#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define mp make_pair
#define pb push_back
#define x first
#define y second
#define pii pair<int, int>
#define p3i pair<pii, int>
#define pll pair<ll, ll>
#define p3l pair<pll, ll>
#define lseg L, (L+R)/2, N*2+1
#define rseg (L+R)/2+1, R, N*2+2
#define ub upper_bound
#define lb lower_bound
#define p_q priority_queue
#define MN 1000000009
bool convex(pll X, pll O, pll Y){
return (X.y-O.y+X.x*X.x-O.x*O.x)*(O.x-Y.x)
<(O.y-Y.y+O.x*O.x-Y.x*Y.x)*(X.x-O.x);
}
set<pll> s[2];
ll n, w[100005], h[100005];
ll dp[100005], ans;
set<pll>::iterator x, y, z;
bool check1(int T, pll X){
z=s[T].lb(X);
if (z==s[T].begin() || z==s[T].end()) return 1;
y=z; --y;
if (y==s[T].begin()) return 1;
x=y; --x;
if (convex(*x, *y, *z)) return 1;
s[T].erase(y);
return 0;
}
bool check2(int T, pll X){
y=s[T].lb(X);
if (y==s[T].begin() || y==s[T].end()) return 1;
z=y; ++z;
if (z==s[T].end()) return 1;
x=y; --x;
if (convex(*x, *y, *z)) return 1;
s[T].erase(y);
return 0;
}
bool check3(int T, pll X){
x=s[T].lb(X);
if (x==s[T].end()) return 1;
y=x; ++y;
if (y==s[T].end()) return 1;
z=y; ++z;
if (z==s[T].end()) return 1;
if (convex(*x, *y, *z)) return 1;
s[T].erase(y);
return 0;
}
void add(int T, pll X){
y=s[T].ub(X);
if (y==s[T].begin() || y==s[T].end());
else {
x=y; --x;
if (!convex(*x, X, *y)) return;
}
s[T].insert(X);
int f=3;
while(f){
f=3;
f-=check1(T, X)+check2(T, X)+check3(T, X);
}
}
ll sum(int T, ll H){
int lo, mid, hi;
ll t2;
if (T==0) t2=1; else t2=-1;
t2=1;
if (T) {lo=-1000000; hi=H;}
else {lo=0; hi=H;}
//cout << "*" << s[T].size() << ' ' << hi << ' ';
while(lo<hi){
mid=(lo+hi+1)/2;
y=s[T].lb(mp(mid, -(1LL << 60)));
//cout << mid << ' ';
if (y==s[T].begin()) lo=mid;
else if (y==s[T].end() || y->x>H) hi=mid-1;
else {
x=y; --x;
if (((H-x->x)*(H-x->x)+t2*x->y<(H-y->x)*(H-y->x)+t2*y->y)) hi=mid-1;
else lo=mid;
}
}
y=s[T].lb(mp(lo, -(1LL << 60)));
if (y==s[T].end()) return (1LL << 60);
ll ret=(H-y->x)*(H-y->x)+t2*y->y;
/*int k;
for (int l=0; l<50; ++l){
k=rand()%1000000;
if (T==2) k=-k;
y=s[T].lb(mp(k, -(1LL << 60)));
if (y==s[T].end()) continue;
ret=min(ret, (H-y->x)*(H-y->x)+t2*y->y);
}*/
return ret;
}
int main() {
srand(time(NULL));
cin >> n;
for (int l=0; l<n; ++l) cin >> h[l];
for (int l=0; l<n; ++l){
cin >> w[l]; ans+=w[l];
}
for (int l=0; l<n; ++l){
if (l==0){
dp[l]=-w[l];
} else {
dp[l]=(1LL << 60);
dp[l]=min(sum(0, h[l]), sum(1, -h[l]))-w[l];
//int C=0;
//for (auto i:s[0]){
// dp[l]=min(i.y-w[l]+(i.x-h[l])*(i.x-h[l]), dp[l]);
//}
}
//cout << dp[l] << endl;
add(0, mp(h[l], dp[l]));
add(1, mp(-h[l], dp[l]));
}
cout << ans+dp[n-1];
return 0;
}
