#include<bits/stdc++.h>
using namespace std;
int n;
long long h[100005],w[100005],b[100005],f[100005];
int sk[300005],ss,t;
const long long M=998244353;
int main(){
	freopen("building.in","r",stdin);
	freopen("building.out","w",stdout);
    mt19937 rd(114514);
	ios::sync_with_stdio(false);
	cin>>n;
	for(int i=1;i<=n;i++){
		cin>>h[i];
	}
	for(int i=1;i<=n;i++){
		cin>>w[i];
		b[i]=b[i-1]+w[i];
	}
	sk[1]=ss=1;
	for(int i=2;i<=n;i++){
        int tt=333,pp=1;
        f[i]=1e18;
        for(int j=max(1,i-6666);j<i;j++){
			if(f[i]>f[j]+b[i-1]-b[j]+(h[i]-h[j])*(h[i]-h[j])){
                f[i]=f[j]+b[i-1]-b[j]+(h[i]-h[j])*(h[i]-h[j]);
                pp=j;
            }        
		}
        for(int j=1;j<=min(5,i-1);j++){
			if(f[i]>f[j]+b[i-1]-b[j]+(h[i]-h[j])*(h[i]-h[j])){
                f[i]=f[j]+b[i-1]-b[j]+(h[i]-h[j])*(h[i]-h[j]);
                pp=j;
            }        
		}
		while(tt--){
            if(ss<=1) t=1;
			else t=rd()%ss+1;
            if(t<0) t=-t;
            t=sk[t];
			if(f[i]>f[t]+b[i-1]-b[t]+(h[i]-h[t])*(h[i]-h[t])) f[i]=f[t]+b[i-1]-b[t]+(h[i]-h[t])*(h[i]-h[t]),pp=t;
		}
		sk[++ss]=pp;
        sk[++ss]=i;
	}
	cout<<f[n];
	return 0;
}