A14098 | Enormous XOR

You are given two integers $l$ and $r$ in binary representation. Let $g(x, y)$ be equal to the [bitwise XOR](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) of all integers from $x$ to $y$ inclusive (that is $x \oplus (x+1) \oplus \dots \oplus (y-1) \oplus y$ ). Let's define $f(l, r)$ as the maximum of all values of $g(x, y)$ satisfying $l \le x \le y \le r$ .

Output $f(l, r)$ .

The first line contains a single integer $n$ ( $1 \le n \le 10^6$ ) — the length of the binary representation of $r$ .

The second line contains the binary representation of $l$ — a string of length $n$ consisting of digits $0$ and $1$ ( $0 \le l < 2^n$ ).

The third line contains the binary representation of $r$ — a string of length $n$ consisting of digits $0$ and $1$ ( $0 \le r < 2^n$ ).

It is guaranteed that $l \le r$ . The binary representation of $r$ does not contain any extra leading zeros (if $r=0$ , the binary representation of it consists of a single zero). The binary representation of $l$ is preceded with leading zeros so that its length is equal to $n$ .

In a single line output the value of $f(l, r)$ for the given pair of $l$ and $r$ in binary representation without extra leading zeros.