#include <bits/stdc++.h>
#define debug printf
#define lp(i,a,b) for(int i = a ; i < b ; i++ )
#define ff first
#define ss second
#define pb push_back
#define mk make_pair
#define ll long long
#define sz size()
#define pii pair<int,int>
#define all(x) x.begin(),x.end()
const int MAXN = 1e5+10 ;
const int MAX = 1e6+10, pat = 1e3+10 ;
const ll inf = 1e18+5 ;
using namespace std ;
struct Line
{
ll a , b ;
Line(ll a = 1 , ll b = 0) : a(a) , b(b) {}
ll get(ll x )
{
if( a > 0 ) return inf ;
return a*x + b ;
}
void print() { printf("%lld %lld\n" ,a , b ) ; }
} tree[MAX*4] ;
int n ;
ll sw[MAXN] , dp[MAXN] , h[MAXN] ;
bool vis[MAX*4] ;
ll q(ll x) { return x*x ; }
int m(int l, int r) { return (l+r)>>1 ; }
void upd(int pos, int l, int r, Line v)
{
if( !vis[pos] )
{
vis[pos] = true ;
tree[pos] = v ;
return ;
}
if( tree[pos].get(l) <= v.get(l) && tree[pos].get(r) <= v.get(r) ) return ;
else if( tree[pos].get(l) > v.get(l) && tree[pos].get(r) > v.get(r) )
return (void)(tree[pos] = v ) ;
if( tree[pos].get(l) > v.get(l) ) swap( tree[pos] , v ) ;
if( tree[pos].get( m(l,r) ) < v.get( m(l,r) ) ) upd( 2*pos+1, m(l,r)+1, r, v ) ;
else
{
swap( tree[pos] , v ) ;
upd( 2*pos , l , m(l,r) , v ) ;
}
}
ll getAns(int pos, int l, int r, ll x)
{
ll ans = tree[pos].get(x) ;
if(l==r) return ans ;
if( x <= m(l,r) ) return min(ans, getAns(pos*2,l,m(l,r) , x) ) ;
return min( ans , getAns(pos*2+1,m(l,r)+1,r, x) ) ;
}
void print(int pos, int l, int r)
{
if( l == r )
{
printf("%d %d -> " , l, r) ;
tree[pos].print() ;
return ;
}
print(pos*2,l,m(l,r)) ;
printf("%d %d -> " , l, r) ;
tree[pos].print() ;
print(pos*2+1,m(l,r)+1, r) ;
}
int main()
{
scanf("%d", &n ) ;
lp(i,1,n+1) scanf("%lld",&h[i]) ;
lp(i,1,n+1)
{
scanf("%lld", &sw[i]) ;
sw[i] += sw[i-1] ;
}
upd( 1 , 0 , MAX-5 , Line(h[n]*(-2) , q(h[n]) + sw[n-1] ) ) ;
for(int i = n-1 ; i > 0 ; i-- )
{
dp[i] = getAns( 1 , 0 , MAX-5 , h[i] ) - sw[i] + q(h[i]) ;
upd(1,0,MAX-5 , Line( h[i] * (-2) , q( h[i] ) + sw[i-1] + dp[i] ) ) ;
}
printf("%lld\n" , dp[1] ) ;
}
