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 Kotlin (1.0.0) (judge verdict: Accepted)

operator fun Pair<Int, Int>.plus(pair: Pair<Int, Int>) = Pair(first + pair.first, second + pair.second)
operator fun Pair<Int, Int>.minus(pair: Pair<Int, Int>) = Pair(first - pair.first, second - pair.second)
fun Pair<Int, Int>.manhattanTo(pair: Pair<Int, Int>) = (this - pair).manhattanLength()
fun Pair<Int, Int>.manhattanLength() = Math.abs(first) + Math.abs(second)

private fun List<IntRange>.zipWithIndices() =
        mapIndexed { first, range ->
            range.map { second -> Pair(first, second) }
        }.flatten()

fun main(args: Array<String>) {
    val (H, W, D) = readLine()!!.split(" ").map { it.toInt() }
    val A = (0 until H).map { readLine()!!.split(" ").map { it.toInt() } }
    val numberCache = {
        val result = mutableMapOf<Int, Pair<Int, Int>>()
        (0 until H).map{ (0 until W) }.zipWithIndices().forEach { pair ->
            val (h, w) = pair
            result[A[h][w]] = Pair(h, w)
        }
        result
    }()

    val mpCache: Map<Int, Int> = {
        val result = mutableMapOf<Int, Int>()
        (1 until D + 1).forEach { width ->
            var index = width
            while (index <= H * W) {
                val prevIndex = index - D
                val totalMp = result[prevIndex]?.let { previous ->
                    val diff = numberCache[prevIndex]!!.manhattanTo(numberCache[index]!!)
                    previous + diff
                } ?: 0

                result[index] = totalMp
                index += width
            }
        }
        result
    }()

    val Q = readLine()!!.toInt()
    (0 until Q).forEach {
        val (L, R) = readLine()!!.split(" ").map { it.toInt() }
        println(mpCache[R]!! - mpCache[L]!!)
    }
}