#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <assert.h>
#include <iostream>
#include <sstream>
#include <vector>
#include <string>
#include <math.h>
#include <queue>
#include <list>
#include <algorithm>
#include <map>
#include <set>
#include <stack>
#include <ctime>
#include <iterator>
using namespace std;
#define ALL(c) (c).begin(),(c).end()
#define IN(x,c) (find(c.begin(),c.end(),x) != (c).end())
#define REP(i,n) for (int i=0;i<(int)(n);i++)
#define FOR(i,a,b) for (int i=(a);i<=(b);i++)
#define INIT(a,v) memset(a,v,sizeof(a))
#define SORT_UNIQUE(c) (sort(c.begin(),c.end()), c.resize(distance(c.begin(),unique(c.begin(),c.end()))))
template<class A, class B> A cvt(B x) { stringstream ss; ss<<x; A y; ss>>y; return y; }
typedef pair<int,int> PII;
typedef long long int64;
#define N 100000
int n;
int64 h[N],w[N];
int64 sqr(int64 x) { return x*x; }
struct line {
char type;
double x;
int64 k, n;
};
bool operator<(line l1, line l2) {
if (l1.type+l2.type>0) return l1.x<l2.x;
else return l1.k>l2.k;
}
set<line> env;
typedef set<line>::iterator sit;
bool hasPrev(sit it) { return it!=env.begin(); }
bool hasNext(sit it) { return it!=env.end() && next(it)!=env.end(); }
double intersect(sit it1, sit it2) {
return (double)(it1->n-it2->n)/(it2->k-it1->k);
}
void calcX(sit it) {
if (hasPrev(it)) {
line l = *it;
l.x = intersect(prev(it), it);
env.insert(env.erase(it), l);
}
}
bool irrelevant(sit it) {
if (hasNext(it) && next(it)->n <= it->n) return true; // x=0 cutoff
return hasPrev(it) && hasNext(it) && intersect(prev(it),next(it)) <= intersect(prev(it),it);
}
void add(int64 k, int64 a) {
sit it;
// handle collinear line
it=env.lower_bound({0,0,k,a});
if (it!=env.end() && it->k==k) {
if (it->n <= a) return;
else env.erase(it);
}
// erase irrelevant lines
it=env.insert({0,0,k,a}).first;
if (irrelevant(it)) { env.erase(it); return; }
while (hasPrev(it) && irrelevant(prev(it))) env.erase(prev(it));
while (hasNext(it) && irrelevant(next(it))) env.erase(next(it));
// recalc left intersection points
if (hasNext(it)) calcX(next(it));
calcX(it);
}
int64 query(int64 x) {
auto it = env.upper_bound((line){1,(double)x,0,0});
it--;
return it->n+x*it->k;
}
int64 g[N];
int64 solve() {
int64 a=0;
REP (i,n) a+=w[i];
g[0]=-w[0];
FOR (i,1,n-1) {
add(-2*h[i-1],g[i-1]+sqr(h[i-1]));
int64 opt=query(h[i]);
g[i]=sqr(h[i])-w[i]+opt;
}
return a+g[n-1];
}
int main() {
cin >> n;
REP (i,n) cin >> h[i];
REP (i,n) cin >> w[i];
cout << solve() << endl;
return 0;
}
