#line 2 "/home/nok0/documents/programming/library/template/header.hpp" #include <bits/stdc++.h> #line 3 "/home/nok0/documents/programming/library/template/def_const.hpp" const int inf = 1000000000; const long long INF = 1000000000000000000ll; #line 4 "/home/nok0/documents/programming/library/template/debug.hpp" namespace viewer { void view(const long long &e) { if(e == INF) std::cerr << "INF"; else if(e == -INF) std::cerr << "-INF"; else std::cerr << e; } void view(const int &e) { if(e == inf) std::cerr << "inf"; else if(e == -inf) std::cerr << "-inf"; else std::cerr << e; } template <typename T> void view(const T &e) { std::cerr << e; } template <typename T, typename U> void view(const std::pair<T, U> &p) { std::cerr << "("; view(p.first); std::cerr << ", "; view(p.second); std::cerr << ")"; } template <class T0, class T1, class T2> void view(const std::tuple<T0, T1, T2> &p) { std::cerr << "("; view(std::get<0>(p)); std::cerr << ", "; view(std::get<1>(p)); std::cerr << ", "; view(std::get<2>(p)); std::cerr << ")"; } template <class T0, class T1, class T2, class T3> void view(const std::tuple<T0, T1, T2, T3> &p) { std::cerr << "("; view(std::get<0>(p)); std::cerr << ", "; view(std::get<1>(p)); std::cerr << ", "; view(std::get<2>(p)); std::cerr << ", "; view(std::get<3>(p)); std::cerr << ")"; } template <typename T> void view(const std::set<T> &s) { if(s.empty()) { std::cerr << "{ }"; return; } std::cerr << "{ "; for(auto &t : s) { view(t); std::cerr << ", "; } std::cerr << "\b\b }"; } template <typename T> void view(const std::unordered_set<T> &s) { if(s.empty()) { std::cerr << "{ }"; return; } std::cerr << "{ "; for(auto &t : s) { view(t); std::cerr << ", "; } std::cerr << "\b\b }"; } template <typename T> void view(const std::multiset<T> &s) { if(s.empty()) { std::cerr << "{ }"; return; } std::cerr << "{ "; for(auto &t : s) { view(t); std::cerr << ", "; } std::cerr << "\b\b }"; } template <typename T> void view(const std::unordered_multiset<T> &s) { if(s.empty()) { std::cerr << "{ }"; return; } std::cerr << "{ "; for(auto &t : s) { view(t); std::cerr << ", "; } std::cerr << "\b\b }"; } template <typename T> void view(const std::vector<T> &v) { if(v.empty()) { std::cerr << "{ }"; return; } std::cerr << "{ "; for(const auto &e : v) { view(e); std::cerr << ", "; } std::cerr << "\b\b }"; } template <typename T, std::size_t ary_size> void view(const std::array<T, ary_size> &v) { if(v.empty()) { std::cerr << "{ }"; return; } std::cerr << "{ "; for(const auto &e : v) { view(e); std::cerr << ", "; } std::cerr << "\b\b }"; } template <typename T> void view(const std::vector<std::vector<T>> &vv) { std::cerr << "{\n"; for(const auto &v : vv) { std::cerr << "\t"; view(v); std::cerr << '\n'; } std::cerr << "}"; } template <typename T, typename U> void view(const std::vector<std::pair<T, U>> &v) { std::cerr << "{\n"; for(const auto &c : v) { std::cerr << "\t("; view(c.first); std::cerr << ", "; view(c.second); std::cerr << ")\n"; } std::cerr << "}"; } template <class T0, class T1, class T2> void view(const std::vector<std::tuple<T0, T1, T2>> &v) { if(v.empty()) { std::cerr << "{ }"; return; } std::cerr << '{'; for(const auto &t : v) { std::cerr << "\n\t"; view(t); std::cerr << ","; } std::cerr << "\n}"; } template <class T0, class T1, class T2, class T3> void view(const std::vector<std::tuple<T0, T1, T2, T3>> &v) { if(v.empty()) { std::cerr << "{ }"; return; } std::cerr << '{'; for(const auto &t : v) { std::cerr << "\n\t"; view(t); std::cerr << ","; } std::cerr << "\n}"; } template <typename T, typename U> void view(const std::map<T, U> &m) { std::cerr << "{\n"; for(const auto &t : m) { std::cerr << "\t["; view(t.first); std::cerr << "] : "; view(t.second); std::cerr << '\n'; } std::cerr << "}"; } template <typename T, typename U> void view(const std::unordered_map<T, U> &m) { std::cerr << "{\n"; for(const auto &t : m) { std::cerr << "\t["; view(t.first); std::cerr << "] : "; view(t.second); std::cerr << '\n'; } std::cerr << "}"; } } // namespace viewer // when compiling : g++ foo.cpp -DLOCAL #ifdef LOCAL void debug_out() {} template <typename Head, typename... Tail> void debug_out(Head H, Tail... T) { viewer::view(H); std::cerr << ", "; debug_out(T...); } #define debug(...) \ do { \ std::cerr << __LINE__ << " [" << #__VA_ARGS__ << "] : ["; \ debug_out(__VA_ARGS__); \ std::cerr << "\b\b]\n"; \ } while(0) #define dump(x) \ do { \ std::cerr << __LINE__ << " " << #x << " : "; \ viewer::view(x); \ std::cerr << '\n'; \ } while(0) #else #define debug(...) (void(0)) #define dump(x) (void(0)) #endif #line 3 "/home/nok0/documents/programming/library/template/def_name.hpp" #define pb push_back #define eb emplace_back #define fi first #define se second #define SZ(x) ((int)(x).size()) #define all(x) (x).begin(), (x).end() #define rall(x) (x).rbegin(), (x).rend() #define popcnt(x) __builtin_popcountll(x) template <class T = int> using V = std::vector<T>; template <class T = int> using VV = std::vector<std::vector<T>>; template <class T> using pqup = std::priority_queue<T, std::vector<T>, std::greater<T>>; using ll = long long; using ld = long double; using int128 = __int128_t; using pii = std::pair<int, int>; using pll = std::pair<long long, long long>; #line 3 "/home/nok0/documents/programming/library/template/fast_io.hpp" struct fast_io { fast_io() { std::ios::sync_with_stdio(false); std::cin.tie(nullptr); std::cout << std::fixed << std::setprecision(15); } } fast_io_; #line 3 "/home/nok0/documents/programming/library/template/input.hpp" template <class T, class U> std::istream &operator>>(std::istream &is, std::pair<T, U> &p) { is >> p.first >> p.second; return is; } template <class T> std::istream &operator>>(std::istream &is, std::vector<T> &v) { for(T &i : v) is >> i; return is; } std::istream &operator>>(std::istream &is, __int128_t &a) { std::string s; is >> s; __int128_t ret = 0; for(int i = 0; i < (int)s.length(); i++) if('0' <= s[i] and s[i] <= '9') ret = 10 * ret + s[i] - '0'; a = ret * (s[0] == '-' ? -1 : 1); return is; } namespace scanner { void scan(int &a) { std::cin >> a; } void scan(long long &a) { std::cin >> a; } void scan(std::string &a) { std::cin >> a; } void scan(char &a) { std::cin >> a; } void scan(char a[]) { std::scanf("%s", a); } void scan(double &a) { std::cin >> a; } void scan(long double &a) { std::cin >> a; } template <class T, class U> void scan(std::pair<T, U> &p) { std::cin >> p; } template <class T> void scan(std::vector<T> &a) { std::cin >> a; } void INPUT() {} template <class Head, class... Tail> void INPUT(Head &head, Tail &...tail) { scan(head); INPUT(tail...); } } // namespace scanner #define VEC(type, name, size) \ std::vector<type> name(size); \ scanner::INPUT(name) #define VVEC(type, name, h, w) \ std::vector<std::vector<type>> name(h, std::vector<type>(w)); \ scanner::INPUT(name) #define INT(...) \ int __VA_ARGS__; \ scanner::INPUT(__VA_ARGS__) #define LL(...) \ long long __VA_ARGS__; \ scanner::INPUT(__VA_ARGS__) #define STR(...) \ std::string __VA_ARGS__; \ scanner::INPUT(__VA_ARGS__) #define CHAR(...) \ char __VA_ARGS__; \ scanner::INPUT(__VA_ARGS__) #define DOUBLE(...) \ double __VA_ARGS__; \ scanner::INPUT(__VA_ARGS__) #define LD(...) \ long double __VA_ARGS__; \ scanner::INPUT(__VA_ARGS__) #line 3 "/home/nok0/documents/programming/library/template/math.hpp" template <class T, class U> inline bool chmin(T &a, const U &b) { return a > b ? a = b, true : false; } template <class T, class U> inline bool chmax(T &a, const U &b) { return a < b ? a = b, true : false; } template <class T> T divup(T x, T y) { return (x + y - 1) / y; } template <class T> T POW(T a, long long n) { T ret = 1; while(n) { if(n & 1) ret *= a; a *= a; n >>= 1; } return ret; } long long POW(long long a, long long n, const int mod) { long long ret = 1; a = (a % mod + mod) % mod; while(n) { if(n & 1) (ret *= a) %= mod; (a *= a) %= mod; n >>= 1; } return ret; } template <class T, class F> 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 <class T, class F> T bin_search(T ok, T ng, const F &f, int loop) { for(int i = 0; i < loop; i++) { T mid = (ok + ng) / 2; (f(mid) ? ok : ng) = mid; } return ok; } #line 3 "/home/nok0/documents/programming/library/template/output.hpp" template <class T, class U> std::ostream &operator<<(std::ostream &os, const std::pair<T, U> &p) { os << p.first << " " << p.second; return os; } template <class T> std::ostream &operator<<(std::ostream &os, const std::vector<T> &a) { for(int i = 0; i < int(a.size()); ++i) { if(i) os << " "; os << a[i]; } return os; } std::ostream &operator<<(std::ostream &dest, __int128_t &value) { std::ostream::sentry s(dest); if(s) { __uint128_t tmp = value < 0 ? -value : value; char buffer[128]; char *d = std::end(buffer); do { --d; *d = "0123456789"[tmp % 10]; tmp /= 10; } while(tmp != 0); if(value < 0) { --d; *d = '-'; } int len = std::end(buffer) - d; if(dest.rdbuf()->sputn(d, len) != len) { dest.setstate(std::ios_base::badbit); } } return dest; } template <class T> void print(const T a) { std::cout << a << '\n'; } template <class Head, class... Tail> void print(Head H, Tail... T) { std::cout << H << ' '; print(T...); } template <class T> void println(const T a) { std::cout << a << '\n'; } template <class T> void println(const std::vector<T> &a) { for(const auto &v : a) std::cout << v << '\n'; } template <class Head, class... Tail> void println(Head H, Tail... T) { std::cout << H << '\n'; println(T...); } void Yes(const bool b = true) { std::cout << (b ? "Yes\n" : "No\n"); } void No() { std::cout << "No\n"; } void YES(const bool b = true) { std::cout << (b ? "YES\n" : "NO\n"); } void NO() { std::cout << "NO\n"; } #line 2 "/home/nok0/documents/programming/library/template/rep.hpp" #define foa(v, a) for(auto &v : a) #define repname(a, b, c, d, e, ...) e #define rep(...) repname(__VA_ARGS__, rep3, rep2, rep1, rep0)(__VA_ARGS__) #define rep0(x) for(int rep_counter = 0; rep_counter < (x); ++rep_counter) #define rep1(i, x) for(int i = 0; i < (x); ++i) #define rep2(i, l, r) for(int i = (l); i < (r); ++i) #define rep3(i, l, r, c) for(int i = (l); i < (r); i += (c)) #define repsname(a, b, c, ...) c #define reps(...) repsname(__VA_ARGS__, reps1, reps0)(__VA_ARGS__) #define reps0(x) for(int reps_counter = 1; reps_counter <= (x); ++reps_counter) #define reps1(i, x) for(int i = 1; i <= (x); ++i) #define rrepname(a, b, c, ...) c #define rrep(...) rrepname(__VA_ARGS__, rrep1, rrep0)(__VA_ARGS__) #define rrep0(x) for(int rrep_counter = (x)-1; rrep_counter >= 0; --rrep_counter) #define rrep1(i, x) for(int i = (x)-1; i >= 0; --i) #line 3 "/home/nok0/documents/programming/library/template/string_converter.hpp" 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 std::string &chars) { return chars.find(c); } template <typename T> auto convert(const T &v) { std::vector<decltype(convert(v[0]))> ret; ret.reserve(size(v)); for(auto &&e : v) ret.emplace_back(convert(e)); return ret; } template <typename T> auto convert(const T &v, const std::string &chars) { std::vector<decltype(convert(v[0], chars))> 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 std::string &chars) { return convert(v, chars); } template <typename T> auto operator()(const T &v, char s = 0) { start = s; return convert(v); } template <typename T> auto operator()(const T &v, const std::string &chars) { return convert(v, chars); } } toint; #line 3 "/home/nok0/documents/programming/library/template/vector.hpp" template <class T> int lb(const std::vector<T> &a, const T x) { return std::distance((a).begin(), std::lower_bound((a).begin(), (a).end(), (x))); } template <class T> int ub(const std::vector<T> &a, const T x) { return std::distance((a).begin(), std::upper_bound((a).begin(), (a).end(), (x))); } template <class T> void UNIQUE(std::vector<T> &a) { std::sort(a.begin(), a.end()); a.erase(std::unique(a.begin(), a.end()), a.end()); } template <class T> std::vector<T> press(std::vector<T> &a) { auto res = a; UNIQUE(res); for(auto &v : a) v = lb(res, v); return res; } #define SORTname(a, b, c, ...) c #define SORT(...) SORTname(__VA_ARGS__, SORT1, SORT0, ...)(__VA_ARGS__) #define SORT0(a) std::sort((a).begin(), (a).end()) #define SORT1(a, c) std::sort((a).begin(), (a).end(), [](const auto x, const auto y) { return x c y; }) template <class T> void ADD(std::vector<T> &a, const T x = 1) { for(auto &v : a) v += x; } template <class T> void SUB(std::vector<T> &a, const T x = 1) { for(auto &v : a) v -= x; } template <class T> struct cum_vector { public: cum_vector() = default; template <class U> cum_vector(const std::vector<U> &vec) : cum((int)vec.size() + 1) { for(int i = 0; i < (int)vec.size(); i++) cum[i + 1] = cum[i] + vec[i]; } T prod(int l, int r) { return cum[r] - cum[l]; } private: std::vector<T> cum; }; std::vector<std::pair<char, int>> rle(const std::string &s) { const int n = s.size(); std::vector<std::pair<char, int>> ret; ret.reserve(n); for(int l = 0; l < n;) { int r = l + 1; for(; r < n and s[l] == s[r]; r++) {} ret.emplace_back(s[l], r - l); l = r; } return ret; } template <class T> std::vector<std::pair<T, int>> rle(const std::vector<T> &v) { const int n = v.size(); std::vector<std::pair<T, int>> ret; ret.reserve(n); for(int l = 0; l < n;) { int r = l + 1; for(; r < n and v[l] == v[r]; r++) {} ret.emplace_back(v[l], r - l); l = r; } return ret; } std::vector<int> iota(int n) { std::vector<int> p(n); std::iota(p.begin(), p.end(), 0); return p; } #line 12 "/home/nok0/documents/programming/library/template/all" using namespace std; #line 2 "a.cpp" // reference: http://www.cs.kent.edu/~dragan/GraphAn/p23-galil.pdf class GeneralWeightedMatching { struct E { int u, v; ll w; }; int n, m, in; vector<vector<E>> G; vector<int> mate, slack, root, par, isS, used; vector<vector<int>> flower, belong; vector<ll> dual; queue<int> que; ll dist(const E &e) { return dual[e.u] + dual[e.v] - e.w; } void update(int u, int v) { if(!slack[v] or dist(G[u][v]) < dist(G[slack[v]][v])) slack[v] = u; } void recalc(int v) { slack[v] = 0; rep(i, 1, n + 1) if(G[i][v].w and root[i] != v and isS[root[i]] == 1) update(i, v); } void push(int v) { if(v <= n) que.push(v); else for(auto &nxt : flower[v]) push(nxt); } void set(int v, int rt) { root[v] = rt; if(v > n) for(auto &nxt : flower[v]) set(nxt, rt); } int findeven(int b, int v) { int pos = find(all(flower[b]), v) - flower[b].begin(); if(pos & 1) { reverse(flower[b].begin() + 1, flower[b].end()); pos = flower[b].size() - pos; } return pos; } void match(int u, int v) { mate[u] = G[u][v].v; if(u > n) { int x = belong[u][G[u][v].u]; int pos = findeven(u, x); rep(i, 0, pos) match(flower[u][i], flower[u][i ^ 1]); match(x, v); rotate(flower[u].begin(), flower[u].begin() + pos, flower[u].end()); } } void link(int u, int v) { for(;;) { int nv = root[mate[u]]; match(u, v); if(!nv) break; v = nv, u = root[par[nv]]; match(v, u); } } void make(int u, int v, int lca) { int id = n + 1; while(id <= m and root[id]) id++; if(id > m) m++; flower[id].clear(); rep(i, 1, m + 1) G[id][i].w = G[i][id].w = 0; rep(i, 1, n + 1) belong[id][i] = 0; isS[id] = 1, dual[id] = 0, mate[id] = mate[lca]; while(u != lca) { flower[id].push_back(u); u = root[mate[u]]; push(u); flower[id].push_back(u); u = root[par[u]]; } flower[id].push_back(lca); reverse(all(flower[id])); while(v != lca) { flower[id].push_back(v); v = root[mate[v]]; push(v); flower[id].push_back(v); v = root[par[v]]; } set(id, id); for(auto &c : flower[id]) { rep(i, 1, m + 1) if(!G[id][i].w or dist(G[c][i]) < dist(G[id][i])) { G[id][i] = G[c][i], G[i][id] = G[i][c]; } rep(i, 1, n + 1) if(belong[c][i]) belong[id][i] = c; } recalc(id); } void expand(int b) { for(auto &c : flower[b]) set(c, c); int x = belong[b][G[b][par[b]].u]; isS[x] = 2, par[x] = par[b]; int pos = findeven(b, x); for(int i = 0; i < pos; i += 2) { int T = flower[b][i], S = flower[b][i + 1]; isS[S] = 1, isS[T] = 2; par[T] = G[S][T].u; slack[S] = slack[T] = 0; push(S); } rep(i, pos + 1, flower[b].size()) { isS[flower[b][i]] = 0; recalc(flower[b][i]); } flower[b].clear(); root[b] = 0; } bool path(const E &e) { int u = root[e.u], v = root[e.v]; if(!isS[v]) { par[v] = e.u; isS[v] = 2; int nu = root[mate[v]]; slack[v] = slack[nu] = 0; isS[nu] = 1; push(nu); } else if(isS[v] == 1) { int lca = 0, bu = u, bv = v; in++; while(bu) { used[bu] = in; bu = root[mate[bu]]; if(bu) bu = root[par[bu]]; } while(bv) { if(used[bv] == in) { lca = bv; break; } bv = root[mate[bv]]; if(bv) bv = root[par[bv]]; } if(lca) make(u, v, lca); else { link(u, v), link(v, u); return true; } } return false; } bool augment() { isS = slack = par = vector<int>(n * 2); que = queue<int>(); rep(i, 1, m + 1) if(root[i] == i and !mate[i]) { isS[i] = 1; push(i); } if(que.empty()) return false; for(;;) { while(!que.empty()) { int v = que.front(); que.pop(); rep(i, 1, n + 1) if(G[v][i].w and root[i] != root[v]) { if(!dist(G[v][i])) { if(path(G[v][i])) return true; } else if(isS[root[i]] != 2) update(v, root[i]); } } ll delta = INF; rep(i, n + 1, m + 1) if(root[i] == i and isS[i] == 2) chmin(delta, dual[i] / 2); rep(i, 1, m + 1) if(root[i] == i and slack[i] and isS[i] != 2) { if(!isS[i]) chmin(delta, dist(G[slack[i]][i])); else chmin(delta, dist(G[slack[i]][i]) / 2); } rep(i, 1, n + 1) { if(isS[root[i]] == 1) { dual[i] -= delta; if(dual[i] <= 0) return false; } else if(isS[root[i]] == 2) dual[i] += delta; } rep(i, n + 1, m + 1) if(root[i] == i and isS[i]) { if(isS[i] == 1) dual[i] += delta * 2; else dual[i] -= delta * 2; } rep(i, 1, m + 1) if(root[i] == i and slack[i] and root[slack[i]] != i) { if(dist(G[slack[i]][i]) == 0 and path(G[slack[i]][i])) return true; } rep(i, n + 1, m + 1) if(root[i] == i and isS[i] == 2 and dual[i] == 0) expand(i); } } public: GeneralWeightedMatching(int _n) : n(_n), m(n), in(0), G(n * 2, vector<E>(n * 2)), mate(n * 2), root(n * 2), used(n * 2), flower(n * 2), belong(n * 2, vector<int>(n * 2)), dual(n * 2) { rep(i, 0, n + 1) { root[i] = i; belong[i][i] = i; if(i) dual[i] = INF; rep(j, 0, n + 1) G[i][j] = E{i, j, 0}; } } void add_edge(int u, int v, ll w) { u++, v++; chmax(G[u][v].w, w * 2); chmax(G[v][u].w, w * 2); } vector<int> run() { while(augment()) ; vector<int> res(n, -1); rep(i, 1, n + 1) if(mate[i]) res[i - 1] = mate[i] - 1; return res; } }; void main_(); int main() { int t = 1; while(t--) main_(); } void main_() { INT(q); VEC(pii, lr, q); VEC(ll, a, 2 * q); cum_vector<ll> cum(a); ll res = 0; for(auto [l, r] : lr) { res += cum.prod(l - 1, r); } GeneralWeightedMatching mt(q); vector es(q, vector(q, 0ll)); rep(i, q) { auto [l, r] = lr[i]; rep(j, i + 1, q) { auto [l2, r2] = lr[j]; int lef = max(l, l2); int rig = min(r, r2); if(lef < rig and ((lef == l and rig == r2) or (lef == l2 and rig == r))) { es[i][j] = cum.prod(lef - 1, rig); mt.add_edge(i, j, es[i][j]); } } } auto vec = mt.run(); rep(i, q) { if(vec[i] > i) { res -= es[i][vec[i]]; } } print(res); }