#pragma region Macros #ifdef noimi #include "my_template.hpp" #else #pragma GCC target("avx2") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #ifdef noimi #define oj_local(a, b) b #else #define oj_local(a, b) a #endif #define LOCAL if(oj_local(0, 1)) #define OJ if(oj_local(1, 0)) using namespace std; using ll = long long; using ull = unsigned long long int; using i128 = __int128_t; using pii = pair; using pll = pair; using ld = long double; template using vc = vector; template using vvc = vector>; template using vvvc = vector>; using vi = vc; using vl = vc; using vpi = vc; using vpl = vc; template using pq = priority_queue; template using pqg = priority_queue, greater>; template int si(const T &x) { return x.size(); } template inline bool chmax(T &a, const S &b) { return (a < b ? a = b, 1 : 0); } template inline bool chmin(T &a, const S &b) { return (a > b ? a = b, 1 : 0); } vi iota(int n) { vi a(n); return iota(a.begin(), a.end(), 0), a; } template vi iota(const vector &a, bool greater = false) { vi res(a.size()); iota(res.begin(), res.end(), 0); sort(res.begin(), res.end(), [&](int i, int j) { if(greater) return a[i] > a[j]; return a[i] < a[j]; }); return res; } // macros #define overload5(a, b, c, d, e, name, ...) name #define overload4(a, b, c, d, name, ...) name #define endl '\n' #define REP0(n) for(ll jidlsjf = 0; jidlsjf < n; ++jidlsjf) #define REP1(i, n) for(ll i = 0; i < (n); ++i) #define REP2(i, a, b) for(ll i = (a); i < (b); ++i) #define REP3(i, a, b, c) for(ll i = (a); i < (b); i += (c)) #define rep(...) overload4(__VA_ARGS__, REP3, REP2, REP1, REP0)(__VA_ARGS__) #define per0(n) for(int jidlsjf = 0; jidlsjf < (n); ++jidlsjf) #define per1(i, n) for(ll i = (n)-1; i >= 0; --i) #define per2(i, a, b) for(ll i = (a)-1; i >= b; --i) #define per3(i, a, b, c) for(ll i = (a)-1; i >= (b); i -= (c)) #define per(...) overload4(__VA_ARGS__, per3, per2, per1, per0)(__VA_ARGS__) #define fore0(a) rep(a.size()) #define fore1(i, a) for(auto &&i : a) #define fore2(a, b, v) for(auto &&[a, b] : v) #define fore3(a, b, c, v) for(auto &&[a, b, c] : v) #define fore4(a, b, c, d, v) for(auto &&[a, b, c, d] : v) #define fore(...) overload5(__VA_ARGS__, fore4, fore3, fore2, fore1, fore0)(__VA_ARGS__) #define setbits(j, n) for(ll iiiii = (n), j = lowbit(iiiii); iiiii; iiiii ^= 1 << j, j = lowbit(iiiii)) #define perm(v) for(bool permrepflag = true; (permrepflag ? exchange(permrepflag, false) : next_permutation(all(v)));) #define fi first #define se second #define pb push_back #define ppb pop_back #define ppf pop_front #define eb emplace_back #define drop(s) cout << #s << endl, exit(0) #define si(c) (int)(c).size() #define lb(c, x) distance((c).begin(), lower_bound(all(c), (x))) #define lbg(c, x) distance((c).begin(), lower_bound(all(c), (x), greater{})) #define ub(c, x) distance((c).begin(), upper_bound(all(c), (x))) #define ubg(c, x) distance((c).begin(), upper_bound(all(c), (x), greater{})) #define rng(v, l, r) v.begin() + (l), v.begin() + (r) #define all(c) begin(c), end(c) #define rall(c) rbegin(c), rend(c) #define SORT(v) sort(all(v)) #define REV(v) reverse(all(v)) #define UNIQUE(x) SORT(x), x.erase(unique(all(x)), x.end()) template T SUM(const S &v) { return accumulate(all(v), T(0)); } #define MIN(v) *min_element(all(v)) #define MAX(v) *max_element(all(v)) #define overload2(_1, _2, name, ...) name #define vec(type, name, ...) vector name(__VA_ARGS__) #define vv(type, name, h, ...) vector> name(h, vector(__VA_ARGS__)) #define vvv(type, name, h, w, ...) vector>> name(h, vector>(w, vector(__VA_ARGS__))) #define vvvv(type, name, a, b, c, ...) \ vector>>> name(a, vector>>(b, vector>(c, vector(__VA_ARGS__)))) constexpr pii dx4[4] = {pii{1, 0}, pii{0, 1}, pii{-1, 0}, pii{0, -1}}; constexpr pii dx8[8] = {{1, 0}, {1, 1}, {0, 1}, {-1, 1}, {-1, 0}, {-1, -1}, {0, -1}, {1, -1}}; namespace yesno_impl { const string YESNO[2] = {"NO", "YES"}; const string YesNo[2] = {"No", "Yes"}; const string yesno[2] = {"no", "yes"}; const string firstsecond[2] = {"second", "first"}; const string FirstSecond[2] = {"Second", "First"}; const string possiblestr[2] = {"impossible", "possible"}; const string Possiblestr[2] = {"Impossible", "Possible"}; void YES(bool t = 1) { cout << YESNO[t] << endl; } void NO(bool t = 1) { YES(!t); } void Yes(bool t = 1) { cout << YesNo[t] << endl; } void No(bool t = 1) { Yes(!t); } void yes(bool t = 1) { cout << yesno[t] << endl; } void no(bool t = 1) { yes(!t); } void first(bool t = 1) { cout << firstsecond[t] << endl; } void First(bool t = 1) { cout << FirstSecond[t] << endl; } void possible(bool t = 1) { cout << possiblestr[t] << endl; } void Possible(bool t = 1) { cout << Possiblestr[t] << endl; } }; // namespace yesno_impl using namespace yesno_impl; #define INT(...) \ int __VA_ARGS__; \ IN(__VA_ARGS__) #define INTd(...) \ int __VA_ARGS__; \ IN2(__VA_ARGS__) #define LL(...) \ ll __VA_ARGS__; \ IN(__VA_ARGS__) #define LLd(...) \ ll __VA_ARGS__; \ IN2(__VA_ARGS__) #define STR(...) \ string __VA_ARGS__; \ IN(__VA_ARGS__) #define CHR(...) \ char __VA_ARGS__; \ IN(__VA_ARGS__) #define DBL(...) \ double __VA_ARGS__; \ IN(__VA_ARGS__) #define VEC(type, name, size) \ vector name(size); \ IN(name) #define VECd(type, name, size) \ vector name(size); \ IN2(name) #define VEC2(type, name1, name2, size) \ vector name1(size), name2(size); \ for(int i = 0; i < size; i++) IN(name1[i], name2[i]) #define VEC2d(type, name1, name2, size) \ vector name1(size), name2(size); \ for(int i = 0; i < size; i++) IN2(name1[i], name2[i]) #define VEC3(type, name1, name2, name3, size) \ vector name1(size), name2(size), name3(size); \ for(int i = 0; i < size; i++) IN(name1[i], name2[i], name3[i]) #define VEC3d(type, name1, name2, name3, size) \ vector name1(size), name2(size), name3(size); \ for(int i = 0; i < size; i++) IN2(name1[i], name2[i], name3[i]) #define VEC4(type, name1, name2, name3, name4, size) \ vector name1(size), name2(size), name3(size), name4(size); \ for(int i = 0; i < size; i++) IN(name1[i], name2[i], name3[i], name4[i]); #define VEC4d(type, name1, name2, name3, name4, size) \ vector name1(size), name2(size), name3(size), name4(size); \ for(int i = 0; i < size; i++) IN2(name1[i], name2[i], name3[i], name4[i]); #define VV(type, name, h, w) \ vector> name(h, vector(w)); \ IN(name) #define VVd(type, name, h, w) \ vector> name(h, vector(w)); \ IN2(name) int scan() { return getchar(); } void scan(int &a) { cin >> a; } void scan(long long &a) { cin >> a; } void scan(char &a) { cin >> a; } void scan(double &a) { cin >> a; } void scan(string &a) { cin >> a; } template void scan(pair &p) { scan(p.first), scan(p.second); } template void scan(vector &); template void scan(vector &a) { for(auto &i : a) scan(i); } template void scan(T &a) { cin >> a; } void IN() {} void IN2() {} template void IN(Head &head, Tail &...tail) { scan(head); IN(tail...); } template void IN2(Head &head, Tail &...tail) { scan(head); --head; IN2(tail...); } template void pat() {} template void pat(Head &h, Tail &...tail) { h += p; pat

(tail...); } template T ceil(T x, S y) { assert(y); return (y < 0 ? ceil(-x, -y) : (x > 0 ? (x + y - 1) / y : x / y)); } template T floor(T x, S y) { assert(y); return (y < 0 ? floor(-x, -y) : (x > 0 ? x / y : x / y - (x % y == 0 ? 0 : 1))); } template U bigmul(const T &x, const S &y, const U &lim) { // clamp(x * y, -lim, lim) if(x < 0 and y < 0) return bigmul(-x, -y, lim); if(x < 0) return -bigmul(-x, y, lim); if(y < 0) return -bigmul(x, -y, lim); return y == 0 or x <= lim / y ? x * y : lim; } template T POW(T x, int n) { T res = 1; for(; n; n >>= 1, x *= x) if(n & 1) res *= x; return res; } template T POW(T x, S n, const ll &mod) { T res = 1; x %= mod; for(; n; n >>= 1, x = x * x % mod) if(n & 1) res = res * x % mod; return res; } vector factor(ll x) { vector ans; for(ll i = 2; i * i <= x; i++) if(x % i == 0) { ans.push_back({i, 1}); while((x /= i) % i == 0) ans.back().second++; } if(x != 1) ans.push_back({x, 1}); return ans; } template vector divisor(T x) { vector ans; for(T i = 1; i * i <= x; i++) if(x % i == 0) { ans.pb(i); if(i * i != x) ans.pb(x / i); } return ans; } template void zip(vector &x) { vector y = x; UNIQUE(y); for(int i = 0; i < x.size(); ++i) { x[i] = lb(y, x[i]); } } template void fold_in(vector &v) {} template void fold_in(vector &v, Head &&a, Tail &&...tail) { for(auto e : a) v.emplace_back(e); fold_in(v, tail...); } template void renumber(vector &v) {} template void renumber(vector &v, Head &&a, Tail &&...tail) { for(auto &&e : a) e = lb(v, e); renumber(v, tail...); } template vector zip(vector &head, Args &&...args) { vector v; fold_in(v, head, args...); sort(all(v)), v.erase(unique(all(v)), v.end()); renumber(v, head, args...); return v; } template void rearrange(const vector &id) {} template void rearrange_exec(const vector &id, vector &v) { vector w(v.size()); rep(i, si(id)) w[i] = v[id[i]]; v.swap(w); } // 並び替える順番, 並び替える vector 達 template void rearrange(const vector &id, Head &a, Tail &...tail) { rearrange_exec(id, a); rearrange(id, tail...); } template vector RUI(const vector &v) { vector res(v.size() + 1); for(int i = 0; i < v.size(); i++) res[i + 1] = res[i] + v[i]; return res; } template void zeta_supersetsum(vector &f) { int n = f.size(); for(int i = 1; i < n; i <<= 1) rep(b, n) if(!(i & b)) f[b] += f[b | i]; } template void zeta_subsetsum(vector &f) { int n = f.size(); for(int i = 1; i < n; i <<= 1) rep(b, n) if(!(i & b)) f[b | i] += f[b]; } template void mobius_subset(vector &f) { int n = f.size(); for(int i = 1; i < n; i <<= 1) rep(b, n) if(!(i & b)) f[b] -= f[b | i]; } template void mobius_superset(vector &f) { int n = f.size(); for(int i = 1; i < n; i <<= 1) rep(b, n) if(!(i & b)) f[b | i] -= f[b]; } // 反時計周りに 90 度回転 template void rot(vector> &v) { if(empty(v)) return; int n = v.size(), m = v[0].size(); vector> res(m, vector(n)); rep(i, n) rep(j, m) res[m - 1 - j][i] = v[i][j]; v.swap(res); } vector counter(const vector &v, int max_num = -1) { if(max_num == -1) max_num = MAX(v); vector res(max_num + 1); fore(e, v) res[e]++; return res; } // x in [l, r) template bool inc(const T &x, const S &l, const S &r) { return l <= x and x < r; } template bool inc(const T &x, const pair &p) { return p.first <= x and x < p.second; } // 便利関数 constexpr ll ten(int n) { return n == 0 ? 1 : ten(n - 1) * 10; } constexpr ll tri(ll n) { return n * (n + 1) / 2; } // l + ... + r constexpr ll tri(ll l, ll r) { return (l + r) * (r - l + 1) / 2; } ll max(int x, ll y) { return max((ll)x, y); } ll max(ll x, int y) { return max(x, (ll)y); } int min(int x, ll y) { return min((ll)x, y); } int min(ll x, int y) { return min(x, (ll)y); } // bit 演算系 #define bit(i) (1LL << i) // (1 << i) #define test(b, i) (b >> i & 1) // b の i bit 目が立っているか ll pow2(int i) { return 1LL << i; } int topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); } int topbit(ll t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); } int lowbit(signed a) { return a == 0 ? 32 : __builtin_ctz(a); } int lowbit(ll a) { return a == 0 ? 64 : __builtin_ctzll(a); } // int allbit(int n) { return (1 << n) - 1; } constexpr ll mask(int n) { return (1LL << n) - 1; } // int popcount(signed t) { return __builtin_popcount(t); } // int popcount(ll t) { return __builtin_popcountll(t); } int popcount(uint64_t t) { return __builtin_popcountll(t); } static inline uint64_t popcount64(uint64_t x) { uint64_t m1 = 0x5555555555555555ll; uint64_t m2 = 0x3333333333333333ll; uint64_t m4 = 0x0F0F0F0F0F0F0F0Fll; uint64_t h01 = 0x0101010101010101ll; x -= (x >> 1) & m1; x = (x & m2) + ((x >> 2) & m2); x = (x + (x >> 4)) & m4; return (x * h01) >> 56; } bool ispow2(int i) { return i && (i & -i) == i; } ll rnd(ll l, ll r) { //[l, r) #ifdef noimi static mt19937_64 gen; #else static mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count()); #endif return uniform_int_distribution(l, r - 1)(gen); } ll rnd(ll n) { return rnd(0, n); } template void random_shuffle(vc &a) { rep(i, si(a)) swap(a[i], a[rnd(0, i + 1)]); } int in() { int x; cin >> x; return x; } ll lin() { unsigned long long x; cin >> x; return x; } template pair operator-(const pair &x) { return pair(-x.first, -x.second); } template pair operator-(const pair &x, const pair &y) { return pair(x.fi - y.fi, x.se - y.se); } template pair operator+(const pair &x, const pair &y) { return pair(x.fi + y.fi, x.se + y.se); } template pair operator&(const pair &l, const pair &r) { return pair(max(l.fi, r.fi), min(l.se, r.se)); } template pair operator+=(pair &l, const pair &r) { return l = l + r; } template pair operator-=(pair &l, const pair &r) { return l = l - r; } template bool intersect(const pair &l, const pair &r) { return (l.se < r.se ? r.fi < l.se : l.fi < r.se); } template vector &operator++(vector &v) { fore(e, v) e++; return v; } template vector operator++(vector &v, int) { auto res = v; fore(e, v) e++; return res; } template vector &operator--(vector &v) { fore(e, v) e--; return v; } template vector operator--(vector &v, int) { auto res = v; fore(e, v) e--; return res; } template void connect(vector &l, const vector &r) { fore(e, r) l.eb(e); } template vector operator+(const vector &l, const vector &r) { vector res(max(si(l), si(r))); rep(i, si(l)) res[i] += l[i]; rep(i, si(r)) res[i] += r[i]; return res; } template vector operator-(const vector &l, const vector &r) { vector res(max(si(l), si(r))); rep(i, si(l)) res[i] += l[i]; rep(i, si(r)) res[i] -= r[i]; return res; } template vector &operator+=(const vector &l, const vector &r) { if(si(l) < si(r)) l.resize(si(r)); rep(i, si(r)) l[i] += r[i]; return l; } template vector &operator-=(const vector &l, const vector &r) { if(si(l) < si(r)) l.resize(si(r)); rep(i, si(r)) l[i] -= r[i]; return l; } template vector &operator+=(vector &v, const T &x) { fore(e, v) e += x; return v; } template vector &operator-=(vector &v, const T &x) { fore(e, v) e -= x; return v; } template struct edge { int from, to; T cost; int id; edge(int to, T cost) : from(-1), to(to), cost(cost) {} edge(int from, int to, T cost) : from(from), to(to), cost(cost) {} edge(int from, int to, T cost, int id) : from(from), to(to), cost(cost), id(id) {} constexpr bool operator<(const edge &rhs) const noexcept { return cost < rhs.cost; } edge &operator=(const int &x) { to = x; return *this; } operator int() const { return to; } friend ostream operator<<(ostream &os, const edge &e) { return os << e.to; } }; template using Edges = vector>; template Edges read_edges(int m, bool weighted = false) { Edges res; res.reserve(m); for(int i = 0; i < m; i++) { int u, v, c = 0; scan(u), scan(v), u--, v--; if(weighted) scan(c); res.eb(u, v, c, i); } return res; } using Tree = vector>; using Graph = vector>; template using Wgraph = vector>>; Graph getG(int n, int m = -1, bool directed = false, int margin = 1) { Tree res(n); if(m == -1) m = n - 1; while(m--) { int a, b; cin >> a >> b; a -= margin, b -= margin; res[a].emplace_back(b); if(!directed) res[b].emplace_back(a); } return res; } Graph getTreeFromPar(int n, int margin = 1) { Graph res(n); for(int i = 1; i < n; i++) { int a; cin >> a; res[a - margin].emplace_back(i); } return res; } template Wgraph getWg(int n, int m = -1, bool directed = false, int margin = 1) { Wgraph res(n); if(m == -1) m = n - 1; while(m--) { int a, b; T c; scan(a), scan(b), scan(c); a -= margin, b -= margin; res[a].emplace_back(b, c); if(!directed) res[b].emplace_back(a, c); } return res; } void add(Graph &G, int x, int y) { G[x].eb(y), G[y].eb(x); } template void add(Wgraph &G, int x, int y, T c) { G[x].eb(y, c), G[y].eb(x, c); } #define TEST \ INT(testcases); \ while(testcases--) i128 abs(const i128 &x) { return x > 0 ? x : -x; } istream &operator>>(istream &is, i128 &v) { string s; is >> s; v = 0; for(int i = 0; i < (int)s.size(); i++) { if(isdigit(s[i])) { v = v * 10 + s[i] - '0'; } } if(s[0] == '-') { v *= -1; } return is; } ostream &operator<<(ostream &os, const i128 &v) { if(v == 0) { return (os << "0"); } i128 num = v; if(v < 0) { os << '-'; num = -num; } string s; for(; num > 0; num /= 10) { s.push_back((char)(num % 10) + '0'); } reverse(s.begin(), s.end()); return (os << s); } namespace aux { template struct tp { static void output(std::ostream &os, const T &v) { os << std::get(v) << (&os == &cerr ? ", " : " "); tp::output(os, v); } }; template struct tp { static void output(std::ostream &os, const T &v) { os << std::get(v); } }; } // namespace aux template std::ostream &operator<<(std::ostream &os, const std::tuple &t) { if(&os == &cerr) { os << '('; } aux::tp, 0, sizeof...(Ts) - 1>::output(os, t); if(&os == &cerr) { os << ')'; } return os; } template std::ostream &operator<<(std::ostream &os, const priority_queue &_pq) { auto pq = _pq; vector res; while(!empty(pq)) res.emplace_back(pq.top()), pq.pop(); return os << res; } template ostream &operator<<(ostream &os, const pair &p) { if(&os == &cerr) { return os << "(" << p.first << ", " << p.second << ")"; } return os << p.first << " " << p.second; } template std::basic_ostream &operator<<(std::basic_ostream &os, const Container &x) { bool f = true; if(&os == &cerr) os << "["; for(auto &y : x) { if(&os == &cerr) os << (f ? "" : ", ") << y; else os << (f ? "" : " ") << y; f = false; } if(&os == &cerr) os << "]"; return os; } #define dump(...) static_cast(0) #define dbg(...) static_cast(0) void OUT() { cout << endl; } template void OUT(const Head &head, const Tail &...tail) { cout << head; if(sizeof...(tail)) cout << ' '; OUT(tail...); } template static constexpr T inf = numeric_limits::max() / 2; template constexpr pair inf> = {inf, inf}; template void OUT2(const T &t, T INF = inf, T res = -1) { OUT(t != INF ? t : res); } template void OUT2(vector &v, T INF = inf, T res = -1) { fore(e, v) if(e == INF) e = res; OUT(v); fore(e, v) if(e == res) e = INF; } template struct REC { F f; REC(F &&f_) : f(forward(f_)) {} template auto operator()(Args &&...args) const { return f(*this, forward(args)...); } }; template vector> runLength(const vector &v) { vector> res; for(auto &e : v) { if(res.empty() or res.back().fi != e) res.eb(e, 1); else res.back().se++; } return res; } vector> runLength(const string &v) { vector> res; for(auto &e : v) { if(res.empty() or res.back().fi != e) res.eb(e, 1); else res.back().se++; } return res; } struct string_converter { char start = 0; char type(const char &c) const { return (islower(c) ? 'a' : isupper(c) ? 'A' : isdigit(c) ? '0' : 0); } int convert(const char &c) { if(!start) start = type(c); return c - start; } int convert(const char &c, const string &chars) { return chars.find(c); } template auto convert(const T &v) { vector ret; ret.reserve(size(v)); for(auto &&e : v) ret.emplace_back(convert(e)); return ret; } template auto convert(const T &v, const string &chars) { vector ret; ret.reserve(size(v)); for(auto &&e : v) ret.emplace_back(convert(e, chars)); return ret; } int operator()(const char &v, char s = 0) { start = s; return convert(v); } int operator()(const char &v, const string &chars) { return convert(v, chars); } template auto operator()(const T &v, char s = 0) { start = s; return convert(v); } template auto operator()(const T &v, const string &chars) { return convert(v, chars); } } toint; template T bin_search(T ok, T ng, const F &f) { while(abs(ok - ng) > 1) { T mid = ok + ng >> 1; (f(mid) ? ok : ng) = mid; } return ok; } template T bin_search_double(T ok, T ng, const F &f, int iter = 80) { while(iter--) { T mid = (ok + ng) / 2; (f(mid) ? ok : ng) = mid; } return ok; } struct Setup_io { Setup_io() { ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0); cout << fixed << setprecision(11); } } setup_io; #endif #pragma endregion // S : 持つデータの型 T : 範囲の型 template struct IntervalManager { struct node { T l, r; S x; node(const T &l, const T &r, const S &x) : l(l), r(r), x(x) {} constexpr bool operator<(const node &rhs) const { if(l != rhs.l) return l < rhs.l; return r < rhs.r; } }; const S unit; set s; IntervalManager(const S &u = S()) : unit(u) {} IntervalManager(const vector &a) { vector setter; for(int l = 0; l < a.size(); l++) { int r = l; for(; r < a.size() and a[l] == a[r]; r++) {} setter.emplace_back(l, r, a[l]); l = r - 1; } s = set(all(setter)); } // x を含んだセグメントのイテレータを返す typename set::iterator getIt(const T &x) { auto it = s.upper_bound(node(x, numeric_limits::max(), 0)); if(it == begin(s)) return end(s); it = prev(it); if(it->l <= x and x < it->r) return it; return end(s); } // x を含んだセグメントの情報を持ってくる node getSeg(const T &x) { auto it = getIt(x); if(it != end(s)) return *it; return node(x, x + 1, unit); } // x 以上をはじめて含むセグメントの iterator が帰ってくる typename set::iterator nextIt(const T &x) { auto it = s.upper_bound(node(x, numeric_limits::max(), 0)); if(it == begin(s)) return it; return prev(it); } // x に設定されてる値を取得 S get(const T &x) { auto it = getIt(x); if(it != end(s)) return it->x; return unit; } S operator[](T k) const { return get(k); } // [l, r) := x を set するときに消える区間加える区間ごとに関数を呼び出す // ただし、内包, 結合される [L, r) := x の区間も一旦消す template void update(T l, T r, const S &x, const ADD &add, const DEL &del) { auto it = s.lower_bound(node{l, 0, x}); while(it != end(s) and it->l <= r) { if(it->l == r) { if(it->x == x) { del(r, it->r, x); r = it->r, it = s.erase(it); } break; } if(it->r <= r) { del(it->l, it->r, it->x); it = s.erase(it); } else { if(it->x == x) { r = it->r; del(it->l, it->r, it->x); it = s.erase(it); } else { del(it->l, r, it->x); node n = *it; it = s.erase(it); it = s.emplace_hint(it, r, n.r, n.x); } } } if(it != begin(s)) { it = prev(it); if(it->r == l) { if(it->x == x) { del(it->l, it->r, it->x); l = it->l; it = s.erase(it); } } else if(l < it->r) { if(it->x == x) { del(it->l, it->r, it->x); l = min(l, it->l); r = max(r, it->r); it = s.erase(it); } else { if(r < it->r) { it = s.emplace_hint(next(it), r, it->r, it->x); it = prev(it); } del(l, min(r, it->r), it->x); node n = *it; it = s.erase(it); it = s.emplace_hint(it, n.l, l, n.x); } } } if(it != end(s)) it = next(it); add(l, r, x); s.emplace_hint(it, l, r, x); } void update(T l, T r, const S &x) { update( l, r, x, [](T, T, S) {}, [](T, T, S) {}); } void show() { for(auto e : s) { cerr << "(" << "[" << e.l << ", " << e.r << "): " << e.x << ") "; } cerr << endl; } }; namespace segtree_impl { namespace internal { // @param n `0 <= n` // @return minimum non-negative `x` s.t. `n <= 2**x` int ceil_pow2(int n) { int x = 0; while((1U << x) < (unsigned int)(n)) x++; return x; } // @param n `1 <= n` // @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0` constexpr int bsf_constexpr(unsigned int n) { int x = 0; while(!(n & (1 << x))) x++; return x; } // @param n `1 <= n` // @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0` int bsf(unsigned int n) { #ifdef _MSC_VER unsigned long index; _BitScanForward(&index, n); return index; #else return __builtin_ctz(n); #endif } } // namespace internal } // namespace segtree_impl namespace segtree_impl { template struct segtree { public: segtree() : segtree(0) {} explicit segtree(int n) : segtree(std::vector(n, e())) {} explicit segtree(const std::vector &v) : _n(int(v.size())) { log = internal::ceil_pow2(_n); size = 1 << log; d = std::vector(2 * size, e()); for(int i = 0; i < _n; i++) d[size + i] = v[i]; for(int i = size - 1; i >= 1; i--) { update(i); } } void set(int p, S x) { assert(0 <= p && p < _n); p += size; d[p] = x; for(int i = 1; i <= log; i++) update(p >> i); } S get(int p) const { assert(0 <= p && p < _n); return d[p + size]; } S operator[](int k) const { return get(k); } S prod(int l, int r) const { #ifdef ONLINE_JUDGE if(l < 0) l = 0; if(r > _n) r = _n; if(l > r) return e(); #endif assert(0 <= l && l <= r && r <= _n); S sml = e(), smr = e(); l += size; r += size; while(l < r) { if(l & 1) sml = op(sml, d[l++]); if(r & 1) smr = op(d[--r], smr); l >>= 1; r >>= 1; } return op(sml, smr); } S all_prod() const { return d[1]; } template int max_right(int l) const { return max_right(l, [](S x) { return f(x); }); } template int max_right(int l, F f) const { #ifdef ONLINE_JUDGE if(l < 0) l = 0; if(l > _n) l = _n; #endif assert(0 <= l && l <= _n); assert(f(e())); if(l == _n) return _n; l += size; S sm = e(); do { while(l % 2 == 0) l >>= 1; if(!f(op(sm, d[l]))) { while(l < size) { l = (2 * l); if(f(op(sm, d[l]))) { sm = op(sm, d[l]); l++; } } return l - size; } sm = op(sm, d[l]); l++; } while((l & -l) != l); return _n; } template int min_left(int r) const { return min_left(r, [](S x) { return f(x); }); } template int min_left(int r, F f) const { #ifdef ONLINE_JUDGE if(r < 0) r = 0; if(r > _n) r = _n; #endif assert(0 <= r && r <= _n); assert(f(e())); if(r == 0) return 0; r += size; S sm = e(); do { r--; while(r > 1 && (r % 2)) r >>= 1; if(!f(op(d[r], sm))) { while(r < size) { r = (2 * r + 1); if(f(op(d[r], sm))) { sm = op(d[r], sm); r--; } } return r + 1 - size; } sm = op(d[r], sm); } while((r & -r) != r); return 0; } friend std::ostream &operator<<(std::ostream &os, segtree &ls) { os << "{"; for(int i = 0; i < ls._n; i++) os << ls.get(i) << (i == ls._n - 1 ? "" : ", "); return os << "}"; } private: int _n, size, log; std::vector d; void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); } }; template constexpr T inf = std::numeric_limits::max() / 2; template constexpr std::pair inf> = {inf, inf}; template T min_func(T x, T y) { return min(x, y); } template T max_func(T x, T y) { return max(x, y); } template T plus_func(T x, T y) { return x + y; } template T set_func(T x, T y) { return (y == ID ? x : y); } template T min_e() { return inf; } template T max_e() { return -inf; } template T plus_e() { return T(); } template using RST = segtree, plus_e>; template using RmT = segtree, min_e>; template using RMT = segtree, max_e>; } // namespace segtree_impl using segtree_impl::RmT; using segtree_impl::RMT; using segtree_impl::RST; using segtree_impl::segtree; struct S { ll lma, rma, ma, sum, s; }; S f(S x, S y) { S res{max(x.lma, x.sum + y.lma), max(y.rma, y.sum + x.rma), -1, x.sum + y.sum, max(x.s, y.s)}; res.ma = max({res.lma, res.rma, x.ma, y.ma, x.rma + y.lma}); return res; } S e() { return {0, 0, -inf, 0, -inf}; } int main() { INT(n); VEC2(ll, a, b, n); INT(q); VEC3(ll, t, x, y, q); vl v; v.eb(0); fore(e, b) v.eb(v.back() + e); rep(i, q) { if(t[i] == 1) v.eb(x[i] - 1), v.eb(x[i]); else { v.eb(x[i] - 1), v.eb(y[i]); } } UNIQUE(v); ll now = 0; vector setter(si(v) - 1); rep(i, n) { int l = lb(v, now); int r = lb(v, (now += b[i])); rep(j, l, r) { ll x = (v[j + 1] - v[j]) * a[i]; ll y = max(x, 0); setter[j] = S{y, y, y, x, a[i]}; } } segtree seg(setter); // rep(i, n) OUT(setter[i].lma, setter[i].rma, setter[i].ma, setter[i].sum, setter[i].s); // OUT(seg.all_prod().ma); rep(i, q) { if(t[i] == 1) { int j = lb(v, x[i] - 1); ll X = y[i]; ll Y = max(X, 0); seg.set(j, S{Y, Y, Y, X, y[i]}); } else { auto s = seg.prod(lb(v, x[i] - 1), lb(v, y[i])); ll res = s.ma; if(res == 0) res = s.s; OUT(res); } } }