#include <iostream>
#include <vector>
#include <tuple>
#include <queue>
#include <stack>
#include <deque>
#include <set>
#include <map>
#include <cmath>
#include <random>
#include <string>
#include <bitset>
#include <cassert>
#include <climits>
#include <algorithm>
#include <unordered_set>
#include <unordered_map>
using namespace std;
#define ll long long
#define f first
#define s second
void __print(int x) { cerr << x; }
void __print(long x) { cerr << x; }
void __print(long long x) { cerr << x; }
void __print(unsigned x) { cerr << x; }
void __print(unsigned long x) { cerr << x; }
void __print(unsigned long long x) { cerr << x; }
void __print(float x) { cerr << x; }
void __print(double x) { cerr << x; }
void __print(long double x) { cerr << x; }
void __print(char x) { cerr << '\'' << x << '\''; }
void __print(const char *x) { cerr << '\"' << x << '\"'; }
void __print(const string &x) { cerr << '\"' << x << '\"'; }
void __print(bool x) { cerr << (x ? "true" : "false"); }
template<typename A> void __print(const A &x);
template<typename A, typename B> void __print(const pair<A, B> &p);
template<typename... A> void __print(const tuple<A...> &t);
template<typename T> void __print(stack<T> s);
template<typename T> void __print(queue<T> q);
template<typename T, typename... U> void __print(priority_queue<T, U...> q);
template<typename A> void __print(const A &x) {
bool first = true;
cerr << '{';
for (const auto &i : x) {
cerr << (first ? "" : ","), __print(i);
first = false;
}
cerr << '}';
}
template<typename A, typename B> void __print(const pair<A, B> &p) {
cerr << '(';
__print(p.f);
cerr << ',';
__print(p.s);
cerr << ')';
}
template<typename... A> void __print(const tuple<A...> &t) {
bool first = true;
cerr << '(';
apply([&first] (const auto &...args) { ((cerr << (first ? "" : ","), __print(args), first = false), ...); }, t);
cerr << ')';
}
template<typename T> void __print(stack<T> s) {
vector<T> debugVector;
while (!s.empty()) {
T t = s.top();
debugVector.push_back(t);
s.pop();
}
reverse(debugVector.begin(), debugVector.end());
__print(debugVector);
}
template<typename T> void __print(queue<T> q) {
vector<T> debugVector;
while (!q.empty()) {
T t = q.front();
debugVector.push_back(t);
q.pop();
}
__print(debugVector);
}
template<typename T, typename... U> void __print(priority_queue<T, U...> q) {
vector<T> debugVector;
while (!q.empty()) {
T t = q.top();
debugVector.push_back(t);
q.pop();
}
__print(debugVector);
}
void _print() { cerr << "]\n"; }
template <typename Head, typename... Tail> void _print(const Head &H, const Tail &...T) {
__print(H);
if (sizeof...(T)) cerr << ", ";
_print(T...);
}
#ifdef DEBUG
#define D(...) cerr << "Line: " << __LINE__ << " [" << #__VA_ARGS__ << "] = ["; _print(__VA_ARGS__)
#else
#define D(...)
#endif
struct Line {
ll m, c;
ll calc(ll x) {
return m * x + c;
}
};
struct LCT {
int lf, rh;
Line l;
LCT *lft, *rht;
LCT(Line tl, int tlf, int trh): lf(tlf), rh(trh), l(tl), lft(NULL), rht(NULL) {};
};
void addLine(LCT *x, Line nl) {
int md = (x->lf + x->rh) / 2;
if (nl.calc(md) < x->l.calc(md)) swap(x->l, nl);
if (x->lf + 1 == x->rh) return;
if (x->l.calc(x->lf) > nl.calc(x->lf)) {
if (!x->lft) {
x->lft = new LCT(nl, x->lf, md);
} else {
addLine(x->lft, nl);
}
} else if (x->l.calc(x->rh - 1) > nl.calc(x->rh - 1)) {
if (!x->rht) {
x->rht = new LCT(nl, md, x->rh);
} else {
addLine(x->rht, nl);
}
}
}
ll query(LCT *x, ll v) {
int md = (x->lf + x->rh) / 2;
ll ret = x->l.calc(v);
if (v < md && x->lft) {
ret = min(ret, query(x->lft, v));
}
if (v >= md && x->rht) {
ret = min(ret, query(x->rht, v));
}
return ret;
}
int n;
vector<ll> h, pref;
ll dp;
LCT *lc;
int main() {
ios_base::sync_with_stdio(false);
cin.tie(0);
cin >> n;
h.resize(n + 1, 0);
pref.resize(n + 1, 0);
for (int i = 1; i <= n; i++) {
cin >> h[i];
}
for (int i = 1; i <= n; i++) {
cin >> pref[i];
pref[i] += pref[i - 1];
}
lc = new LCT({-2 * h[1], h[1] * h[1] - pref[1]}, 0, 1e9 + 5);
for (int i = 2; i <= n; i++) {
dp = query(lc, h[i]) + h[i] * h[i] + pref[i - 1];
addLine(lc, {-2 * h[i], h[i] * h[i] + dp - pref[i]});
}
cout << dp << "\n";
}
