Score : $400$ points

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.

4
1011

9999999999

$S$ is so long, so let us instead count the number of times 1011 occurs in the concatenation of $3$ copies of 110, that is, 110110110. We can see it occurs twice:

• $1$ 1011 $0110$
• $1101$ 1011 $0$

22
1011011011011011011011

9999999993