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.

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 $t_i = 2$
• $1\\leq c_i\\leq C$

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.

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