Stroll

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:

• 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)

If at a certain point, they are in a cell outside the city they get bored. A cell (i,j) is inside the city if and only if 1 ≤ i ≤ N and 1 ≤ j ≤ M. All the cells that aren't inside are considered outside the city. Now, Xorin and Xorina are wondering: 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 ≤ 1000
0 ≤ K ≤ N*M

Sample

Input	Output
2 2 2 LR	2

Note

They can't begin in the first column because they'll get outside the city after the first move.