There are ~88418~ paths in a ~7 \times 7~ grid from the upper-left square to the lower-left square. Each path corresponds to a ~48~-character description consisting of characters D (down), U (up), L (left) and R (right).

For example, the path corresponds to the description DRURRRRRDDDLUULDDDLDRRURDDLLLLLURULURRUULDLLDDDD.

You are given a description of a path which may also contain characters ? (any direction). Your task is to calculate the number of paths that match the description.

Input

• The only input line has a ~48~-character string of characters ?, D, U, L and R.

Output

• Print one integer: the total number of paths.

Example Input

??????R??????U??????????????????????????LD????D?

Example Output

201