// dp[1] = 0
// dp[i] = min(dp[j] + (h[i]-h[j])^2 + pfx[i-1] - pfx[j])
// dp[i] = min(dp[j] + h[i]^2 - 2*h[i]*h[j] + h[j]^2 + pfx[i-1] - pfx[j])
// dp[i] = pfx[i-1] + h[i]^2 + min(dp[j] - 2*h[i]*h[j] + h[j]^2 - pfx[j])
//
// --------i-------- ----ij------ ------------j----------
// dp[i] = pfx[i-1] + h[i]^2 + min(-2*h[i]*h[j] + dp[j] + h[j]^2 - pfx[j])
#include <iostream>
#include <fstream>
#include <vector>
#include <queue>
#include <utility>
#include <algorithm>
#include <cstring>
struct Line {
int64_t m, b;
Line():
m(0), b(0x3f3f3f3f3f3f3f3f) {}
Line(int64_t m, int64_t b):
m(m), b(b) {}
int64_t operator() (int x) {
return m*x + b;
}
};
class LiChaoTree {
private:
int n;
std::vector<Line> tree;
public:
LiChaoTree(int n): n(n) {
tree.assign(4*n+1,Line());
}
void add_line(int node, int l, int r, Line line) {
if (l+1==r) {
if (tree[node](l) > line(l)) {
tree[node] = line;
}
return;
}
int m = (l+r)>>1;
if (tree[node].m > line.m) {
std::swap(tree[node],line);
}
if (tree[node](m) > line(m)) {
std::swap(tree[node],line);
add_line(node<<1|1,m,r,line);
}
else {
add_line(node<<1,l,m,line);
}
}
int64_t query(int node, int l, int r, int x) {
if (l+1==r) {
return tree[node](x);
}
int m = (l+r)>>1;
if (x<m) {
return std::min(tree[node](x), query(node<<1,l,m,x));
}
else {
return std::min(tree[node](x), query(node<<1|1,m,r,x));
}
}
};
int x;
int height[100005];
int cost[100005];
int64_t pfx_cost[100005];
int64_t dp[100005];
int main() {
std::cin >> x;
for (int i = 1; i <= x; i++) {
std::cin >> height[i];
}
for (int i = 1; i <= x; i++) {
std::cin >> cost[i];
pfx_cost[i] = pfx_cost[i-1] + cost[i];
}
LiChaoTree tree(1000005);
for (int i = 1; i <= x; i++) {
if (i==1) {
dp[i] = 0;
}
else {
dp[i] = pfx_cost[i-1] + 1LL*height[i]*height[i] + tree.query(1,0,1000001,height[i]);
}
tree.add_line(1,0,1000001,Line(-2LL*height[i],dp[i]+1LL*height[i]*height[i]-pfx_cost[i]));
}
std::cout << dp[x] << "\n";
}
