# 2019 USACO January

# Mountain View

From her pasture on the farm, Bessie the cow has a wonderful view of a mountain range on the horizon. There are **n** mountains in the range **1**...`10`

. If we think of Bessie's field of vision as the ^{5}**xy** plane, then each mountain is a triangle whose base rests on the **x** axis. The two sides of the mountain are both at **45** degrees to the base, so the peak of the mountain forms a right angle. Mountain **i** is therefore precisely described by the location (`x`

, _{i}`y`

) of its peak. No two mountains have exactly the same peak location._{i}

Bessie is trying to count all of the mountains, but since they all have roughly the same colour, she cannot see a mountain if its peak lies on or within the triangular shape of any other mountain.

Determine the number of distinct peaks, and therefore mountains, that Bessie can see.

#### Input

The first line contains **n** (**1** ≤ **n** ≤ `10`

). Each of the remaining ^{5}**n** lines contains `x`

(_{i}**0** ≤ `x`

≤ _{i}`10`

) and ^{9}`y`

(_{i}**1** ≤ `y`

≤ _{i}`10`

) describing the location of one mountain's peak.^{9}

#### Output

Print the number of mountains that Bessie can distinguish.

#### Example

In this example, Bessie can see the first and last mountain. The second mountain is obscured by the first.

3 4 6 7 2 2 5

2