Number of Peanuts

A large old tree stands in the middle of a forest. A squirrel named Darami lives inside a hollow in that tree, and every day she takes a walk through the forest in a very peculiar way.

Darami starts from the old tree facing north, and every second she acts according to the following rules:

• If there is a peanut under her feet, she picks it up, turns 90 degrees to the right, and moves forward 1 m.
• If there is no peanut under her feet, she puts down one peanut where she stands, turns 90 degrees to the left, and moves forward 1 m.

Darami is so fast that she moves exactly 1 m every second, and so strong that she never runs out of peanuts to carry. Find the number of peanuts lying on the ground after $t$ seconds.

The first line contains the number of peanuts $n$ ($0 \le n \le 7$) lying on the ground at the moment Darami leaves the tree (second 0).

Each of the next $n$ lines contains the position of one peanut as two integers $x$ and $y$ ($-2 \le x, y \le 2$), separated by a space. This means the peanut is located $x$ meters to the east and $y$ meters to the south of the starting point. At most one peanut lies at any single position.

The last line contains the integer $t$ ($0 \le t \le 10^9$), the number of seconds Darami walks.

Print, on the first line, the number of peanuts lying on the ground after $t$ seconds.