Uolevi is in a forest. Given the coordinates of Uolevi and all trees in the forest, calculate how many trees Uolevi can see at the moment. Uolevi can see a tree if it's not directly behind another tree from Uolevi's location.

Input

The first line contains a single integer $n$, the number of trees in the forest. Second line contains integers $x_u$ and $y_u$ denoting Uolevi's location in the forest. Next $n$ lines each contain two integers $x_i$ and $y_i$, the locations of the trees in the forest.

There are no two trees sharing the same location, and Uolevi is not in the same location with a tree.

Output

Output the number of trees Uolevi can see.

Constraints

• $1 \le n \le 2000$
• $-10^6 \le x_u, y_u \le 10^6$
• $-10^6 \le x_i, y_i \le 10^6$

Example

Input:

4
1 -1
0 1
-2 3
3 -1
-1 3

Output:

3