Problem Statement

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.

Constraints

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

Input

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}

Output

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