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.

• 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.

• 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.

• 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.

Input

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

Output

Print the answer.

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.

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

见题面 Input 部分

见题面 Output 部分