#include<bits/stdc++.h>
using namespace std;
#define FOR(i, a, b) for(int i = a; i < b; ++i)
#define REP(i, n) FOR(i, 0, n)
#define _ << " " <<
#define sz(x) ((int) x.size())
#define pb(x) push_back(x)
#define TRACE(x) cerr << #x << " = " << x << endl
#define int long long
typedef long long ll;
typedef pair<ll, ll> point;
typedef long double ld;
const int MAXN = 1e5 + 5, MAXV = 105;
const ll inf = 1e16;
int n, h[MAXN], w[MAXN];
ll dp[MAXN];
ld ccw(point A, point B, point C){
return (ld)A.first * (B.second - C.second) +
(ld)B.first * (C.second - A.second) +
(ld)C.first * (A.second - B.second);
}
void merge(vector <point> <, vector <point> &rt, vector <point> &hull){
int pnt1 = 0, pnt2 = 0;
vector <point> v;
while(pnt1 < sz(lt) || pnt2 < sz(rt)){
if(pnt1 == sz(lt))
v.pb(rt[pnt2 ++]);
else if(pnt2 == sz(rt))
v.pb(lt[pnt1 ++]);
else if(lt[pnt1].first == rt[pnt2].first){
if(lt[pnt1].second < rt[pnt2].second)
v.pb(lt[pnt1 ++]);
else
v.pb(rt[pnt2 ++]);
}
else if(lt[pnt1].first < rt[pnt2].first)
v.pb(lt[pnt1 ++]);
else
v.pb(rt[pnt2 ++]);
}
hull.clear();
for(auto it : v){
while(sz(hull) > 1 && ccw( hull[ sz(hull) - 2 ], hull.back(), it) <= 0)
hull.pop_back();
hull.pb(it);
}
}
ll check(ll x, point y){
return x * y.first + y.second;
}
void eval(int x, vector <point> &hull){
if(hull.empty())
return;
int lo = 0, hi = sz(hull) - 1;
while(lo < hi){
int mid = (lo + hi) >> 1;
if(mid + 1 > hi)
lo = mid;
if( check(h[x], hull[mid]) > check(h[x], hull[mid + 1]) )
lo = mid + 1;
else
hi = mid;
}
//TRACE(check(h[x], hull[lo]));
//TRACE(hull[lo].first); TRACE(hull[lo].second);
dp[x] = min(dp[x], check(h[x], hull[lo]) + w[x - 1] + h[x] * h[x]);
}
void solve(int lo, int hi, vector <point> &hull){
if(lo > hi) return;
if(lo == hi){
hull.pb(point(-2 * h[lo], dp[lo] + h[lo] * h[lo] - w[lo]));
return;
}
vector <point> lt, rt;
int mid = (lo + hi) >> 1;
FOR(i, lo, hi + 1)
eval(i, hull);
solve(lo, mid, lt);
FOR(i, mid + 1, hi + 1)
eval(i, lt);
solve(mid + 1, hi, rt);
vector <point> tmp;
merge(lt, rt, tmp);
merge(hull, tmp, hull);
}
signed main(){
ios_base::sync_with_stdio(false); cin.tie(0);
fill(dp, dp + MAXN, inf);
dp[1] = 0;
cin >> n;
REP(i, n)
cin >> h[i + 1];
REP(i, n){
cin >> w[i + 1];
if(i > 0)
w[i + 1] += w[i];
}
/*FOR(i, 2, n + 1){
dp[i] = inf;
FOR(j, 1, i){
dp[i] = min(dp[i], dp[j] + (h[i] - h[j]) * (h[i] - h[j]) + w[i - 1] - w[j] );
}
}*/
vector <point> v;
solve(1, n, v);
cout << dp[n];
}
