#include<bits/stdc++.h>
using namespace std;
const int MAXN=1e5+5;
const int sqr=320;
const long long INF=1e18;
double intersect(pair<long long,long long> a,pair<long long,long long> b)
{
if(a.first==b.first) return INF;
return (double)(b.second-a.second)/(a.first-b.first);
}
long long dp[MAXN],pref[MAXN],H[MAXN],cnt[MAXN];
double range[MAXN/sqr+5][sqr+5];
vector< pair<long long,long long> > vi[MAXN/sqr+5];
void build(int l,int r,int idx)
{
vector< pair<long long,long long> > vv;
for(int i=l;i<=r;i++) vv.push_back({-H[i]*2,dp[i]+H[i]*H[i]-pref[i]});
sort(vv.begin(),vv.end(),greater< pair<long long,long long> >());
range[idx][0]=-INF,range[idx][1]=INF;
for(auto v:vv)
{
while(!vi[idx].empty()&&range[idx][cnt[idx]]>intersect(v,vi[idx].back())) cnt[idx]--,vi[idx].pop_back();
if(!vi[idx].empty()) range[idx][++cnt[idx]]=intersect(v,vi[idx].back()),range[idx][cnt[idx]+1]=INF;
vi[idx].push_back(v);
}
}
long long get(int idx,long long val)
{
int pos=upper_bound(range[idx],range[idx]+cnt[idx]+2,val)-range[idx]-1;
return vi[idx][pos].first*val+vi[idx][pos].second;
}
int main()
{
ios::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
int n;
cin>>n;
int pre=1,cnt=0;
for(int i=1;i<=n;i++) cin>>H[i];
for(int i=1;i<=n;i++)
{
cin>>pref[i];
pref[i]+=pref[i-1];
if(i==1) dp[i]=0;
else
{
dp[i]=INF;
for(int j=pre;j<i;j++) dp[i]=min(dp[i],dp[j]+pref[i-1]-pref[j]+(H[i]-H[j])*(H[i]-H[j]));
for(int j=1;j<=cnt;j++) dp[i]=min(dp[i],get(j,H[i])+H[i]*H[i]+pref[i-1]);
if(i%sqr==0)
{
pre=i+1;
build(pre-sqr,i,++cnt);
}
}
}
cout<<dp[n];
}
