Flower Bouquet Selection

You are given a rectangular garden represented as an n x m grid where each cell contains a flower denoted by an uppercase letter or a dot . indicating an empty spot. Your task is to determine if you can pick a bouquet by selecting a contiguous subgrid (a rectangle) having an area equal to p (height \(\times\) width = p) so that all cells in that subgrid contain the same type of flower (and none is a dot).

For example, consider a subgrid of size 2 x 2 (i.e., 4 cells) and p = 4. If all cells have the letter A, then you can form a bouquet. Otherwise, the bouquet cannot be picked.

Output YES if such a subgrid exists; otherwise, output NO.

inputFormat

The first line contains an integer t representing the number of test cases. Each test case begins with a line containing three integers n, m, and p, where n and m denote the number of rows and columns of the garden, respectively, and p is the required bouquet area such that \(\text{height} \times \text{width} = p\) (in \(\LaTeX\) this is represented as \(\text{height} \times \text{width} = p\) ). Following this, there are n lines, each containing a string of length m that describes a row of the garden grid. A cell contains an uppercase letter (flower type) or a dot (.) indicating an empty spot.

outputFormat

For each test case, print a single line containing YES if it is possible to pick a bouquet by selecting a contiguous subgrid with area p in which all cells contain the same flower (and are not dots), otherwise print NO.

## sample

2
3 4 4
A..B
.A.B
AAAA
4 4 5
B.BB
BCDD
BCCD
BBBB

YES
NO

</p>