/*==============================================================================================================
__ __ _____ ______ _______
| | | | / __ \ / _____| / ______|
__| |__ __| |__ |_| | | | | | |
|__| __| |__| __| | | | |____ | |_____
| | _____ _ | | ____ __ __ ____ _____ _____ / / \ ___ \ | ___ \
| | / _ \ | | | | / _/ | | | | / _ \ / __ \ / _ \ / / | | | | | |
| |_ | |_| | | | | |_ | | | |_| | | |_| | | | | | | |_| | / /___ ____| | | |___| |
\____\ \____/| |_| \____\ |_| \_____/ \_____/ |_| |_| \____ | |______| |______/ \_______/
| |
__/ |
|___/
Pratice, practice, and practice
Where is the bug, delete it there
Try, try, try again until you succeed
I hated every minute of training, but I said, 'Don't quit. Suffer now and live the rest of your life as a champion.' - Mohamed Ali
You may not be the best, but must be the most effort
Even the things and people you like, you don't have the courage to take, you are destined to be a failure.
Difficult means more time
Pain + Reflection = Progress
==============================================================================================================*/
#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define ld long double
#define endl '\n'
const ll mod = 1e9+7;
struct LiChao_tree //offline + get min
{
struct line
{
ll a, b;
ll get(ll x) {return a*x+b;}
};
ll n;
vector<line> tree;
vector<ll> compress;
LiChao_tree(vector<ll> _compress_x)
{
n=_compress_x.size()+5;
compress=_compress_x;
sort(compress.begin(), compress.end());
compress.resize(unique(compress.begin(), compress.end())-compress.begin());
tree.resize(4*n+5, {0, LLONG_MAX}); //LLONG_MIN
}
ll getid(ll val) {return lower_bound(compress.begin(), compress.end(), val)-compress.begin();}
void insert(ll id, ll l, ll r, line newL)
{
if (l==r)
{
if (newL.get(compress[l])<tree[id].get(compress[l])) tree[id]=newL; //thay dau >
return;
}
ll m=(l+r)/2;
bool lef=newL.get(compress[l])<tree[id].get(compress[l]); //thay dau >
bool mid=newL.get(compress[m])<tree[id].get(compress[m]); //thay dau >
if (mid==true) swap(newL, tree[id]);
if (lef!=mid) insert(id*2, l, m, newL);
else insert(id*2+1, m+1, r, newL);
}
void insert(ll a, ll b)
{
line newL={a, b};
insert(1, 0, n-1, newL);
}
ll query(ll id, ll l, ll r, ll x)
{
if (l==r) return tree[id].get(compress[x]);
ll m=(l+r)/2;
if (x<=m) return min(tree[id].get(compress[x]), query(id*2, l, m, x)); //max()
return min(tree[id].get(compress[x]), query(id*2+1, m+1, r, x)); //max()
}
ll query(ll x)
{
ll pos=getid(x);
return query(1, 0, n-1, pos);
}
};
ll n, tot, h[100005], w[100005], dp[100005];
void solve()
{
cin>>n;
for (ll i=1; i<=n; i++) cin>>h[i];
for (ll i=1; i<=n; i++) cin>>w[i];
vector<ll> v;
for (ll i=1; i<=n; i++) v.push_back(h[i]), tot+=w[i];
sort(v.begin(), v.end());
v.resize(unique(v.begin(), v.end())-v.begin());
LiChao_tree seg(v);
dp[1]=-w[1];
for (ll i=2; i<=n; i++)
{
seg.insert(-2*h[i-1], dp[i-1]+h[i-1]*h[i-1]);
dp[i]=seg.query(h[i])-w[i]+h[i]*h[i];
}
cout<<tot+dp[n];
}
int main()
{
ios_base::sync_with_stdio(false); cin.tie(NULL);
clock_t start = clock();
//#ifndef ONLINE_JUDGE
//freopen("_input.txt", "r", stdin);
//freopen("_output.txt", "w", stdout);
//#endif
solve();
clock_t end = clock();
cerr<<"Time: "<<fixed<<setprecision(10)<<double(end-start)/double(CLOCKS_PER_SEC)<<"\n";
return 0;
}
