Willson the Canada Goose is like any other Canada Goose - he likes to fly around and practice honking.
Today, he will be flying around a city containing buildings. Each building is a rectangle with a side parallel to the axis. The lower left corner of the building is at , and the upper right corner is at . A building can overlap with another building. It is possible for a building to be completely contained within another building. Also, it is possible that two different buildings represent the same rectangle.
However, corners are dangerous for Willson to fly into - much more dangerous than walls. A corner is an integer coordinate where exactly of the adjacent squares is contained within a building. The other adjacent squares are not contained within a building.
Could you tell Willson the number of corners that he needs to look out for?
|1||30||All coordinates satisfy .|
|2||20||All coordinates satisfy .|
|3||30||All coordinates satisfy .|
|4||20||All coordinates satisfy .|
Note: Python users are recommended to submit with PyPy. Also, Python users are recommended to optimize their memory usage.
The first line of input will contain a single integer, .
lines of input follow. The line will contain four integers . The lower left corner of the building is at , and the upper right corner is at . Also, it is guaranteed that and .
Output the number of corners that are formed by the buildings.
6 1 1 2 2 1 2 2 3 2 2 3 3 6 1 7 4 5 2 8 3 6 2 7 3
Explanation for Sample Output
In the following diagram, the buildings are shown in red and the corners are shown in the black circles.