#include<bits/stdc++.h>
using namespace std;
// define
#define execute cerr << "Time elapsed: " << (1.0 * clock() / CLOCKS_PER_SEC) << "s";
#define ll long long
#define ld long double
#define ii pair<int,int>
#define se second
#define fi first
#define iii pair<int,ii>
#define all(v) v.begin(),v.end()
#define bit(x,i) (((x)>>(i))&1LL)
#define flip(x,i) ((x)^(1LL<<(i)))
#define ms(d,x) memset(d,x,sizeof(d))
#define sitingfake 1
#define orz 1
template<typename T> bool maximize(T &a, const T &b)
{
if(a < b) {a = b; return 1;}
return 0;
}
template<typename T> bool minimize(T &a, const T &b)
{
if(a > b) {a = b;return 1;}
return 0;
}
//constant
const ll mod = 1e9+7;
const long long linf = 4557430888798830399;
const int inf = 1061109567;
const int maxarr = 1e6+5;
const int dx[] = {0,1,-1,0};
const int dy[] = {1,0,0,-1};
//code
const int maxn = 1e5 + 7;
ll h[maxn],pre[maxn];
int n;
struct Line {
mutable ll k, m, p;
bool operator<(const Line& o) const { return k < o.k; }
bool operator<(ll x) const { return p < x; }
};
struct LineContainer : multiset<Line, less<>> {
// (for doubles, use inf = 1/.0, div(a,b) = a/b)
static const ll inf = LLONG_MAX;
ll div(ll a, ll b) { // floored division
return a / b - ((a ^ b) < 0 && a % b); }
bool isect(iterator x, iterator y) {
if (y == end()) return x->p = inf, 0;
if (x->k == y->k) x->p = x->m > y->m ? inf : -inf;
else x->p = div(y->m - x->m, x->k - y->k);
return x->p >= y->p;
}
void AddLine(ll k, ll m) {
iterator z = insert({k, m, 0}), y = z++, x = y;
while (isect(y, z)) z = erase(z);
if (x != begin() && isect(--x, y)) isect(x, y = erase(y));
while ((y = x) != begin() && (--x)->p >= y->p)
isect(x, erase(y));
}
void Free()
{
while(!empty())
{
erase(begin());
}
return;
}
ll get(ll x) {
assert(!empty());
Line l = *lower_bound(x);
return l.k * x + l.m;
}
/**
notice : this is LineContainer for Max Query, however, if we need Min Query just add the "-"
in our AddLine and answer
exp : cht.AddLine(-a,-b) for Min Q; ans = - cht.get(x)
when query x the Line gives us maximum ans for x , our ans just ans = - ans
**/
};
void solve(void)
{
cin >> n;
for(int i=1;i<=n;i++)
{
cin >> h[i];
}
for(int i=1;i<=n;i++)
{
int x; cin >> x;
pre[i] = pre[i-1] + x;
}
LineContainer cht;
cht.AddLine(2 * h[1], -(h[1] * h[1] - pre[1]));
for(int i=2;i<=n;i++)
{
ll tmp = -cht.get(h[i]) + pre[i-1] + h[i] * h[i];
cht.AddLine(2 * h[i],-(tmp + h[i] * h[i] - pre[i]));
if(i == n) cout << tmp;
}
}
signed main()
{
ios_base::sync_with_stdio(0);
cin.tie(0);
cout.tie(0);
#define task ""
if(fopen(task".inp","r"))
{
freopen(task".inp","r",stdin);
freopen(task".out","w",stdout);
}
int tc; tc = 1;
while(tc--) solve();
//execute;
}
/**
6
3 8 7 1 6 6
0 -1 9 1 2 0
**/
