#include using namespace std; template struct ConvexHullTrick { struct Line { // f: y=ax+b Numeric a; Numeric b; Line(Numeric _a, Numeric _b) : a(_a), b(_b) {} bool operator< (Line &l) { if (a != l.a) return a < l.a; else return b < l.b; } }; private: vector lines; bool isMinimumQuery; bool isMonotonicQuery; bool compare(Numeric a, Numeric b) { if (isMinimumQuery) return b <= a; else return a <= b; } public: // constructor ConvexHullTrick(bool monotonic, bool minimum = true) : isMinimumQuery(minimum), isMonotonicQuery(monotonic) {} // check the necessity of line2 bool check(Line l1, Line l2, Line l3) { if (l1 < l3) swap(l3, l1); return compare((l3.b-l2.b)*(l2.a-l1.a), (l2.b-l1.b)*(l3.a-l2.a)); } // add the line: y=ax+b void add(Numeric a, Numeric b) { Line line(a, b); int size = (int) lines.size(); if (size >= 1 && lines[size-1].a == line.a){ if (!compare(lines[size-1].b, line.b)) return; } while (size >= 2 && check(lines[size-2], lines[size-1], line)){ lines.pop_back(); --size; } lines.emplace_back(line); } // get the value of line(x) Numeric f(Line line, Numeric x) { return line.a * x + line.b; } // solve Numeric solve(Numeric x) { if (isMonotonicQuery) { static int head = 0; while (lines.size() - head >= 2 && compare(f(lines[head], x), f(lines[head+1], x))) ++head; return f(lines[head], x); } else { int low = -1; int high = lines.size()-1; while (high - low > 1) { int mid = (high+low)/2; if (compare(f(lines[mid], x), f(lines[mid+1], x))) low = mid; else high = mid; } return f(lines[high], x); } } }; int main(){ cin.tie(0); ios::sync_with_stdio(false); int n; cin >> n; vector a(n), x(n), y(n); for (int i = 0; i < n; i++) { cin >> a[n-i-1]; } for (int i = 0; i < n; i++) { cin >> x[n-i-1]; } for (int i = 0; i < n; i++) { cin >> y[n-i-1]; } ConvexHullTrick convexhulltrick(true); vector dp(n+1, 0); for (int i = 0; i < n; i++) { convexhulltrick.add(2*a[i], dp[i]+a[i]*a[i]); dp[i+1] = convexhulltrick.solve(-x[i]) + x[i]*x[i] + y[i] * y[i]; } cout << dp[n] << endl; return 0; }