Gym101915E、Minesweeper （DFS）

                                                      Minesweeper

Have you ever played Minesweeper? It’s a cute little game that originates from the 1960s, and has been written for many computing platforms in use today.

The game consists of a two dimensional grid, and there are two types of cells in it.

A mined cell, and an empty cell, which contains a single digit that indicates how many adjacent cells contain mines. Eech cell has at most 8 adjacent cells.

In this version of the game, you are going to build a level with the following rules:

• Every mined cell has to be a neighbor of at least one empty cell.

   

• Every empty cell can have at most M adjacent mines.

For instance, the following is 4 * 5 valid grid with 12 mines (which are represented by an '*' character) and the maximum number for the empty cells is M = 3 :

3 * * 3 1

* * * * 2

* * * * 2

3 * * 3 1

We are interested in the maximum number of mines that a grid with those properties can contain, can you find the answer for us?

 

Input

The first line contains a single integer T denoting the number of test cases.

Each test case consists of one line which contains three space separated integers:

The number of the rows in the grid r. (2 ≤ r ≤ 6).

The number of the columns in the grid c. (2 ≤ c ≤ 6).

The maximum number that any empty cell can contain. (1 ≤ M ≤ 8).

Output

For each test print one line containing one integer, the maximum number of mines that a grid can contain.

Example

Input

2
4 5 3
3 3 4

Output

12
6

Note

The grid in the statement is a valid grid for the first sample.

 

一、原题地址

点我传送

 

二、大致题意

扫雷游戏，给定的是n*m大小的棋盘，还有其中能存在的最大数字K。规定在一个3*3的格子里元素不能全部是雷。

询问在符合规定的情况下，雷最多能放多少个。

 

三、思路

每个格子可以是雷也可以是数字，所以可以枚举（一开始我是打算枚举全部的数字，9个出口果然超时）每个格子是雷还是数字。对于雷我们先放置1，我们的check应该是检查他的周围有没有存在数字，而对于数字我们先放置0，然后需要check他的周围雷的数量会不会超过K个，这样的检查可以保证一个棋盘是一定符合状态的，但是这并不一定是我们所求的。但是随着DFS的深入，更新的是一定会慢慢增大，直到找到我们需要的答案。

对于一个格子(x,y)该放置什么，我们检索他的右上角(x-1,y-1)能否符合情况雷或者数字的情况。但对于最后一行和最右边的一列，我们还需要分别检索(x,y-1)和(x-1,y)，只要画一张图就很好理解了。

看到时间限制是15秒，本来以为还需要先打表将答案记录下来。但是交了两发最后还是发现直接读取n,m，K会快两倍。说明T的数据范围并不是很大。

 

四、代码

#include 
#include
#include
#include
#include
#include
#include
#include