Since it's Valentines, XORin and XORina will take a stroll in a romantic city. The city can be represented as a N x M board. This time they will respect a pattern. The pattern is a string, each character having the following meaning:

The second line contains K(the length of the pattern).

The next line contains the pattern.

0 ≤ K ≤ N*M

- U - they move from the current cell (i,j) to the cell in front of them (i-1,j)
- D - they move from the current cell (i,j) to the cell behind them (i+1,j)
- L - they move from the current cell (i,j) to the cell in their left (i,j-1)
- R - they move from the current cell (i,j) to the cell in their right (i,j+1)

*Given the pattern, in how many different cells can they start their stroll such that they don't get bored?***Can you find the answer for them?**## Input

The first line of the input contains N and M.The second line contains K(the length of the pattern).

The next line contains the pattern.

## Output

Print the number of valid starting cells.## Constraints

1 ≤ N, M ≤ 10000 ≤ K ≤ N*M

## Sample

Input | Output |
---|---|

2 2 2 LR | 2 |