// Li-chao Tree
/* documents
https://wiki.vnoi.info/vi/algo/data-structures/lichao-tree
https://cp-algorithms.com/geometry/convex_hull_trick.html
*/
#include <bits/stdc++.h>
using namespace std;
#define all(v) v.begin(),v.end()
#define pb push_back
#define ll long long
#define ld long double
#define fi first
#define se second
#define mk make_pair
typedef pair<int,int> pii;
const int maxn = 1e5 + 10;
ll a[maxn],pre[maxn],dp[maxn];
// Code Li-chao Tree
struct Line // y = ax + b
{
ll a,b;
Line():a(0),b(0){}
Line(ll A,ll B) : a(A),b(B){}
ll cal(ll x) const {return a * x + b;}
};
struct Lichao
{
vector<Line> t;
Lichao(){}
// Initialize tree with given size (for segment tree)
Lichao(int sz) : t(sz, Line(0,LLONG_MAX) ){}
// Insert a new line 'f' into the segment tree
void add_line(int l,int r,Line f) // O( log(sz) )
{
if(l > r)return;
int mid = (l + r)/2;
// Swap if new line is better at midpoint
if( f.cal(mid) < t[mid].cal(mid) ) swap(t[mid],f);
if(l == r) return; // Leaf node reached
if(f.a > t[mid].a) add_line(l,mid-1,f); // higher slope -> left side of the convex hull
if(f.a < t[mid].a) add_line(mid+1,r,f); // otherwise
}
// pos: query x-coordinate
ll cal(int l,int r,int pos) // O( log(sz) )
{
if(l > r || l > pos || r < pos)return LLONG_MAX;
int mid = (l + r)/2;
ll ans = t[mid].cal(pos);
if(l == r)return ans; // Leaf node
// Query both children and return minimum value for pos
ans = min(ans, cal(l,mid-1,pos));
ans = min(ans, cal(mid+1,r,pos) );
return ans;
}
};
// End Code Li-chao Tree
int main()
{
ios_base::sync_with_stdio(false);
cin.tie(0);
// https://oj.uz/problem/view/CEOI17_building?locale=en
int n;
cin>>n;
for(int i = 1;i<=n;i++)cin>>a[i];
for(int i = 1;i<=n;i++)
{
cin>>pre[i];
pre[i] += pre[i-1];
}
Lichao tree(1000000 + 10); // Initialize Li-chao tree to cover possible x values
for(int i = 1;i<=n;i++)
{
if(i == 1)
{
dp[i] = 0;
}
else
{
dp[i] = tree.cal(0,1000000,a[i]) + a[i] * a[i] + pre[i-1];
}
// Add new line for future DP queries (state transition)
tree.add_line(0,1000000,Line( a[i] * -2, a[i] * a[i] +dp[i] - pre[i] ));
}
cout<<dp[n];
return 0;
}
