Problem:
Score : 400 points

Problem Statement

We have a grid with H rows and W columns. The square at the i-th row and the j-th column will be called Square (i,j).

The integers from 1 through H×W are written throughout the grid, and the integer written in Square (i,j) is A_{i,j}.

You, a magical girl, can teleport a piece placed on Square (i,j) to Square (x,y) by consuming |x-i|+|y-j| magic points.

You now have to take Q practical tests of your ability as a magical girl.

The i-th test will be conducted as follows:

Initially, a piece is placed on the square where the integer L_i is written.

Let x be the integer written in the square occupied by the piece. Repeatedly move the piece to the square where the integer x+D is written, as long as x is not R_i. The test ends when x=R_i.

Here, it is guaranteed that R_i-L_i is a multiple of D.

For each test, find the sum of magic points consumed during that test.

Constraints

1 \leq H,W \leq 300

1 \leq D \leq H×W

1 \leq A_{i,j} \leq H×W

A_{i,j} \neq A_{x,y} ((i,j) \neq (x,y))

1 \leq Q \leq 10^5

1 \leq L_i \leq R_i \leq H×W

(R_i-L_i) is a multiple of D.

Input

Input is given from Standard Input in the following format:

H W D
A_{1,1} A_{1,2} ... A_{1,W}
:
A_{H,1} A_{H,2} ... A_{H,W}
Q
L_1 R_1
:
L_Q R_Q

Output

For each test, print the sum of magic points consumed during that test.

Output should be in the order the tests are conducted.

Sample Input 1

3 3 2
1 4 3
2 5 7
8 9 6
1
4 8

Sample Output 1

5

4 is written in Square (1,2).

6 is written in Square (3,3).

8 is written in Square (3,1).

Thus, the sum of magic points consumed during the first test is (|3-1|+|3-2|)+(|3-3|+|1-3|)=5.

Sample Input 2

4 2 3
3 7
1 4
5 2
6 8
2
2 2
2 2

Sample Output 2

0
0

Note that there may be a test where the piece is not moved at all, and there may be multiple identical tests.

Sample Input 3

5 5 4
13 25 7 15 17
16 22 20 2 9
14 11 12 1 19
10 6 23 8 18
3 21 5 24 4
3
13 13
2 10
13 13

Sample Output 3

0
5
0

Solution in Haskell (GHC 7.10.3) (judge verdict: Time Limit Exceeded)


import Control.Monad
import Data.Array.IO

main = do
  (h:w:d:_) <- getLine >>= return . map read . words :: IO [Int]
  a <- replicateM h getLine >>= return . map (map read . words) :: IO [[Int]]
  q <- readLn :: IO Int
  qs <- getContents >>= return . map ((\(l:r:_) -> (l,r)) . map read . words) . lines :: IO [(Int, Int)]

  arr <- newArray (1,h*w) (-1,-1) :: IO (IOArray Int (Int,Int))
  dists <- newArray (1,h*w) (-1) :: IO (IOArray Int Int)

  forM_ [1..h] $ \y -> do
    forM_ [1..w] $ \x -> do
      writeArray arr ((a!!(y-1))!!(x-1)) (x,y)

  forM_ [1..h*w] $ \i -> do
    p1 <- readArray arr i
    p2 <- readArray arr (if i+d<=h*w then (i+d) else i)
    writeArray dists i (dist p1 p2)


  forM_ qs $ \(l,r) -> do
    list <- forM (init $ takeWhile (<=r) (iterate (+d) l)) $ \i -> readArray dists i
    print $ sum list

  where
    dist (x1,y1) (x2,y2) = abs (x2-x1) + abs (y2-y1)