Average Brightness Query

You are given a grayscale image represented as a 2D array of integers. Each integer in the array represents the brightness of a pixel. You need to process a series of queries to calculate the average brightness of a specified rectangular region of the image. For each query, the average brightness is computed using floor division:

\( \text{Average} = \left\lfloor \frac{\sum_{(i,j) \in R} image[i][j]}{\text{number of pixels in } R} \right\rfloor \)

The coordinates for the queries are provided in 1-indexed format.

inputFormat

The input is given from standard input (stdin) as follows:

1. The first line contains three space-separated integers \(n\), \(m\), and \(q\) where \(n\) is the number of rows, \(m\) is the number of columns of the image, and \(q\) is the number of queries.
2. The next \(n\) lines each contain \(m\) space-separated integers representing the brightness values of the image.
3. The following \(q\) lines each contain four space-separated integers \(x_1\), \(y_1\), \(x_2\), and \(y_2\) describing a query rectangle, where \((x_1, y_1)\) is the top-left corner and \((x_2, y_2)\) is the bottom-right corner (inclusive).

outputFormat

For each query, output a single line containing one integer: the average brightness (using floor division) of the specified rectangular region.

## sample

4 4 2
30 50 70 10
20 80 90 50
40 60 100 30
70 10 20 80
1 1 2 2
3 2 4 4

45
50

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