#include #define rep(i, n) for (int i = 0; i < (int)(n); i++) #define rrep(i, n) for (int i = (int)(n - 1); i >= 0; i--) #define all(x) (x).begin(), (x).end() #define sz(x) int(x.size()) using namespace std; using ll = long long; const int INF = 1e9; const ll LINF = 1e18; template bool chmax(T& a, const T& b) { if (a < b) { a = b; return 1; } return 0; } template bool chmin(T& a, const T& b) { if (b < a) { a = b; return 1; } return 0; } template vector make_vec(size_t a) { return vector(a); } template auto make_vec(size_t a, Ts... ts) { return vector(ts...))>(a, make_vec(ts...)); } template istream& operator>>(istream& is, vector& v) { for (int i = 0; i < int(v.size()); i++) { is >> v[i]; } return is; } template ostream& operator<<(ostream& os, const vector& v) { for (int i = 0; i < int(v.size()); i++) { os << v[i]; if (i < int(v.size()) - 1) os << ' '; } return os; } // DynamicLiChaoTree LCT(ll min_index,ll max_index); などする // xの動きうる最大範囲が[min_index,max_index) // void add_line(T a,T b): 直線 ax+b を追加 // void add_segment_line(T Llim,T Rlim,T a,T b): [Llim,Rlim]の線分 ax+b を追加 // T get(T x): min(ax+b) を返す template struct DynamicLiChaoTree { private: struct Line { T slope, intercept; Line() : slope(0), intercept(numeric_limits::max()) { } Line(T a, T b) : slope(a), intercept(b) { } T f(T x) { return slope * x + intercept; } }; struct node { Line line; node *left, *right; node(Line line) : line(line), left(nullptr), right(nullptr) { } }; const long long min_index, max_index; node* root; node* add_line(node*& t, long long l, long long r, Line line) const { if (l == r) return nullptr; if (!t) { t = new node(line); return t; } long long m = (l + r) >> 1; bool L = (line.f(l) <= t->line.f(l)); bool M = (line.f(m) <= t->line.f(m)); bool R = (line.f(r) <= t->line.f(r)); if (L && R) { t->line = line; return t; } if (!L && !R) { return t; } if (M) { swap(t->line, line); } if (L != M) { t->left = add_line(t->left, l, m, line); } else { t->right = add_line(t->right, m + 1, r, line); } return t; } node* add_segment_line(node*& t, long long Llim, long long Rlim, long long l, long long r, Line line) { if (r <= Llim || Rlim <= l) return t; if (Llim <= l && r <= Rlim) return add_line(t, l, r, line); if (t == nullptr) t = new node(Line()); long long m = (l + r) >> 1; t->left = add_segment_line(t->left, Llim, Rlim, l, m, line); t->right = add_segment_line(t->right, Llim, Rlim, m, r, line); return t; } public: DynamicLiChaoTree(T min_index, T max_index) : min_index(min_index), max_index(max_index), root(nullptr) { } void add_line(T a, T b) { Line line = Line{a, b}; add_line(root, min_index, max_index, line); } void add_segment_line(T Llim, T Rlim, T a, T b) { Line line = Line{a, b}; add_segment_line(root, Llim, Rlim, min_index, max_index, line); } T get(long long x) { node* t = root; long long l = min_index, r = max_index; T ret = numeric_limits::max(); while (r - l > 0 && t != nullptr) { long long m = (l + r) >> 1; ret = min(ret, t->line.f(x)); if (x < m) { r = m; t = t->left; } else { l = m; t = t->right; } } return ret; } }; int main() { int n; cin >> n; vector a(n), x(n), y(n); cin >> a >> x >> y; vector dp(n + 1, LINF); dp[0] = 0; DynamicLiChaoTree lct(0, 100100); rep(i, n) { lct.add_segment_line(-1, x[i], -1, dp[i] + x[i] + y[i]); lct.add_segment_line(x[i], 100100, 1, dp[i] - x[i] + y[i]); dp[i + 1] = lct.get(a[i]); } cout << dp[n] << '\n'; }