Lamps

A long hallway has $N$ lamps in a row. The lamps are numbered 1 through $N$ from left to right. Each lamp is either off or on.

A special mechanism changes the lamp states. In one operation you can do one of the following three things.

• Choose integers $p$ and $q$ with $1 \le p \le q \le N$, and turn off lamps $p$, $p+1$, $\cdots$, $q$.
• Choose integers $p$ and $q$ with $1 \le p \le q \le N$, and turn on lamps $p$, $p+1$, $\cdots$, $q$.
• Choose integers $p$ and $q$ with $1 \le p \le q \le N$, and flip lamps $p$, $p+1$, $\cdots$, $q$ (off becomes on, on becomes off).

The initial lamp states are given as a string $A$ of length $N$. The $i$-th character ($1 \le i \le N$) of $A$ is 0 if lamp $i$ is off and 1 if it is on. The desired states are given as a string $B$ of length $N$, encoded the same way. You want to reach the states in $B$ using as few operations as possible.

Given $N$, $A$, and $B$, print the minimum number of operations needed to reach the desired states.

The first line contains $N$. The second line contains $A$. The third line contains $B$.

Print one line containing the minimum number of operations needed to reach the desired lamp states.

• $1 \le N \le 1\ 000\ 000$.
• $A$ and $B$ are strings of length $N$.
• The characters of $A$ and $B$ are 0 or 1.