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Nuts

Time limit = 1 second(s)

In the very middle of the Hundred Acre Wood there is a huge oak. Squirrel Barbara lives in one of this oak's hollows. Each day she walks along the forest in a quite unusual way. She starts her walk near the oak, facing North, and in each unit of time she performs a move in the following way:

*) If there is a nut in her current location then she picks it up, turns 90 right and walks straight for 1 meter.

*) If there is no nut where Barbara is standing then she drops a nut in her current location, turns 90 left and also walks straight for 1 meter.

Your task is to count the number of nuts that are lying on the ground after t units of time.

Input

The first line of the input file contains one integer n (0<=n<=7), denoting the number of nuts that were lying on the ground at time 0. The following n lines describe the nuts' locations: each of them contains two integers x and y (-2<=x,y<=2), separated by a single space. Such line means that the nut lies x meters to the East and y meters to the South from the oak. You can assume that no two nuts lie in the same location. The last line of input contains one integer t (0<=t<=1000000000), denoting the number of units of time that passed since Barbara started her walk.

Output

The first and only line of the input file should contain one non-negative integer, denoting the number of nuts that are lying on the ground after t units of time. We assume that Barbara has an unlimited number of nuts.

Input#1
2
0 0
-2 1
8
Output#1
6

Author:
Tomasz Idziaszek (monsoon)

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