#include "mountains.h"
#include <bits/stdc++.h>
using namespace std ;
const int MAX = 2005 ;
int dp[MAX][MAX] ;
int n ;
vector<int>v ;
/*long double slope(int a , int b , int a2 , int b2)
{
long double x = a * 1.0000 ;
long double y = b * 1.0000 ;
long double x2 = a2 * 1.0000 ;
long double y2 = b2 * 1.0000 ;
return ((y2-y) / (x2-x)) ;
}*/
bool check(int a,int b,int c)
{
return 1ll * (v[a]*1ll - v[b] * 1ll) * (a*1ll - c*1ll) > 1ll * (v[a] * 1ll - v[c] * 1ll) * (a * 1ll - b * 1ll);
}
int solve(int l , int r)
{
if(l >= r)
return (l == r) ;
int &ret = dp[l][r] ;
if(ret != -1)
return ret ;
int MAX = 0 , idx = l ;
for(int i = l ; i <= r ; ++i)
{
if(v[i] > MAX)
MAX = v[i] , idx = i ;
}
int choice1 = solve(l , idx-1) + solve(idx+1 , r) ;
int choice2 = 0;
int last = idx+1 ;
for(int i = last ; i <= r ; ++i)
{
i = last ;
for(int j = i+1 ; j <= r ; ++j)
{
last = j ;
if(!check(idx , i , j))
{
choice2 += solve(i+1 , j-1) ;
break;
}
}
if(last == r && check(idx , i , r))
choice2 += solve(i+1 , r) ;
}
last = idx - 1 ;
for(int i = last ; i >= l ; --i)
{
i = last ;
for(int j = i-1 ; j >= l ; --j)
{
last = j ;
if(!check(j , i , idx))
{
choice2 += solve(j+1 , i-1) ;
break;
}
}
if(last == l && check(l , i , idx))
choice2 += solve(l , i-1) ;
}
choice2++ ;
ret = max(choice1 , choice2) ;
return ret ;
}
int maximum_deevs(vector<int>x)
{
memset(dp , -1 , sizeof(dp)) ;
v = x ;
n = v.size() ;
return solve(0 , n-1) ;
}
/*int main()
{
int n ;
cin>>n ;
vector<int>x(n) ;
for(auto &i : x)
cin>>i ;
cout<<maximum_deevs(x)<<"\n" ;
return 0 ;
}*/
