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)

require 'pp'
# IS_DEBUG = true
IS_DEBUG = false
def dputs str
	if(IS_DEBUG)
		puts str
	end
end
def dpp str
	if(IS_DEBUG)
		pp str
	end
end

require 'pp'

H,W,D=gets.chomp.split(' ').map{|n| n.to_i}
# number -> address map
# %D = r, upto
B={}
# ACC[r][q]
ACC=Array.new(H*W+1)

#Array.new(H*W+1)

0.upto(H-1){|i|
	gets.chomp.split(' ').map{|n| n.to_i}.each_with_index{|n,j|
		# puts "n,i,j:#{n},#{i},#{j}"
		B[n]=[i,j]
	}
}
# pp B

# precomputation
X=0
Y=1
1.upto(D){|i|
	prv = B[i]
	ACC[i]=0
	1.upto(H*W/D){|j|
		puts "i,j = #{i},#{j}"
		cur = B[D*j+i]
		if(cur.nil?)
			break
		else
			diff = (prv[X]-cur[X]).abs+(prv[Y]-cur[Y]).abs
			ACC[i+D*j]=diff
			prv = cur
		end
	}
}
# accum
1.upto(D){|i|
	1.upto(H*W/D){|j|
		if(ACC[i+D*j].nil?)
			break
		else
			ACC[i+D*j]+=ACC[i+D*(j-1)]
		end
	}
}
pp ACC


Q,d=gets.chomp.split(' ').map{|n| n.to_i}
#I=Array.new(Q)
L=0
R=1
cache = {}
0.upto(Q-1){|i|	
	sum=0
	LR = gets.chomp.split(' ').map{|n| n.to_i}
	# puts "#{LR[L]},#{LR[R]}, #{D})"
	c = cache[[LR[L],LR[R]].join("-")]
	if(!c.nil?)
		puts c
	else
		puts ACC[LR[R]]-ACC[LR[L]]
	end
}