201095: [AtCoder]ARC109 F - 1D Kingdom Builder

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.

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.

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.

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