Practical Skill Test

AtCoder

IDabc089_d

Time2000ms

Memory256MB

Difficulty—

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: $H$ $W$ $D$ $A_{1,1}$ $A_{1,2}$ $...$ $A_{1,W}$ $:$ $A_{H,1}$ $A_{H,2}$ $...$ $A_{H,W}$ $Q$ $L_1$ $R_1$ $:$ $L_Q$ $R_Q$ [samples]

Samples

Input #1

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 $(|3-1|+|3-2|)+(|3-3|+|1-3|)=5$.

Input #2

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.

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

Output #3

0
5
0

API Response (JSON)

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    "name": "Practical Skill Test",
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      "time_limit": 2000,
      "memory_limit": 262144
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    "difficulty": "None",
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      "statement_type": "Markdown",
      "content": "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 $(i,j)$.\nThe integers from $1$ through $H×W$ are written throughout the grid, a...",
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