#include<bits/stdc++.h>
using namespace std;
#define inf 0x3f3f3f3f
#define sz(x) int((x).size())
#define fi first
#define se second
typedef long long ll;
typedef pair<int, int> ii;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
int Random(int l, int r) {
return uniform_int_distribution<int>(l, r)(rng);
}
const int MAXN = 100005;
ll dp[MAXN], sumCost[MAXN];
int height[MAXN], costRemove[MAXN], nArr;
ll brute(void) {
for (int i = 2; i <= nArr; ++i)
dp[i] = 1e18;
for (int i = 1; i < nArr; ++i) {
for (int j = i + 1; j <= nArr; ++j) {
dp[j] = min(dp[j], dp[i] + 1LL * height[i] * height[i] + 1LL * height[j] * height[j] - 2LL * height[i] * height[j] + sumCost[j - 1] - sumCost[i]);
}
}
return dp[nArr];
}
const int MINCOORD = 0;
const int MAXCOORD = 1e6;
struct Line {
ll a, b;
Line(ll _a = 0, ll _b = 1e18) : a(_a), b(_b) {};
inline ll get(ll x) const {
return a * x + b;
}
};
struct Lichao {
struct Node {
Line line;
int L, R;
};
vector<Node> tree;
void init(void) {
tree.clear();
tree.push_back({Line(), -1, -1});
}
void update(int id, int l, int r, Line lines) {
while(1) {
Line low(lines), high(tree[id].line);
if(low.get(l) > high.get(l))
swap(low, high);
tree[id].line = low;
if(low.get(r) <= high.get(r))
return;
int mid = (l + r) >> 1;
//cout << l << ' ' << r << ' ' << low.get(mid) << ' ' << high.get(mid) << ' ' << low.a << ' ' << low.b << ' ' << high.a << ' ' << high.b << '\n';
if(low.get(mid) <= high.get(mid)) {
if(tree[id].R == -1)
tree[id].R = sz(tree), tree.push_back({Line(), -1, -1});
id = tree[id].R;
lines = high, l = mid + 1;
} else {
if(tree[id].L == -1)
tree[id].L = sz(tree), tree.push_back({Line(), -1, -1});
tree[id].line = high;
id = tree[id].L;
lines = low, r = mid;
}
}
}
ll query(int id, int l, int r, int x) {
ll res(tree[id].line.get(x));
while(l < r) {
int mid = (l + r) >> 1;
if(x <= mid) {
id = tree[id].L;
r = mid;
} else {
id = tree[id].R;
l = mid + 1;
}
//cout << '.' << id << ' ' << l << ' ' << r << ' ' << x << '\n';
if(id == -1)
break;
res = min(res, tree[id].line.get(x));
}
return res;
}
} lichao;
ll magicFunc(void) {
lichao.init();
lichao.update(0, MINCOORD, MAXCOORD, Line(-2 * height[1], 1LL * height[1] * height[1] - sumCost[1]));
for (int i = 2; i <= nArr; ++i) {
dp[i] = lichao.query(0, MINCOORD, MAXCOORD, height[i]) + 1LL * height[i] * height[i] + sumCost[i - 1];
lichao.update(0, MINCOORD, MAXCOORD, Line(-2 * height[i], dp[i] + 1LL * height[i] * height[i] - sumCost[i]));
//cout << dp[i] << " \n"[i == nArr];
}
return dp[nArr];
}
void process(void) {
cin >> nArr;
for (int i = 1; i <= nArr; ++i) {
cin >> height[i];
//height[i] = Random(0, 1e6); cout << height[i] << " \n"[i == nArr];
}
for (int i = 1; i <= nArr; ++i) {
cin >> costRemove[i];
//costRemove[i] = Random(-1e6, 1e6); cout << costRemove[i] << " \n"[i == nArr];
sumCost[i] = sumCost[i - 1] + costRemove[i];
}
//cout << brute() << '\n';
cout << magicFunc() << '\n';
}
int main(void) {
ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
process();
return 0;
}
