Contest: Task: Related: TaskB TaskD

Score : $700$ points

Nuske has a grid with $N$ rows and $M$ columns of squares. The rows are numbered $1$ through $N$ from top to bottom, and the columns are numbered $1$ through $M$ from left to right. Each square in the grid is painted in either blue or white. If $S_{i,j}$ is $1$, the square at the $i$-th row and $j$-th column is blue; if $S_{i,j}$ is $0$, the square is white. For every pair of two blue square $a$ and $b$, there is at most one path that starts from $a$, repeatedly proceeds to an adjacent (side by side) blue square and finally reaches $b$, without traversing the same square more than once.

Phantom Thnook, Nuske's eternal rival, gives $Q$ queries to Nuske. The $i$-th query consists of four integers $x_{i,1}$, $y_{i,1}$, $x_{i,2}$ and $y_{i,2}$ and asks him the following: when the rectangular region of the grid bounded by (and including) the $x_{i,1}$-th row, $x_{i,2}$-th row, $y_{i,1}$-th column and $y_{i,2}$-th column is cut out, how many connected components consisting of blue squares there are in the region?

Process all the queries.

- $1 ≤ N,M ≤ 2000$
- $1 ≤ Q ≤ 200000$
- $S_{i,j}$ is either $0$ or $1$.
- $S_{i,j}$ satisfies the condition explained in the statement.
- $1 ≤ x_{i,1} ≤ x_{i,2} ≤ N(1 ≤ i ≤ Q)$
- $1 ≤ y_{i,1} ≤ y_{i,2} ≤ M(1 ≤ i ≤ Q)$

The input is given from Standard Input in the following format:

$N$ $M$ $Q$ $S_{1,1}$..$S_{1,M}$ : $S_{N,1}$..$S_{N,M}$ $x_{1,1}$ $y_{i,1}$ $x_{i,2}$ $y_{i,2}$ : $x_{Q,1}$ $y_{Q,1}$ $x_{Q,2}$ $y_{Q,2}$

For each query, print the number of the connected components consisting of blue squares in the region.

3 4 4 1101 0110 1101 1 1 3 4 1 1 3 1 2 2 3 4 1 2 2 4

3 2 2 2

In the first query, the whole grid is specified. There are three components consisting of blue squares, and thus $3$ should be printed.

In the second query, the region within the red frame is specified. There are two components consisting of blue squares, and thus $2$ should be printed. Note that squares that belong to the same component in the original grid may belong to different components.

5 5 6 11010 01110 10101 11101 01010 1 1 5 5 1 2 4 5 2 3 3 4 3 3 3 3 3 1 3 5 1 1 3 4

3 2 1 1 3 2