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: Runtime Error)

H, W, D = gets.split(' ').map(&:to_i)

ary = Array.new( H, nil )
[*0..(H-1)].each{|i|
  ary[i] = gets.split(' ').map(&:to_i)
}

Q = gets.to_i
ls = Array.new( Q, nil )
rs = Array.new( Q, nil )

[*0..(Q-1)].each{|i|
  ls[i], rs[i] = gets.split(' ').map(&:to_i)
}

# 「1 から HxW までの整数が重複なく書かれており」より、
# 番号で座標を逆引きできるようにする
grid_x = Array.new(H*W + 1)  # 1 は遊び
grid_y = Array.new(H*W + 1)  # 1 は遊び

[*0..(H-1)].each{|i|
  [*0..(W-1)].each{|j|
    x = ary[i][j]
    grid_x[x] = i
    grid_y[x] = j
  }
}

# 差分 D で固定なので, 次の値までの距離を予め計算しておく
dist = Array.new(H*W + 1, nil)
[*1..(H*W-D)].each{|i|
  dist[i] = (grid_x[i+D] - grid_x[i]).abs + (grid_y[i+D] - grid_y[i]).abs
}
#p dist

# 100 個ずつまとめて計算したもの
dist100 = Array.new(H*W + 1, nil)
[*0..(H*W-1)].each{|i|
  break if i + D*100 >= H*W
  sum = 0
  [*0..(100-1)].each{|it|
    sum += dist[i + D*it]
  }
  dist100[i] = sum
}


# main loop
[*0..(Q-1)].each{|istep|
  l = ls[istep]
  r = rs[istep]

  if l >= r then
    puts 0
    next
  end

  n = 1 + ((r-l) / D)

  sum = 0
  it = 0
#  [*0..(n-2)].each{|it|
  while it <= (n-2) do
    if it + 100 < (n-2) then
      sum += dist100[l + D*it]
      it += 100
    else
      sum += dist[l + D*it]
      it += 1
    end
  end

  puts sum
}