Problem Statement

You are given strings $S$ and $T$ of length $N$ each, consisting of lowercase English letters.

For a string $X$ and an integer $i$, let $f(X,i)$ be the string obtained by performing on $X$ the following operation $i$ times:

• Remove the first character of $X$ and append the same character to the end of $X$.

Find the number of integer pairs $(i,j)$ satisfying $0 \\le i,j \\le N-1$ such that $f(S,i)$ is lexicographically smaller than or equal to $f(T,j)$.

What is the lexicographical order?

Simply put, the lexicographical order is the order in which the words are arranged in a dictionary. Let us define it formally by describing an algorithm of finding the ordering of two distinct strings $S$ and $T$ consisting of lowercase English letters.

Here, we denote "the $i$-th character of a string $S$" by $S_i$. Also, we write $S \\lt T$ and $S \\gt T$ if $S$ is lexicographically smaller and larger than $T$, respectively.

1. Let $L$ be the smallest of the lengths of $S$ and $T$. For $i=1,2,\\dots,L$, we check if $S_i$ equals $T_i$.
2. If there is an $i$ such that $S_i \\neq T_i$, let $j$ be the smallest such $i$. Comparing $S_j$ and $T_j$, we terminate the algorithm by determining that $S \\lt T$ if $S_j$ is smaller than $T_j$ in the alphabetical order, and that $S \\gt T$ otherwise.
3. If there is no $i$ such that $S_i \\neq T_i$, comparing the lengths of $S$ and $T$, we terminate the algorithm by determining that $S \\lt T$ if $S$ is shorter than $T$, and that $S \\gt T$ otherwise.

Constraints

• $1 \\le N \\le 2 \\times 10^5$
• $S$ and $T$ are strings of length $N$ each, consisting of lowercase English letters.
• $N$ is an integer.

Input

The input is given from Standard Input in the following format:

$N$ $S$ $T$

Output

Print the answer.

Sample Input 1

3
adb
cab

Sample Output 1

4

There are $4$ pairs of $(i, j)$ satisfying the conditions: $(0,0),(0,2),(2,0)$, and $(2,2)$.

$(i,j)=(1,2)$ does not satisfy the conditions because $f(S,i)=$dba and $f(T,j)=$bca.

Sample Input 2

10
wsiuhwijsl
pwqoketvun

Sample Output 2

56