# #550. 「LibreOJ Round #8」Matching

#### 题目描述

Given a grid with rows and columns, in this grid, you can choose two different grid points and match them into a pair. Notice that a point can only be matched with no more than one point. It means unmatched points are allowed. We define a weight function for a pair of points as the following form:

The weight of a possible matching scheme is defined as the sum of weights that the matching pairs given. Your task is to calculate the maximum possible weight of all matching schemes.

#### 输入格式

The first line contains a single integer which means the number of the test cases.

Each of the following lines contains three integers which means the height and the width of the grid, and the constant in the weight function.

#### 输出格式

Write to the standard output.

For each test case, output a line containing a single integer — the maximum of the weight of possible matching plans.

#### 样例输入 1

4
1 1 0
1 2 0
2 2 1
2 3 1


#### 样例输出 1

0
1
4
7


#### 样例输入 2

6
23 66 12
233 666 123
2333 6666 1234
23333 6666 1234
2333 66666 1234
23333 66666 12345


#### 样例输出 2

33759
34876089
34987610889
1166494448889
2682884270889
34998761108889


#### Sample Input 1

4
1 1 0
1 2 0
2 2 1
2 3 1


#### Sample Output 1

0
1
4
7


#### Sample Explanation 1

As for grid, there is no point for the only one to match, so the answer is .

As for grid, we match the only two points into a pair, so the answer is .

As for grid, we match the top left point and the bottom right one into a pair, the top right point and the bottom left one into a pair. The answer is , as shown by the following picture.

As for grid, we match the top left point and the bottom middle one, the top middle point and the bottom right one, the top right point and the bottom left one. The answer is , as shown by the following picture.

#### Sample Input 2

6
23 66 12
233 666 123
2333 6666 1234
23333 6666 1234
2333 66666 1234
23333 66666 12345


#### Sample Output 2

33759
34876089
34987610889
1166494448889
2682884270889
34998761108889


#### 数据范围与提示

For all test cases, .

Detailed constraints and hints are as follows (blank grids denote the same constraints as mentioned above):