A proper string is defined as a string whose every index has either 'S'(denotes safe index), else has the count of adjacent safe indexes to the current index. So for any index values possible are $,0,1,2 satisfying the above mentioned condition. Given a string with some missing entries (denoted by "X') your task is to count the number of ways the missing indexes in the string can be filled to get a "proper" string.

Input:

string s with characters S/0/1/2/X.

X denotes empty index and S denotes safe index.

(1<-string size <-100000)

Output:

Print the number of ways empty indexes can be filled to create a proper string modulo 10^9+7.

Sample:

X1X

2($10,015)

2X

0 (not possible)

8(000, 150, 051, 510, S51, 155, S25, SSS)

Can you solve it ?