Problem Statement

We have an $H\times W$ grid. Initially, the squares are unpainted.
You will paint these squares. There are $C colors available, numbered 1, 2, \ldots, C$.
The painting process will be given as Q queries. The i-th query contains integers t_i, n_i, c_i, which represents the following action.

• If t_i = 1: paint all squares in the n_i-th row with Color c_i.
• If t_i = 2: paint all squares in the n_i-th column with Color c_i.

Painting a square with Color c makes the color of that square Color c, regardless of its previous state.
Find the number of squares painted in each of Color $1, 2, \ldots, C$ after the whole process.

Input

Input is given from Standard Input in the following format:
H W C Q
t_1 n_1 c_1
$\vdots$
t_Q n_Q c_Q

Output

Print a line containing the numbers of squares painted in Color $1, 2, \ldots, C$, with spaces in between.

Constraints

• $2\leq H\leq 10^9$
• $2\leq W\leq 10^9$
• $1\leq C\leq 3\times 10^5$
• $1\leq Q\leq 3\times 10^5$
• $t_i\in$ {1,2}
• $1\leq n_i\leq H$ if t_i = 1
• $1\leq n_i\leq W$ if t_i = 2
• $1\leq c_i\leq C$

Sample Input 1

4 5 6 5
1 1 6
1 3 3
2 2 4
2 4 2
1 1 2

Sample Output 1

0 8 3 3 0 0

The process changes the colors of the squares as follows. Here, . denotes an unpainted square.
..... 66666 66666 64666 64626 22222
..... ..... ..... .4... .4.2. .4.2.
..... ..... 33333 34333 34323 34323
..... ..... ..... .4... .4.2. .4.2.

Sample Input 2

1000000000 1000000000 3 5
1 1 2
1 2 2
1 3 2
1 4 2
1 5 2

Sample Output 2

0 5000000000 0

见题面 Input 部分

见题面 Output 部分