#include <bits/stdc++.h>
using namespace std;
#define TRACE(x) cerr << #x << " :: " << x << endl
#define _ << " " <<
#define SZ(x) (int)(x).size()
#define ALL(x) (x).begin(),(x).end()
#define FOR(i,a,b) for(int i=(a);i<=(b);++i)
#define RFOR(i,a,b) for (int i=(a);i>=(b);--i)
#define SQ(x) ((ll)(x)*(x))
using ll=long long;
using ld=long double;
using ii=pair<int,int>;
const int mxN = 1e5+5;
int N, H[mxN], W[mxN];
ll pW[mxN], dp[mxN];
struct Line {
ll m, c;
ll eval(ll x) { return m*x + c; }
};
struct Hull {
Line dq[mxN];
int s, e;
inline void reset() { s = e = 0; }
Hull() { reset(); }
inline ld intersect(Line a, Line b) {
return (ld)(a.c - b.c) / (b.m - a.m);
}
void add(ll m, ll c) {
Line l = {m,c};
while (e-s > 1 && dq[e-1].m > m && intersect(l,dq[e-1]) <= intersect(dq[e-1],dq[e-2])) --e;
if (e > s && dq[e-1].m == m) {
if (dq[e-1].c > c) --e;
else return;
}
dq[e++] = l;
}
ll query(ll x) {
while (e-s > 1 && dq[s].eval(x) >= dq[s+1].eval(x)) ++s;
return dq[s].eval(x);
}
} ch;
void cdq(int l, int r) {
if (l == r) return;
int m = (l+r)/2;
cdq(l,m);
ch.reset();
vector<ii> slopes, queries;
FOR(i,l,m){
slopes.emplace_back(-2*H[i],i);
}
FOR(i,m+1,r){
queries.emplace_back(H[i],i);
}
sort(ALL(slopes),greater<ii>());
sort(ALL(queries));
// (H[i]-H[j])^2 + pW[i-1]-pW[j] + dp[j];
for (auto& s : slopes) {
int i = s.second;
ch.add(-2*H[i], SQ(H[i]) - pW[i] + dp[i]);
}
for (auto& q : queries) {
int i = q.second;
dp[i] = min(dp[i], ch.query(H[i]) + SQ(H[i]) + pW[i-1]);
}
cdq(m+1,r);
}
int main() {
//freopen("in.txt","r",stdin);
ios::sync_with_stdio(false);
cin.tie(0);
cin >> N;
FOR(i,1,N){ cin >> H[i]; }
FOR(i,1,N){ cin >> W[i]; pW[i] = pW[i-1] + W[i]; }
dp[1] = 0;
FOR(i,2,N) dp[i] = 1e18;
cdq(1,N);
cout << dp[N] << '\n';
}
