Knights in Chessboard

Given an m x n chessboard where you want to place chess knights. You have to find the number of maximum knights that can be placed in the chessboard such that no two knights attack each other.

Those who are not familiar with chess knights, note that a chess knight can attack 8 positions in the board as shown in the picture below.

Input

Input starts with an integer T (≤ 41000), denoting the number of test cases.

Each case contains two integers m, n (1 ≤ m, n ≤ 200). Here m and n corresponds to the number of rows and the number of columns of the board respectively.

Output

For each case, print the case number and maximum number of knights that can be placed in the board considering the above restrictions.

Sample Input

8 8

3 7

4 10

Sample Output

Case 1: 32

Case 2: 11

Case 3: 20

思路

可以发现当n或者m等于1时，可以全选，n或者m等于2时，可以每次选一个田字（如下图），其他情况可以全选棋盘上的白色或者黑色。

代码

 1 #include <bits/stdc++.h>
 2 using namespace std;
 3 
 4 int main()
 5 {
 6     int t;
 7     cin >> t;
 8     for (int i = 1; i <= t; i++)
 9     {
10         int n, m;
11         scanf("%d %d", &n, &m);
12         printf("Case %d: ", i);
13         int ans;
14         if (n > m)
15             swap(n, m);
16         if (n == 1)
17             ans = m;
18         else if (n == 2)
19             ans = m / 4 * 4 + min(2, m % 4) * 2;
20         else
21             ans = (n * m + 1) / 2;
22         printf("%d\n", ans);
23     }
24 }