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 Ruby (2.3.3) (judge verdict: Wrong Answer)

INF = 9999999999999999999999999999

h, w, d = gets.chomp.split.map(&:to_i)
matrix = Array.new(h) { gets.chomp.split.map(&:to_i) }
 
pos = Array.new(h * w + 1).tap do |y|
  matrix.each.with_index do |row, i|
    row.each.with_index do |num, j|
      y[num] = [i, j]
    end
  end
end

tests = Array.new(gets.chomp.to_i) { gets.chomp.split.map(&:to_i) }

answer = {}
prev_l, prev_r, prev_cost = INF, INF, INF
tests.sort_by { |x| [-x[0], x[1]] }.each do |l, r|
  next if answer.key?([l, r])
  
  if (prev_l - l).abs + (prev_r - r).abs < (l - r).abs \
    and (prev_l - l).abs % d == 0 and (prev_r - r).abs % d == 0
    cost = prev_cost
    
    min_l = [prev_l, l].min
    max_l = [prev_l, l].max
    until min_l == max_l
      x1, y1 = pos[min_l]
      x2, y2 = pos[min_l+d]
      
      if min_l == prev_l
        cost += (x1 - x2).abs + (y1 - y2).abs
      else
        cost -= (x1 - x2).abs + (y1 - y2).abs
      end
      min_l += d
    end
    
    min_r = [prev_r, r].min
    max_r = [prev_r, r].max
    until min_r == max_r
      x1, y1 = pos[min_r]
      x2, y2 = pos[min_r+d]
      
      if min_r == prev_r
        cost += (x1 - x2).abs + (y1 - y2).abs
      else
        cost -= (x1 - x2).abs + (y1 - y2).abs
      end
      min_r += d
    end
  else
    cost = 0
    tmp_l = l
    until tmp_l == r
      x1, y1 = pos[tmp_l]
      x2, y2 = pos[tmp_l+d]
      
      cost += (x1 - x2).abs + (y1 - y2).abs
      tmp_l += d
    end
  end
  answer[[l, r]] = cost
  
  prev_l, prev_r, prev_cost = l, r, cost
end

tests.each do |l, r|
  puts answer[[l, r]]
end