Problem Statement

Let $S$ be the concatenation of $10^{10}$ copies of the string 110. (For reference, the concatenation of $3$ copies of 110 is 110110110.)

We have a string $T$ of length $N$.

Find the number of times $T$ occurs in $S$ as a contiguous substring.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $T$ is a string of length $N$ consisting of 0 and 1.

Input

Input is given from Standard Input in the following format:

N
T

Output

Print the number of times $T$ occurs in $S$ as a contiguous substring.