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E. Vladik and Entertaining Flags

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputIn 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.

Input

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.

Output

For each segment print the result on the corresponding line.

Example

Input

4 5 4

1 1 1 1 1

1 2 2 3 3

1 1 1 2 5

4 4 5 5 5

1 5

2 5

1 2

4 5

Output

6

7

3

4

Note

Partitioning on components for every segment from first test case:

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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