// header file
#include <bits/stdc++.h>
// pragma
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
// macros
#define endl "\n"
#define ll long long
#define mp make_pair
#define ins insert
#define lb lower_bound
#define pb push_back
#define ub upper_bound
#define lll __int128
#define fi first
#define se second
using namespace std;
ll sqr(ll a) {
return a * a;
}
const ll is_query = -(1LL<<62);
struct line {
ll m, b;
mutable function<const line*()> succ;
bool operator<(const line &rhs) const {
if(rhs.b != is_query)
return m < rhs.m;
const line* s = succ();
if(!s)
return 0;
ll x = rhs.m;
return b - s -> b < (s -> m - m) * x;
}
};
struct dynamic_hull : public multiset<line> {
const ll inf = LLONG_MAX;
bool bad(iterator y) {
auto z = next(y);
// basically if the line is the same
// if the line is the same then we will pick the lower line
if(y == begin()) {
if(z == end()) return 0;
return y -> m == z -> m && y -> b <= z -> b;
}
auto x = prev(y);
if(z == end()) {
return y -> m == x -> m && y -> b <= x -> b;
}
// v1 is with prev
ll v1 = (x -> b - y -> b);
// check in case slope is same
if(y -> m == x -> m)
v1 = x -> b > y -> b ? inf : -inf;
else
v1 /= (y -> m - x -> m);
// v2 is with next
ll v2 = (y -> b - z -> b);
if(z -> m == y -> m)
v2 = y -> b > z -> b ? inf : -inf;
else
v2 /= (z -> m - y -> m);
return v1 >= v2;
}
void insert_line(ll m, ll b) {
auto y = insert({m, b});
y -> succ = [=] {return next (y) == end() ? 0 : &*next(y); };
if(bad(y)) {
erase(y);
return;
}
while(next(y) != end() && bad(next(y)))
erase(next(y));
while(y != begin() && bad(prev(y)))
erase(prev(y));
}
ll eval(ll x) {
auto l = *lower_bound((line) {x, is_query});
return l.m * x + l.b;
}
};
dynamic_hull cht;
int main() {
ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
int n;
cin >> n;
int h[n], w[n];
for(int i = 0; i < n; ++i)
cin >> h[i];
for(int i = 0; i < n; ++i)
cin >> w[i];
// we choose first and we choose last
// the problem is we need to choose some number of pillars
// the factors of choosing a pillar
// height
// cost of removing the pillar
// use dynamic cht dp opt
ll dp[n], pref[n];
memset(dp, 0, sizeof(dp));
pref[0] = 0;
for(int i = 1; i < n; ++i)
pref[i] = pref[i - 1] + w[i];
cht.insert_line(2 * h[0], -sqr(h[0]));
for(int i = 1; i < n; ++i) {
dp[i] = -cht.eval(h[i]) + pref[i - 1] + sqr(h[i]);
cht.insert_line(2 * h[i], -(dp[i] + sqr(h[i]) - pref[i]));
}
cout << dp[n - 1] << endl;
return 0;
}
