Bombing

JAG land is a country, which is represented as an $M \times M$ grid. Its top-left cell is $(1,1)$ and its bottom-right cell is $(M,M)$.

Suddenly, a bomber invaded JAG land and dropped bombs to the country. Its bombing pattern is always fixed and represented by an $N \times N$ grid. Each symbol in the bombing pattern is either 'X' (bomb) or '.' (empty).

Here, suppose that a bomber is in $(b\_r,b\_c)$ in the land and drops a bomb. The cell $(b\_r+i-1,b\_c+j-1)$ will be damaged if the symbol in the $i$-th row and the $j$-th column of the bombing pattern is 'X' ($1 \le i,j \le N$).

Initially, the bomber reached $(1,1)$ in JAG land. The bomber repeated to move to either of 4-directions and then dropped a bomb just $L$ times. During this attack, the values of the coordinates of the bomber were between 1 and $M−N+1$, inclusive, while it dropped bombs. Finally, the bomber left the country.

The moving pattern of the bomber is described as $L$ characters. The $i$-th character corresponds to the $i$-th move and the meaning of each character is as follows.

'U' --- up, 'D' --- down, 'L' --- left and 'R' --- right. 

Your task is to write a program to analyze the damage situation in JAG land. To investigate damage overview in the land, calculate the number of cells which were damaged by the bomber at least $K$ times.

The first line of the input contains four integers $N$, $M$, $K$ and $L$ ($1 \le N \le M \le 500$, $1 \le K \le L \le 2 \cdot 10^5$). The following $N$ lines represent the bombing pattern. $B\_i$ is a string of length $N$. Each character of $B\_i$ is either 'X or '.'. The last line denotes the moving pattern. $S$ is a string of length $L$, which consists of either 'U', 'D', 'L' or 'R'. It's guaranteed that the values of the coordinates of the bomber are between 1 and $M−N+1$, inclusive, while it drops bombs in the country.

Print the number of cells which were damaged by the bomber at least $K$ times.