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.Arrow
import Control.Monad
import Data.List
import qualified Data.ByteString.Char8 as B
import qualified Data.Vector as V
import Data.Ord

main :: IO ()
main = readLine >>= main'
    where
        main' [h, w, d] = readContents h >>= main'' . build h w d 
        main'' vs = readLn >>= readContents >>= printRes . solve vs
        printRes = mapM_ print 

build :: Int -> Int -> Int -> [[Int]] -> V.Vector Int
build h w d as = V.fromList . (0 :) . map snd . sortBy (comparing fst) . concat $ buildLoop bs
    where
        bs = sortBy cmpf . concatMap mf $ zip [1..] as
        mf (i, xs) = map (\(j, a) -> (a, (i, j))) $ zip [1..] xs
        cmpf (la, _) (ra, _) = (comparing (`mod` d)) la ra `mappend` compare la ra

        buildLoop (x@(a, _) : xs) = ss : buildLoop ts
            where
                (ss, ts) = innerLoop (a `mod` d) $ x : xs
        buildLoop _ = []

        innerLoop m (x : xs) = ((fst x, 0) : res1, rs)
            where
                (res1, rs) = loop 0 x xs
                loop pv (_, (lp, rp)) (y@(ya, (ly, ry)) : ys)
                    | ya `mod` d == m = ((ya, nv) : us, vs)
                    | otherwise = ([], y : ys)
                    where
                        nv = pv + abs (lp - ly) + abs (rp - ry) 
                        (us, vs) = loop nv y ys
                loop _ _ _ = ([], [])
        innerLoop _ _ = ([], [])


solve :: V.Vector Int -> [[Int]] -> [Int]
solve vs = map (\[l, r] -> vs V.! r - vs V.! l)

readLine :: IO [Int]
readLine = unfoldr (\s -> second (maybe B.empty snd . B.uncons) <$> B.readInt s) <$> B.getLine

readContents :: Int -> IO [[Int]]
readContents = flip replicateM readLine