There are k attackers in an n ∗ m chessboard. The i-th attacker is located in (Xi,Yi), with a attacking range of Ri. Asquare(X,Y)isattackedbythei-thattackerifandonlyif|X−Xi|+|Y −Yi|≤Ri. 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 443 111 311 331 1 10 1 111 0 Sample Output Case 1: 10 Case 2: 2