#line 1 "/home/maspy/compro/library/my_template.hpp" #if defined(LOCAL) #include #else #pragma GCC optimize("Ofast") #pragma GCC optimize("unroll-loops") #include using namespace std; using ll = long long; using u32 = unsigned int; using u64 = unsigned long long; using i128 = __int128; using u128 = unsigned __int128; using f128 = __float128; template constexpr T infty = 0; template <> constexpr int infty = 1'000'000'000; template <> constexpr ll infty = ll(infty) * infty * 2; template <> constexpr u32 infty = infty; template <> constexpr u64 infty = infty; template <> constexpr i128 infty = i128(infty) * infty; template <> constexpr double infty = infty; template <> constexpr long double infty = infty; using pi = pair; using vi = vector; template using vc = vector; template using vvc = vector>; template using vvvc = vector>; template using vvvvc = vector>; template using vvvvvc = vector>; template using pq = priority_queue; template using pqg = priority_queue, greater>; #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__)))) // https://trap.jp/post/1224/ #define FOR1(a) for (ll _ = 0; _ < ll(a); ++_) #define FOR2(i, a) for (ll i = 0; i < ll(a); ++i) #define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i) #define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c)) #define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i) #define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i) #define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i) #define overload4(a, b, c, d, e, ...) e #define overload3(a, b, c, d, ...) d #define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__) #define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__) #define FOR_subset(t, s) \ for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s))) #define all(x) x.begin(), x.end() #define len(x) ll(x.size()) #define elif else if #define eb emplace_back #define mp make_pair #define mt make_tuple #define fi first #define se second #define stoi stoll int popcnt(int x) { return __builtin_popcount(x); } int popcnt(u32 x) { return __builtin_popcount(x); } int popcnt(ll x) { return __builtin_popcountll(x); } int popcnt(u64 x) { return __builtin_popcountll(x); } int popcnt_mod_2(int x) { return __builtin_parity(x); } int popcnt_mod_2(u32 x) { return __builtin_parity(x); } int popcnt_mod_2(ll x) { return __builtin_parityll(x); } int popcnt_mod_2(u64 x) { return __builtin_parityll(x); } // (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2) int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); } int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); } int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } // (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2) int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); } int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); } int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } template T floor(T a, T b) { return a / b - (a % b && (a ^ b) < 0); } template T ceil(T x, T y) { return floor(x + y - 1, y); } template T bmod(T x, T y) { return x - y * floor(x, y); } template pair divmod(T x, T y) { T q = floor(x, y); return {q, x - q * y}; } template T SUM(const vector &A) { T sm = 0; for (auto &&a: A) sm += a; return sm; } #define MIN(v) *min_element(all(v)) #define MAX(v) *max_element(all(v)) #define LB(c, x) distance((c).begin(), lower_bound(all(c), (x))) #define UB(c, x) distance((c).begin(), upper_bound(all(c), (x))) #define UNIQUE(x) \ sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit() template T POP(deque &que) { T a = que.front(); que.pop_front(); return a; } template T POP(pq &que) { T a = que.top(); que.pop(); return a; } template T POP(pqg &que) { T a = que.top(); que.pop(); return a; } template T POP(vc &que) { T a = que.back(); que.pop_back(); return a; } template ll binary_search(F check, ll ok, ll ng, bool check_ok = true) { if (check_ok) assert(check(ok)); while (abs(ok - ng) > 1) { auto x = (ng + ok) / 2; (check(x) ? ok : ng) = x; } return ok; } template double binary_search_real(F check, double ok, double ng, int iter = 100) { FOR(iter) { double x = (ok + ng) / 2; (check(x) ? ok : ng) = x; } return (ok + ng) / 2; } 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); } // ? は -1 vc s_to_vi(const string &S, char first_char) { vc A(S.size()); FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); } return A; } template vector cumsum(vector &A, int off = 1) { int N = A.size(); vector B(N + 1); FOR(i, N) { B[i + 1] = B[i] + A[i]; } if (off == 0) B.erase(B.begin()); return B; } // stable sort template vector argsort(const vector &A) { vector ids(len(A)); iota(all(ids), 0); sort(all(ids), [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); }); return ids; } // A[I[0]], A[I[1]], ... template vc rearrange(const vc &A, const vc &I) { vc B(len(I)); FOR(i, len(I)) B[i] = A[I[i]]; return B; } #endif #line 1 "/home/maspy/compro/library/other/io.hpp" #define FASTIO #include // https://judge.yosupo.jp/submission/21623 namespace fastio { static constexpr uint32_t SZ = 1 << 17; char ibuf[SZ]; char obuf[SZ]; char out[100]; // pointer of ibuf, obuf uint32_t pil = 0, pir = 0, por = 0; struct Pre { char num[10000][4]; constexpr Pre() : num() { for (int i = 0; i < 10000; i++) { int n = i; for (int j = 3; j >= 0; j--) { num[i][j] = n % 10 | '0'; n /= 10; } } } } constexpr pre; inline void load() { memcpy(ibuf, ibuf + pil, pir - pil); pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin); pil = 0; if (pir < SZ) ibuf[pir++] = '\n'; } inline void flush() { fwrite(obuf, 1, por, stdout); por = 0; } void rd(char &c) { do { if (pil + 1 > pir) load(); c = ibuf[pil++]; } while (isspace(c)); } void rd(string &x) { x.clear(); char c; do { if (pil + 1 > pir) load(); c = ibuf[pil++]; } while (isspace(c)); do { x += c; if (pil == pir) load(); c = ibuf[pil++]; } while (!isspace(c)); } template void rd_real(T &x) { string s; rd(s); x = stod(s); } template void rd_integer(T &x) { if (pil + 100 > pir) load(); char c; do c = ibuf[pil++]; while (c < '-'); bool minus = 0; if constexpr (is_signed::value || is_same_v) { if (c == '-') { minus = 1, c = ibuf[pil++]; } } x = 0; while ('0' <= c) { x = x * 10 + (c & 15), c = ibuf[pil++]; } if constexpr (is_signed::value || is_same_v) { if (minus) x = -x; } } void rd(int &x) { rd_integer(x); } void rd(ll &x) { rd_integer(x); } void rd(i128 &x) { rd_integer(x); } void rd(u32 &x) { rd_integer(x); } void rd(u64 &x) { rd_integer(x); } void rd(u128 &x) { rd_integer(x); } void rd(double &x) { rd_real(x); } void rd(long double &x) { rd_real(x); } void rd(f128 &x) { rd_real(x); } template void rd(pair &p) { return rd(p.first), rd(p.second); } template void rd_tuple(T &t) { if constexpr (N < std::tuple_size::value) { auto &x = std::get(t); rd(x); rd_tuple(t); } } template void rd(tuple &tpl) { rd_tuple(tpl); } template void rd(array &x) { for (auto &d: x) rd(d); } template void rd(vc &x) { for (auto &d: x) rd(d); } void read() {} template void read(H &h, T &... t) { rd(h), read(t...); } void wt(const char c) { if (por == SZ) flush(); obuf[por++] = c; } void wt(const string s) { for (char c: s) wt(c); } void wt(const char *s) { size_t len = strlen(s); for (size_t i = 0; i < len; i++) wt(s[i]); } template void wt_integer(T x) { if (por > SZ - 100) flush(); if (x < 0) { obuf[por++] = '-', x = -x; } int outi; for (outi = 96; x >= 10000; outi -= 4) { memcpy(out + outi, pre.num[x % 10000], 4); x /= 10000; } if (x >= 1000) { memcpy(obuf + por, pre.num[x], 4); por += 4; } else if (x >= 100) { memcpy(obuf + por, pre.num[x] + 1, 3); por += 3; } else if (x >= 10) { int q = (x * 103) >> 10; obuf[por] = q | '0'; obuf[por + 1] = (x - q * 10) | '0'; por += 2; } else obuf[por++] = x | '0'; memcpy(obuf + por, out + outi + 4, 96 - outi); por += 96 - outi; } template void wt_real(T x) { ostringstream oss; oss << fixed << setprecision(15) << double(x); string s = oss.str(); wt(s); } void wt(int x) { wt_integer(x); } void wt(ll x) { wt_integer(x); } void wt(i128 x) { wt_integer(x); } void wt(u32 x) { wt_integer(x); } void wt(u64 x) { wt_integer(x); } void wt(u128 x) { wt_integer(x); } void wt(double x) { wt_real(x); } void wt(long double x) { wt_real(x); } void wt(f128 x) { wt_real(x); } template void wt(const pair val) { wt(val.first); wt(' '); wt(val.second); } template void wt_tuple(const T t) { if constexpr (N < std::tuple_size::value) { if constexpr (N > 0) { wt(' '); } const auto x = std::get(t); wt(x); wt_tuple(t); } } template void wt(tuple tpl) { wt_tuple(tpl); } template void wt(const array val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) wt(' '); wt(val[i]); } } template void wt(const vector val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) wt(' '); wt(val[i]); } } void print() { wt('\n'); } template void print(Head &&head, Tail &&... tail) { wt(head); if (sizeof...(Tail)) wt(' '); print(forward(tail)...); } // gcc expansion. called automaticall after main. void __attribute__((destructor)) _d() { flush(); } } // namespace fastio using fastio::read; using fastio::print; using fastio::flush; #define INT(...) \ int __VA_ARGS__; \ read(__VA_ARGS__) #define LL(...) \ ll __VA_ARGS__; \ read(__VA_ARGS__) #define U32(...) \ u32 __VA_ARGS__; \ read(__VA_ARGS__) #define U64(...) \ u64 __VA_ARGS__; \ read(__VA_ARGS__) #define STR(...) \ string __VA_ARGS__; \ read(__VA_ARGS__) #define CHAR(...) \ char __VA_ARGS__; \ read(__VA_ARGS__) #define DBL(...) \ double __VA_ARGS__; \ read(__VA_ARGS__) #define VEC(type, name, size) \ vector name(size); \ read(name) #define VV(type, name, h, w) \ vector> name(h, vector(w)); \ read(name) void YES(bool t = 1) { print(t ? "YES" : "NO"); } void NO(bool t = 1) { YES(!t); } void Yes(bool t = 1) { print(t ? "Yes" : "No"); } void No(bool t = 1) { Yes(!t); } void yes(bool t = 1) { print(t ? "yes" : "no"); } void no(bool t = 1) { yes(!t); } #line 3 "main.cpp" #define rep(i, a, b) for (int i = (int)(a); i < (int)(b); i++) #define ALL(v) (v).begin(), (v).end() const int inf = 0x3fffffff; const ll INF = 0x1fffffffffffffff; // https://judge.yosupo.jp/submission/81021 class GeneralWeightedMatching { struct E { int u, v; ll w; }; int n, m, in; vector> G; vector mate, slack, root, par, isS, used; vector> flower, belong; vector dual; queue 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(n * 2); que = queue(); 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(n * 2)), mate(n * 2), root(n * 2), used(n * 2), flower(n * 2), belong(n * 2, vector(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 run() { while (augment()) ; vector res(n, -1); rep(i, 1, n + 1) if (mate[i]) res[i - 1] = mate[i] - 1; return res; } }; void solve() { LL(N); vi L(N), R(N); FOR(i, N) { LL(a, b); L[i] = a - 1, R[i] = b - 1; } VEC(ll, A, 2 * N - 1); auto Ac = cumsum(A); ll ANS = 0; FOR(i, N) ANS += Ac[R[i]] - Ac[L[i]]; vv(ll, mat, N, N); FOR(i, N) FOR(j, N) { if (L[i] < L[j] && L[j] < R[i] && R[i] < R[j]) { ll w = Ac[R[i]] - Ac[L[j]]; mat[i][j] = mat[j][i] = w; } } GeneralWeightedMatching X(N); FOR(j, N) FOR(i, j) if (mat[i][j] > 0) X.add_edge(i, j, mat[i][j]); auto match = X.run(); FOR(i, N) { int j = match[i]; if (i < j) { ANS -= mat[i][j]; } } // print(match); print(ANS); } signed main() { solve(); return 0; }