Grid Path Description

There are $8841888418$ paths in a $7\times 77\; \backslash times\; 7$ grid from the upper-left square to the lower-left square. Each path corresponds to a $4848$-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 $4848$-character string of characters ?, D, U, L and R.

Output

Print one integer: the total number of paths.