator[](size_type index) { return fold(index, index + 1); } void update(const size_type index, const homomorphism &homo) { update(index, index + 1, homo); } void update(size_type first, size_type last, const homomorphism &homo) { assert(last <= size_orig); if(first >= last) return; first += size_ext, last += size_ext - 1; for(size_type i = height; i; --i) push(first >> i), push(last >> i); for(size_type l = first, r = last + 1; last; l >>= 1, r >>= 1) { if(l < r) { if(l & 1) apply(l++, homo); if(r & 1) apply(--r, homo); } if(first >>= 1, last >>= 1) { recalc(first), recalc(last); } } } monoid fold() { return fold(0, size_orig); } monoid fold(size_type first, size_type last) { assert(last <= size_orig); if(first >= last) return monoid{}; first += size_ext, last += size_ext - 1; monoid left_val{}, right_val{}; for(size_type l = first, r = last + 1; last; l >>= 1, r >>= 1) { if(l < r) { if(l & 1) left_val = left_val + data[l++]; if(r & 1) right_val = data[--r] + right_val; } if(first >>= 1, last >>= 1) { lazy[first].apply(left_val); lazy[last].apply(right_val); } } return left_val + right_val; } template size_type left_search(size_type right, const pred_type pred) { assert(right <= size_orig); right += size_ext - 1; for(size_type i{height}; i; --i) push(right >> i); ++right; 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); left += size_ext; for(size_type i{height}; i; --i) push(left >> i); 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 lazy_segment_tree #include #include #include template class matrix { struct identity_wrapper { template struct check { static Ring identity() { return Ring::identity(); } }; template struct check { static Ring identity() { return 1; } }; operator Ring() { return check::value>::identity(); } }; using row_type = std::valarray; using data_type = std::valarray; data_type data; friend std::istream &operator>>(std::istream &is, matrix &mat) { for(size_t i = 0; i != mat.rows(); ++i) for(size_t j = 0; j != mat.columns(); ++j) is >> mat[i][j]; return is; } friend std::ostream &operator<<(std::ostream &os, const matrix &mat) { for(size_t i = 0; i != mat.rows(); ++i) { if(i) os << "\n"; for(size_t j = 0; j != mat.columns(); ++j) os << (j ? " " : "") << mat[i][j]; } return os; } friend matrix transpose(const matrix &mat) { matrix res(mat.columns(), mat.rows()); for(size_t i{mat.columns()}; i--;) for(size_t j{mat.rows()}; j--;) res[i][j] = mat[j][i]; return res; } public: explicit matrix(size_t _n = 1) : matrix(_n, _n) {} matrix(size_t _r, size_t _c) : data(row_type(_c), _r) {} matrix(const data_type &_data) : data(_data) {} size_t rows() const { return data.size(); } size_t columns() const { return data[0].size(); } row_type &operator[](const size_t i) { assert(i < data.size()); return data[i]; } const row_type &operator[](const size_t i) const { assert(i < data.size()); return data[i]; } matrix operator-() const { return {-data}; } matrix &operator+=(const matrix &rhs) { data += rhs.data; return *this; } matrix &operator-=(const matrix &rhs) { data -= rhs.data; return *this; } matrix &operator*=(matrix rhs) noexcept { assert(columns() == rhs.rows()); rhs = transpose(rhs); for(row_type &row : data) { const row_type copied{row}; for(size_t j{rhs.rows()}; j--;) row[j] = (copied * rhs[j]).sum(); } return *this; } matrix operator+(const matrix &rhs) const { return matrix{*this} += rhs; } matrix operator-(const matrix &rhs) const { return matrix{*this} -= rhs; } matrix operator*(const matrix &rhs) const { return matrix{*this} *= rhs; } friend row_type &operator*=(row_type &lhs, const matrix &rhs) { return lhs = lhs * rhs; } friend row_type operator*(row_type &lhs, const matrix &rhs) { assert(lhs.size() == rhs.rows()); row_type res(rhs.columns()); for(size_t k{lhs.size()}; k--;) for(size_t j{rhs.columns()}; j--;) res[j] += lhs[k] * rhs[k][j]; return res; } static matrix identity(const size_t _n) { matrix ide(_n); for(size_t i{_n}; i--;) ide[i][i] = identity_wrapper(); return ide; } friend matrix pow(matrix mat, unsigned long long exp) { matrix res{identity(mat.rows())}; for(assert(mat.rows() == mat.columns()); exp; mat *= mat, exp >>= 1) if(exp & 1) res *= mat; return res; } }; // class matrix #pragma endregion 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 { i64 squs=0,lins=0,cnt=0; // binary operation mono operator+(const mono& rhs) const { return mono{*this} += rhs; } // operation assignment mono &operator+=(const mono &rhs) { squs+=rhs.squs; lins+=rhs.lins; cnt+=rhs.cnt; return *this; } }; struct homo { i64 val=0; // compose void operator*=(const homo& rhs) { val+=rhs.val; } // apply self to an element in S template void apply(S &rhs) const { rhs.squs+=rhs.lins*val*2+val*val*rhs.cnt; rhs.lins+=rhs.cnt*val; } }; struct solver { solver() { int n; cin>>n; vector> tre(n); for(int i=1; i>u>>v; u--,v--; tre[u].emplace_back(v); tre[v].emplace_back(u); } vector ans(n); make_recursive( [&](auto dfs, int v, int p)->int { i64 su=0,sq=0; for(int to: tre[v]) { if(to==p) continue; i64 sz=dfs(to,v); su+=sz; sq+=sz*sz; } ans[v]=su*su-sq+su*2+1; return su+1; } ) (0,-1); for(i64 x: ans) cout << x << "\n"; } };