CF811E.Vladik and Entertaining Flags

In his spare time Vladik estimates beauty of the flags.

Every flag could be represented as the matrix $n×m$ which consists of positive integers.

Let's define the beauty of the flag as number of components in its matrix. We call component a set of cells with same numbers and between any pair of cells from that set there exists a path through adjacent cells from same component. Here is the example of the partitioning some flag matrix into components:

But this time he decided to change something in the process. Now he wants to estimate not the entire flag, but some segment. Segment of flag can be described as a submatrix of the flag matrix with opposite corners at $(1,l)$ and $(n,r)$ , where conditions $1<=l<=r<=m$ are satisfied.

Help Vladik to calculate the beauty for some segments of the given flag.

First line contains three space-separated integers $n$ , $m$ , $q$ ( $1<=n<=10$ , $1<=m,q<=10^{5}$ ) — dimensions of flag matrix and number of segments respectively.

Each of next $n$ lines contains $m$ space-separated integers — description of flag matrix. All elements of flag matrix is positive integers not exceeding $10^{6}$ .

Each of next $q$ lines contains two space-separated integers $l$ , $r$ ( $1<=l<=r<=m$ ) — borders of segment which beauty Vladik wants to know.

For each segment print the result on the corresponding line.

Partitioning on components for every segment from first test case: