Firs conversation

In forest dark
Where cunning fox
A fir grows-up
And hare with tops…

The hares decided to intensify firs conversation on the eve of New-year. For this was creation some lines of conversation. First of all they coved a plot of forest by wire in perimeter (protuberant polygon), the strongest hare was responsible. In the center of this line creation next fence, where stay more weak hare etc. So, every fir was in conversation. The elder hare ask yours advise when he wrote a graph of duty of hares in the forest. Count. How many guards we need for one shift of duty on firs conversation.

Input

In the first line of inputs data we have N quantity of firs. Next we have 2N numbers. It is firs coordinates of forest.

1 ≤ N ≤ 100, -1000 ≤ Xi, Yi ≤ 1000.

Output

One number is quantity of hares for firs conversations.