The Cake is a Dessert

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Points: 10
Time limit: 4.5s
Memory limit: 1G

Problem type

At the end of a tasty meal, Capba just wants some tasty dessert. Today, his cafeteria is serving a rectangular cake, with a coordinate system carved on its delicious graham cracker crust base. The cake can be thought of as a 2D grid of squares, with square (1,1) at the bottom-left, and (N,M) at the top-right (1 \le N, M \le 5\,000).

The cake also has K (0 \le K \le 200\,000) different icings on it, numbered from 1 to K, which have been applied in a strange fashion. Icing i covers all squares in the rectangle from (x_i,y_i) to (X_i,Y_i) (1 \le x_i, X_i \le N, 1 \le y_i, Y_i \le M), inclusive, with 1 cubic centimeter (1\ \text{cm}^3) of icing each. If icings overlap, there will be squares with multiple layers of icing on them; for example, some of the squares in the sample input below are covered by 2\ \text{cm}^3 of icing.

Capba likes icing… but then, he also doesn't like too much icing. He considers Q (1 \le Q \le 200\,000) choices, numbered from 1 to Q, regarding which part of the cake to eat. Choice i involves cutting out and rapidly consuming the rectangle from (A_i,B_i) to (C_i,D_i) (1 \le A_i \le C_i \le N, 1 \le B_i \le D_i \le M), inclusive.

To decide on the best choice, he first wants to know how much icing is present in each potential piece of cake.

Input Specification

Line 1: N, M, K.
Next K lines: x_i, y_i, X_i, Y_i.
Next line: Q.
Next Q lines: A_i, B_i, C_i, D_i.

Output Specification

Q lines. Line i should contain the amount of icing present on the piece of cake described by choice i, in \text{cm}^3.

Note: The answers may overflow 32-bit integers.

Sample Input

6 5 3
1 3 4 5
1 1 6 1
2 2 3 3
2 1 2 2
5 2 6 5
2 4 2 4
3 1 4 2
2 1 4 4

Sample Output


Explanation for Sample Output

The cake has the following amounts of icing on it (in \text{cm}^3):


To answer the queries, just look at the diagram above and add up the numbers in each rectangle.


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