Problem A
Attacker
Input: Standard Input

Output: Standard Output

There are k attackers in an n * m chessboard.

The i-th attacker is located in (X_i, Y_i), with a attacking range of R_i.

A square (X, Y) is attacked by the i-th attacker if and only if |X - X_i| + |Y - Y_i| <= R_i.

Count the number of squares on the chessboard attacked by at least one attacker.

Input




There are several input cases. The first line contains three integers n, m, k (1 ≤ n,m ≤ 100000000, 1 ≤ k ≤ 20000). In the following k lines, each line contains three integers Xi, Yi, Ri (1 ≤ Xi ≤ n, 1≤ Yi ≤ m, 1 ≤ Ri ≤1000000), the position and attack range of each attacker.
 

The last case is followed by a single zero, which should not be processed.

 
Output

For each case, print the case number and the answer.
 

Sample Input	Sample Output
4 4 3 1 1 1 3 1 1 3 3 1 1 10 1 1 1 1 0	Case 1: 10 Case 2: 2

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Problemsetter: Chen Qifeng
Supplied by: Rujia Liu