#include <bits/stdc++.h>
#define N 100005
using namespace std;
long long h[N],w[N];
long long dp[N];
set<pair<pair<int,int>,pair<long long,long long>>> s;
set<pair<pair<long long,long long>,pair<int,int>>> p;
long long get(int x){
auto a = *prev(s.lower_bound({{x+1,0},{0,0}}));
return a.second.second * x + a.second.first;
}
long long intersect(long long a,long long b,long long c,long long d){
return (d - b + a - c - 1)/(a - c);
}
long long intersect2(long long a,long long b,long long c,long long d){
if(a - c >= 0)return 1e9;
return (d - b)/(a - c);
}
void add(long long a,long long b){
int l = 1e6 +5, r = 0;
auto it = p.lower_bound({{b,-1e18},{-1e18,-1e18}});
if(it == p.end())l = 0;
while(it != p.end()){
if(it->first.second >= a)break;
long long point = intersect(a,b,it->first.second,it->first.first);
if(point > it->second.second)break;
l = min((long long)l,max(point,(long long)it->second.first));
r = max(r,it->second.second);
if(point > it->second.first)break;
it = next(it);
}
it = p.lower_bound({{b,-1e18},{-1e18,-1e18}});
if(it == p.begin())r = 1e6;
while(it != p.begin()){
it = prev(it);
long long point = intersect2(a,b,it->first.second,it->first.first);
if(point < it->second.first)break;
r = max((long long)r,min(point,(long long)it->second.second));
l = min(l,it->second.first);
if(point < it->second.second)break;
}
if(l > r){
return;
}
if(s.lower_bound({{l,-1e18},{-1e18,-1e18}}) != s.begin()){
auto x = *prev(s.lower_bound({{l,-1e18},{-1e18,-1e18}}));
if(x.first.second != l-1){
s.erase(x);
p.erase({x.second,x.first});
if(x.first.second > r){
int tmp = x.first.first;
x.first.first = r+1;
s.insert(x);
p.insert({x.second,x.first});
x.first.first = tmp;
}
x.first.second = l-1;
s.insert(x);
p.insert({x.second,x.first});
}
}
if(s.lower_bound({{r+1,-1e18},{-1e18,-1e18}}) != s.begin()){
auto x = *prev(s.lower_bound({{r+1,-1e18},{-1e18,-1e18}}));
if(x.first.second > r){
s.erase(x);
p.erase({x.second,x.first});
x.first.first = r+1;
s.insert(x);
p.insert({x.second,x.first});
}
}
while(s.lower_bound({{l,-1e18},{-1e18,-1e18}}) != s.end()){
auto x = *s.lower_bound({{l,-1e18},{-1e18,-1e18}});
if(x.first.first <= r){
s.erase(x);
p.erase({x.second,x.first});
}
else break;
}
s.insert({{l,r},{b,a}});
p.insert({{b,a},{l,r}});
}
void solve(){
int n;
cin >> n;
long long sum = 0;
for(int i=1;i<=n;i++){
cin >> h[i];
}
for(int i=1;i<=n;i++){
cin >> w[i];
sum += w[i];
}
dp[1] = sum - w[1];
s.insert({{0,1e6},{-(dp[1] + h[1] * h[1]),2*h[1]}});
p.insert({{-(dp[1] + h[1] * h[1]),2*h[1]},{0,1e6}});
for(int i=2;i<=n;i++){
dp[i] = -get(h[i]) + h[i]*h[i] - w[i];
add(2*h[i],-(dp[i] + h[i]*h[i]));
}
cout << dp[n];
}
int main(){
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
#ifdef Local
freopen("in.txt","r",stdin);
freopen("out.txt","w",stdout);
#endif
int t = 1;
//cin >> t;
while(t--){
solve();
}
#ifdef Local
cout << endl << fixed << setprecision(2) << 1000.0 * clock() / CLOCKS_PER_SEC << " milliseconds.";
#endif
}
