There are \(88418\) paths in a \(7×7\) 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

Sample input

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

Sample output

201