#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define pll pair<ll,ll>
#define pii pair<int,int>
#define fs first
#define sc second
#define tlll tuple<ll,ll,ll>
const ll inf = 1e18;
const ll mxn = 1e6+10;
struct line{
ll m,b;
line(){
m = 0;
b = inf;
}
line(ll mm,ll bb):m(mm),b(bb){}
ll operator()(ll x){
return m*x+b;
}
};
struct SEG{
line seg[mxn*4];
SEG(){}
void addline(int now,int l,int r,line k){
if(l == r){
if(seg[now](l)>k(l))swap(seg[now],k);
return;
}
int mid = (l+r)>>1;
if(seg[now](mid)>k(mid))swap(seg[now],k);
if(seg[now].m<k.m)addline(now*2+1,l,mid,k);
else addline(now*2+2,mid+1,r,k);
return;
}
ll getval(int now,int l,int r,int p){
if(l == r)return seg[now](p);
int mid = (l+r)>>1;
if(mid>=p)return min(seg[now](p),getval(now*2+1,l,mid,p));
else return min(seg[now](p),getval(now*2+2,mid+1,r,p));
}
};
SEG seg;
ll H[mxn],pref[mxn];
ll N;
ll dp[mxn];
int main(){
ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);
cin>>N;
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];
seg.addline(0,0,mxn-1,line(-H[1]*2,dp[1]+H[1]*H[1]-pref[1]));
for(int i = 2;i<=N;i++){
dp[i] = seg.getval(0,0,mxn-1,H[i])+pref[i-1]+H[i]*H[i];
seg.addline(0,0,mxn-1,line(-H[i]*2,dp[i]+H[i]*H[i]-pref[i]));
}
cout<<dp[N];
}
