Painting Patterns

Lukas has a very large grid. Initially every cell is white. He has three patterns, numbered 1 to 3 (from left to right):

XXXX    X.X.    X.X.
....    X.X.    .X.X
XXXX    X.X.    X.X.
....    X.X.    .X.X

Each pattern is periodic and can be extended to fill a rectangle of any size. Lukas paints the grid $N$ times. Each time he chooses an axis-aligned rectangle and one pattern, then paints the cells inside the rectangle black according to that pattern (an X in the pattern paints the cell black, a . leaves it unchanged). The pattern is anchored so that its top-left corner coincides with the top-left corner of the rectangle: the grid point with the smallest $x$ coordinate and the largest $y$ coordinate.

When painted areas overlap, the OR rule applies: a cell is black if it was painted black by at least one operation. For example, applying pattern 1 and then pattern 3 to the same $4 \times 4$ rectangle yields:

XXXX
.X.X
XXXX
.X.X

After all $N$ operations, compute the number of black cells.

The first line contains an integer $N$ ($0 \le N \le 100000$). Each of the next $N$ lines contains five integers $x_1$, $y_1$, $x_2$, $y_2$, $p$, where $(x_1, y_1)$ and $(x_2, y_2)$ are two opposite corners of the rectangle (given as grid points), and $p$ ($1 \le p \le 3$) is the pattern number. All coordinates have absolute value at most $10^9$, and every rectangle is at least one unit wide and one unit tall.

Print a single integer: the number of black cells after all operations.