For a set $S$ of points in a plane and a point $p$ in the plane, the function $f(p, S)$ has a value of 1 if and only if $p$ is inside the convex hull of $S$ (including the boundary of the convex hull of $S$), and 0 otherwise.
Given two sets of points in the plane, $P = \{p_1, p_2, \dots, p_N\}$ and $A = \{a_1, a_2, \dots, a_M\}$, we call a point $a_i$ in $A$ an extreme point if and only if it satisfies:
$$\sum_{j \neq i} f(a_i, P \cup \{a_j\}) = 0$$
In other words, $a_i$ is not inside the convex hull formed by $P$ and any point $a_j$ in $A$ where $j \neq i$.
Please count the number of extreme points in set $A$.
Input
The first line contains two space-separated positive integers $N$ and $M$. The second line contains $N$ space-separated pairs of integers, where the $i$-th pair $(x_i^p, y_i^p)$ represents the coordinates of point $p_i$. The third line contains $M$ space-separated pairs of integers, where the $j$-th pair $(x_j^a, y_j^a)$ represents the coordinates of point $a_j$.
For any single set, the input data guarantees that no two points have the same coordinates.
Output
Output a single integer representing the number of extreme points in set $A$.
Examples
Input 1
4 5 6 3 7 -1 -6 -5 1 5 -5 -5 7 -5 9 -9 -10 11 -5 -6
Output 1
3
Note 1
The extreme points are $(-10, 11)$, $(9, -9)$, and $(-5, -6)$.
Constraints
- For 10% of the data, $M = 1$.
- For 30% of the data, $N, M \le 50$.
- For another 30% of the data, $N \le 10$, $M \le 20000$.
- For 100% of the data, $3 \le N \le 10^5$, $1 \le M \le 10^5$, $|x_i|, |y_i| \le 10^6$, and the area of the convex hull of set $P$ is non-zero.