// includes #include // macros #define ll long long int #define pb emplace_back #define mk make_pair #define pq priority_queue #define FOR(i, a, b) for(int i=(a);i<(b);++i) #define rep(i, n) FOR(i, 0, n) #define rrep(i, n) for(int i=((int)(n)-1);i>=0;i--) #define irep(itr, st) for(auto itr = (st).begin(); itr != (st).end(); ++itr) #define irrep(itr, st) for(auto itr = (st).rbegin(); itr != (st).rend(); ++itr) #define vrep(v, i) for(int i = 0; i < (v).size(); i++) #define all(x) (x).begin(),(x).end() #define sz(x) ((int)(x).size()) #define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end()) #define FI first #define SE second #define dump(a, n) for(int i = 0; i < n; i++)cout << a[i] << "\n "[i + 1 != n]; #define dump2(a, n, m) for(int i = 0; i < n; i++)for(int j = 0; j < m; j++)cout << a[i][j] << "\n "[j + 1 != m]; #define bit(n) (1LL<<(n)) #define INT(n) int n; cin >> n; #define LL(n) ll n; cin >> n; #define DOUBLE(n) double n; cin >> n; using namespace std; 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(a > b){a = b; return 1;} return 0;} template istream &operator>>(istream &is, vector &vec){for(auto &v: vec)is >> v; return is;} template ostream &operator<<(ostream &os, const vector& vec){for(int i = 0; i < vec.size(); i++){ os << vec[i]; if(i + 1 != vec.size())os << " ";} return os;} template ostream &operator<<(ostream &os, const set& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;} template ostream &operator<<(ostream &os, const unordered_set& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;} template ostream &operator<<(ostream &os, const multiset& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;} template ostream &operator<<(ostream &os, const unordered_multiset& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;} template ostream &operator<<(ostream &os, const pair &p){os << p.first << " " << p.second; return os;} template ostream &operator<<(ostream &os, const map &mp){for(auto itr = mp.begin(); itr != mp.end(); ++itr){ os << itr->first << ":" << itr->second; auto titr = itr; if(++titr != mp.end())os << " "; } return os;} template ostream &operator<<(ostream &os, const unordered_map &mp){for(auto itr = mp.begin(); itr != mp.end(); ++itr){ os << itr->first << ":" << itr->second; auto titr = itr; if(++titr != mp.end())os << " "; } return os;} // types typedef pair P; typedef pair Pl; typedef pair Pll; typedef pair Pd; typedef complex cd; // constants const int inf = 1e9; const ll linf = 1LL << 50; const double EPS = 1e-10; const int mod = 1e9 + 7; const int dx[4] = {-1, 0, 1, 0}; const int dy[4] = {0, -1, 0, 1}; // solve template struct SegmentTree_ { function f; function g; int n; T def; vector vec; SegmentTree_(){} SegmentTree_(int n_, function f_, function g_, T def_, vector v=vector()){ f = f_; g = g_; def = def_; // initialize vector n = 1; while(n < n_){ n *= 2; } vec = vector(2*n -1, def); // initialize segment tree for(int i = 0; i < v.size(); i++){ vec[i + n - 1] = v[i]; } for(int i = n - 2; i >= 0; i--){ vec[i] = f(vec[2*i+1], vec[2*i+2]); } } void update(int k, const E &val){ k = k + n - 1; vec[k] = g(vec[k], val); while(k > 0){ k = (k - 1) / 2; vec[k] = f(vec[2*k+1], vec[2*k+2]); } } // [l, r) -> [a, b) (at k) T query(int a, int b, int k, int l, int r){ if(r <= a || b <= l)return def; if(a <= l && r <= b)return vec[k]; T ld = query(a, b, 2*k+1, l, (l+r)/2); T rd = query(a, b, 2*k+2, (l+r)/2, r); return f(ld, rd); } T query(int a, int b){ return query(a, b, 0, 0, n); } }; template using SegmentTree = struct SegmentTree_; using SegmentTreeI = SegmentTree; using SegmentTreeL = SegmentTree; ll dp[300010]; int main(int argc, char const* argv[]) { ios_base::sync_with_stdio(false); cin.tie(0); cout << fixed << setprecision(20); INT(n); vector a(n), x(n), y(n); cin >> a >> x >> y; SegmentTreeL segp = SegmentTreeL(n, [](ll a, ll b){return min(a, b);}, [](ll a,ll b){return b;}, linf, vector()); SegmentTreeL segm = SegmentTreeL(n, [](ll a, ll b){return min(a, b);}, [](ll a,ll b){return b;}, linf, vector()); segp.update(0, y[0] + x[0]); segm.update(0, y[0] - x[0]); rep(i, n + 1)dp[i] = linf; dp[0] = 0; rep(i, n){ int idx = lower_bound(all(x), a[i]) - x.begin(); dp[i+1] = min(dp[i+1], segp.query(idx, n) - a[i]); dp[i+1] = min(dp[i+1], segm.query(0, idx) + a[i]); if(i + 1 < n){ segp.update(i + 1, dp[i+1] + y[i+1] + x[i+1]); segm.update(i + 1, dp[i+1] + y[i+1] - x[i+1]); } } cout << dp[n] << endl; return 0; }