The Dutch Farmer

Did you know? Tulips were so valuable in the $17^{th}$ century that they caused an economic phenomenon known as Tulip Mania - some bulbs were worth more than houses.

A field of tulips is represented as an axis-aligned rectangle, with irrigation sprinklers placed on its four sides. These sprinklers spray a fertilizing solution over the field.

The Dutch farmer, Jakob, wants to determine how many tulips will ripen faster because they are planted in a special fertilized zone.

There are $N$ tulips planted at locations $(X_i,\ Y_i)$ for $i=0\ldots N-1$. A tulip is considered to be in the fertilized zone if, together with the four corners of the rectangle, it forms

• two acute-angled triangles, and
• two obtuse-angled triangles.

Your task is to count how many tulips meet this condition.

Input data

The input file consists of:

• A line containing integers $\mathtt{topLeftX}$, $\mathtt{topLeftY}$.
• A line containing integers $\mathtt{topRightX}$, $\mathtt{topRightY}$.
• A line containing integers $\mathtt{bottomRightX}$, $\mathtt{bottomRightY}$.
• A line containing integers $\mathtt{bottomLeftX}$, $\mathtt{bottomLeftY}$.
• A line containing integer $N$.
• $N$ lines, the $i$-th of which consisting of integers $X_{i}$, $Y_{i}$.

Output data

The output file must contain a single line consisting of integer $K$, the number of tulips in the special zone.

Constraints and clarifications

• All points, including the rectangle's corners, lie within the geometric space $[-1 \ 500, 1 \ 500] \cdot [-1 \ 500, 1 \ 500]$.
• The rectangle is axis-aligned, that is, the sides of the rectangle are parallel to the axes.
• $1 \le N \le 100 \ 000$.
• All tulips are inside the rectangle. There is no tulip located on a side of the rectangle.
• All tulip locations are unique (there are no identical $(X_i,\ Y_i)$ positions).

Example 1

stdin

0 5
10 5
10 0
0 0
5
2 3
1 4
4 1
9 1
6 3

stdout

4

Explanation

In the following figures, the $\textcolor{red}{red}$ areas are covered with fertilizer, while the $\textcolor{blue}{blue}$ areas are not.

In the first sample case, the only tulip outside the fertilized area is located at position $(2,\ 3)$.

Example 2

stdin

0 35
35 35
35 0
0 0
10
17 8
16 5
32 27
18 32
8 18
17 30
14 19
5 11
2 32
2 11

stdout

4

Explanation

In the second sample case, the tulips inside the fertilized area are located at the points: $(32,\ 27)$, $(14,\ 19)$, $(5,\ 11)$,
and $(2,\ 32)$.