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: Accepted)

import Control.Monad
import Data.List
import qualified Data.ByteString.Char8 as B
import qualified Data.Vector as V
import qualified Data.Vector.Unboxed as UV
import qualified Data.Vector.Unboxed.Mutable as MV

main = do
    (h:w:d:_)<-map read.words<$>getLine::IO[Int]
    as<-fmap concat $ replicateM h $ map read.words<$>getLine::IO[Int]
    q<-readLn::IO Int
    lrs<-replicateM q $ unfoldr (B.readInt.B.dropWhile(==' '))<$>B.getLine::IO[[Int]]
    --
    lij <- MV.replicate (h*w) (0,0) :: IO (MV.IOVector (Int,Int))
    forM_ (zip [(i,j)|i<-[1..h],j<-[1..w]] as) $ \((i,j),a) ->
        MV.unsafeWrite lij (a-1) (i,j)
    --
    spp <- fmap V.fromList $ forM [0..d-1] $ \s -> do
        sp <- forM [s,(s+d)..(h*w)-d-1] $ \l -> do
            (si,sj) <- MV.unsafeRead lij l
            (ei,ej) <- MV.unsafeRead lij (l+d)
            return $ abs (si-ei) + abs(sj-ej)
        return $ UV.fromList $ scanl (+) 0 sp
    --
    putStr $ unlines $ map show $ map (solve spp d) lrs
--
solve spp d (l:r:_) = (p r1 r2) - (p l1 l2) 
    where
        l1 = (l+(d-1)) `mod` d
        l2 = (l-1) `div` d
        r1 = (r+(d-1)) `mod` d
        r2 = (r-1) `div` d
        p a b = (spp V.! a) UV.! b