There are $N$ chairs in a row and and no one on the chairs.Each chair is blue or red.Then comes $N$ students one by one numbered 1,2,3,..,N.For each student, he will find an empty chair to sit on.He wonĄŻt sit on the chair if the chair is satisfied the following three conditions.
1.The chair has both left and right adjacent chairs.
2.The left and right adjacent chairs are not empty.
3.The left and right adjacent chairsĄŻ color are different.
If the current student canĄŻt find a chair to sit on, he will go away.
For each student, he may have many choices of chairs to sit on. Your task is to find the number of distinct situations that all students have sat on a chair. As the answer can be rather large, find remainder after dividing the number by $1000000007({10}^{9}+7)$.
Input
There are several test cases.
In each test case:
The first line contains a integer $N(1\leq N\leq 100)$.The second line contains $N$ integers.Each integer is either 0 or 1.Integer 0 means blue and 1 means red.
Output
For each test case, output the remainder of division of the resulting number by $1000000007({10}^{9}+7)$.
