#include <iostream>
#include <vector>
#include <algorithm>
#include <set>
#include <climits>
using namespace std;
using ll = long long;
const ll inf = LLONG_MAX;
int n;
vector<ll> H,W;
vector<ll> dp,sp;
struct Line
{
ll m,k;
mutable ll x;
bool operator<(const Line &other) const
{
return m>other.m;///pante descrescatoare pt minim
}
bool operator<(ll other) const
{
return x<other;
}
ll operator()(ll x) const
{
return m*x+k;
}
};
struct CHT : multiset<Line,less<>>
{
ll div(ll a,ll b)
{
return a/b-((a%b) && ((a^b)<0));
}
bool isect(iterator a,iterator b)
{
if(b==end())
{
///practic a ii ultima linie deci se intersecteaza f departe
a->x=inf;
return 0;
}
if(a->m==b->m)
{
if(a->k<b->k)
a->x=inf;
else
a->x=-inf;
}
else
{
a->x=div(b->k-a->k,a->m-b->m);
}
return a->x>=b->x; ///daca e adv sterg b
}
void add(ll m,ll k)
{
auto c=insert({m,k,0}),b=c++,a=b;
while(isect(b,c))
c=erase(c);
if(a!=begin() && isect(--a,b))
isect(a,b=erase(b));
while((b=a)!=begin() && (--a)->x>=b->x)
isect(a,erase(b));
}
ll query(ll x)
{
Line line=*lower_bound(x);
return line(x);
}
};
int main()
{
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cout.tie(NULL);
cin>>n;
H=W=vector<ll>(n+1);
dp=sp=vector<ll>(n+1);
for(int i=1;i<=n;i++)
cin>>H[i];
for(int i=1;i<=n;i++)
cin>>W[i],sp[i]=sp[i-1]+W[i];
for(int i=1;i<=n;i++)
dp[i]=inf;
dp[1]=0;
CHT hull;
for(int i=1;i<=n;i++)
{
if(i==1)
{
hull.add(-2*H[i],H[i]*H[i]-sp[i]+dp[i]);
continue;
}
dp[i]=hull.query(H[i])+sp[i-1]+H[i]*H[i];
hull.add(-2*H[i],H[i]*H[i]-sp[i]+dp[i]);
}
cout<<dp[n];
return 0;
}
