You received an $$$n\times m$$$ grid from a mysterious source. The source also gave you a magic positive integer constant $$$k$$$.

The source told you to color the grid with some colors, satisfying the following condition:

- If $$$(x_1,y_1)$$$, $$$(x_2,y_2)$$$ are two distinct cells with the same color, then $$$\max(|x_1-x_2|,|y_1-y_2|)\ge k$$$.

You don't like using too many colors. Please find the minimum number of colors needed to color the grid.

Input format:
Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1\le t\le1000$$$). The description of the test cases follows.

The only line of each test case consists of three positive integers $$$n$$$, $$$m$$$, $$$k$$$ ($$$1\le n,m,k\le10^4$$$) — the dimensions of the grid and the magic constant.
Output format:
For each test case, print a single integer — the minimum number of colors needed to color the grid.
Example Input 0:
6
3 3 2
5 1 10000
7 3 4
3 2 7
8 9 6
2 5 4

Example Output 0:
4
5
12
6
36
8

Notes:
In the first test case, one of the optimal constructions is:

In the second test case, the color of all cells must be pairwise different, so the answer is $$$5$$$.

Example input:
6
3 3 2
5 1 10000
7 3 4
3 2 7
8 9 6
2 5 4


Example output:
4
5
12
6
36
8