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Description

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 Format

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

Output Format

Print one integer: the total number of paths.

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

201

Hint

Source

CSES