Question
Counting Zero-Product Subsequences
You are given an array of KaTeX can only parse string typed expression integers. Your task is to count the number of non-empty subsequences whose product is equal to KaTeX can only parse string typed expression.
A subsequence is formed by deleting zero or more elements from the array without changing the order of the remaining elements.
Since the answer can be very large, print it modulo KaTeX can only parse string typed expression.
Input
The first line contains a single integer KaTeX can only parse string typed expression — the size of the array.
The second line contains KaTeX can only parse string typed expression integers, representing the elements of the array — KaTeX can only parse string typed expression.
The second line contains KaTeX can only parse string typed expression integers, representing the elements of the array — KaTeX can only parse string typed expression.
Output
Print a single integer — the number of non-empty subsequences whose product is equal to KaTeX can only parse string typed expression, taken modulo KaTeX can only parse string typed expression.
Example
Input
4
1 0 2 0
Output
12
Explanation
Subsequences with product KaTeX can only parse string typed expression:
KaTeX can only parse string typed expression (using the first zero)
KaTeX can only parse string typed expression (using the second zero)
KaTeX can only parse string typed expression
KaTeX can only parse string typed expression (with the second zero)
KaTeX can only parse string typed expression
KaTeX can only parse string typed expression
KaTeX can only parse string typed expression
KaTeX can only parse string typed expression
KaTeX can only parse string typed expression
KaTeX can only parse string typed expression
KaTeX can only parse string typed expression
KaTeX can only parse string typed expression
Total such subsequences = KaTeX can only parse string typed expression.
4
1 0 2 0
Output
12
Explanation
Subsequences with product KaTeX can only parse string typed expression:
KaTeX can only parse string typed expression (using the first zero)
KaTeX can only parse string typed expression (using the second zero)
KaTeX can only parse string typed expression
KaTeX can only parse string typed expression (with the second zero)
KaTeX can only parse string typed expression
KaTeX can only parse string typed expression
KaTeX can only parse string typed expression
KaTeX can only parse string typed expression
KaTeX can only parse string typed expression
KaTeX can only parse string typed expression
KaTeX can only parse string typed expression
KaTeX can only parse string typed expression
Total such subsequences = KaTeX can only parse string typed expression.