Cross Coloring

2000ms

262144K

Description:

There is a sheet of paper that can be represented with a grid of size $$$n \times m$$$: $$$n$$$ rows and $$$m$$$ columns of cells. All cells are colored in white initially.

$$$q$$$ operations have been applied to the sheet. The $$$i$$$-th of them can be described as follows:

$$$x_i$$$ $$$y_i$$$ — choose one of $$$k$$$ non-white colors and color the entire row $$$x_i$$$ and the entire column $$$y_i$$$ in it. The new color is applied to each cell, regardless of whether the cell was colored before the operation.

The sheet after applying all $$$q$$$ operations is called a coloring. Two colorings are different if there exists at least one cell that is colored in different colors.

How many different colorings are there? Print the number modulo $$$998\,244\,353$$$.

Input:

The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of testcases.

The first line of the testcase contains four integers $$$n, m, k$$$ and $$$q$$$ ($$$1 \le n, m, k, q \le 2 \cdot 10^5$$$) — the size of the sheet, the number of non-white colors and the number of operations.

The $$$i$$$-th of the following $$$q$$$ lines contains a description of the $$$i$$$-th operation — two integers $$$x_i$$$ and $$$y_i$$$ ($$$1 \le x_i \le n$$$; $$$1 \le y_i \le m$$$) — the row and the column the operation is applied to.

The sum of $$$q$$$ over all testcases doesn't exceed $$$2 \cdot 10^5$$$.

Output:

For each testcase, print a single integer — the number of different colorings modulo $$$998\,244\,353$$$.

Sample Input:

Sample Output:

3
4

Informação

Provedor Codeforces

Código CF1644D