#include <iostream>
#include <fstream>
#include <set>
#include <vector>
#include <map>
#include <limits>
using namespace std;
const long double inf=numeric_limits <long double>::infinity();
const long double MAX_SLOPE=1e6+5;
const int NMAX=1e5;
struct line
{
long double slope, intercept;
line (long double _slope, long double _intercept)
{
slope=_slope;
intercept=_intercept;
}
long long operator () (long long x)
{
return slope*x+intercept;
}
};
line ultra_slopper (MAX_SLOPE, 0);
bool operator < (line a, line b)
{
if (a.slope==b.slope)
return a.intercept<b.intercept;
return a.slope<b.slope;
}
long double meet (line a, line b)
{
return (long double) (a.intercept-b.intercept)/ (long double) (b.slope-a.slope);
}
class ConvexHull
{
public:
set <pair <long double, line>> prevX;
map <line, pair <long double, long double>> limits;
ConvexHull (line a)
{
limits[a]={-inf, inf};
prevX.insert ({-inf, a});
}
void insert (line function)
{
if (limits.count (function))
return;
auto poz=limits.insert ({function, {0, 0}}).first;
if (poz!=limits.begin() && prev (poz) -> first.slope==function.slope)
{
limits.erase (poz);
return;
}
if (next (poz)!=limits.end() && next (poz) -> first.slope==function.slope)
{
prevX.erase ({next (poz) -> second.first, next(poz) -> first});
limits.erase (next (poz));
}
if (poz!=limits.begin() && next (poz)!=limits.end() && meet (next (poz) -> first, function)>=next (poz) -> second.second && meet (prev (poz) -> first, function)<=prev (poz) -> second.first)
{
limits.erase (poz);
return;
}
while (next(poz)!=limits.end())
{
if (meet (next (poz) -> first, function)<=next (poz) -> second.first)
{
prevX.erase ({next (poz) -> second.first, next (poz) -> first});
limits.erase (next (poz));
}
else
{
next (poz) -> second.second=meet (next (poz) -> first, function);
poz -> second.first=meet (next (poz) -> first, function);
break;
}
}
if (next (poz)==limits.end())
{
poz -> second.first=-inf;
}
while (poz!=limits.begin())
{
if (meet (prev (poz) -> first, function)>=prev (poz) -> second.second)
{
prevX.erase ({prev (poz) -> second.first, prev (poz) -> first});
limits.erase (prev (poz));
}
else
{
prevX.erase ({prev (poz) -> second.first, prev (poz) -> first});
prev (poz) -> second.first=meet (prev (poz) -> first, function);
prevX.insert ({prev (poz) -> second.first, prev (poz) -> first});
poz -> second.second=meet (prev (poz) -> first, function);
break;
}
}
if (poz==limits.begin())
{
poz -> second.second=inf;
}
prevX.insert ({poz -> second.first, function});
}
long long query (long long x)
{
line seg=prev (prevX.upper_bound ({x, ultra_slopper})) -> second;
return seg (x);
}
};
long long int n, h[NMAX+5], dp[NMAX+5], v[NMAX+5];
int main ()
{
cin >> n;
for (int i=1;i<=n;i++)
{
cin >> h[i];
}
for (int i=1;i<=n;i++)
{
cin >> v[i];
}
int sum=v[1];
ConvexHull cht (line (h[1], -sum+h[1]*h[1]+dp[1]));
for (int i=2;i<=n;i++)
{
dp[i]=sum+h[i]*h[i]+cht.query (-2*h[i]);
sum+=v[i];
cht.insert (line (h[i], -sum+h[i]*h[i]+dp[i]));
}
cout << dp[n];
return 0;
}
