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 LuaJIT (2.0.4) (judge verdict: Time Limit Exceeded)

local mfl, mab = math.floor, math.abs
local h, w, d = io.read("*n", "*n", "*n")
local n = h * w
local map = {}
local cost = {}
for i = 1, n do
  map[i] = io.read("*n")
  cost[i] = 0
end
for t_i_d = 1, d do
  local src_x, src_y = 0, 0
  local costsum = 0
  local i_d = t_i_d
  while i_d <= n do
    for i = 1, n do
      if map[i] == i_d then
        local dst_x, dst_y = 1 + (i - 1) % w, 1 + mfl((i - 1) / w)
        costsum = costsum + mab(dst_x - src_x) + mab(dst_y - src_y)
        cost[i_d] = costsum
        src_x, src_y = dst_x, dst_y
        break
      end
    end
    i_d = i_d + d
  end
end
local q = io.read("*n")
for i = 1, q do
  local l, r = io.read("*n", "*n")
  print(cost[r] - cost[l])
end