Problem Statement

Snuke is playing with a board composed of infinitely many squares lining up in a row.
Each square has an assigned integer; for each integer i, Square i and Square i+1 are adjacent.
Additionally, each square is painted white or black.
A string s of length n consisting of w and b represents the colors of the squares of this board, as follows:

• For each $i = 1, 2, \dots, n, Square i$ is white if the i-th character of s is w, and black if that character is b;
• For each $i \leq 0, Square i$ is white;
• For each i > n, Square i is black.

Snuke has infinitely many white pieces and infinitely many black pieces. He will put these pieces on the board as follows:

• (1) Choose a piece of the color of his choice.
• (2) Among the squares adjacent to a square that already contains a piece, look for squares of the same color as the chosen piece.
• (2a) If there are such squares, choose one of them and put the piece on it;
• (2b) if there is no such square, choose a square of the same color as the chosen piece and put the piece on it.

The board initially has no piece on it.
You are given a string t of length n consisting of o and _. Find the minimum number of pieces Snuke needs to put on the board to have a piece on every square i among Squares 1,..,n such that the i-th character of t is o.
It is guaranteed that t has at least one occurrence of o.

Input

Input is given from Standard Input in the following format:
n
s
t

Output

Print the minimum number of pieces Snuke needs to put on the board.

Constraints

• $1 \leq n \leq 10^5$
• |s| = |t| = n
• s consists of w and b.
• t consists of o and _.
• t has at least one occurrence of o.

Sample Input 1

3
wbb
o_o

Sample Output 1

2

Let us use W to represent a white square that needs a piece on it, B to represent a black square that needs a piece on it, w to represent a white square that does not need a piece on it, and b to represent a black square that does not need a piece on it.
We have the following board:
...wwwwwwWbBbbbbb...

If we put pieces in the following order, two pieces is enough:
...wwwwwwWbBbbbbb...
2 1

Note that if we put a piece on the white square first, we will need three or more pieces:
...wwwwwwWbBbbbbb...
123

Sample Input 2

4
wwww
o__o

Sample Output 2

3

If we put pieces in the following order, three pieces is enough:
...wwwwwWwwWbbbbb...
1 32

Sample Input 3

9
bbwbwbwbb
o_o_o_o

Sample Output 3

5

If we put pieces in the following order, five pieces is enough:
...wwwwwbBwBwBwBbbbbbb...
12 3 4 5

Sample Input 4

17
wwwwbbbbbbbbwwwwb
__o__o_o_ooo__oo_

Sample Output 4

11

见题面 Input 部分

见题面 Output 部分