E. Enormous XOR
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given two integers $$$l$$$ and $$$r$$$ in binary representation. Let $$$g(x, y)$$$ be equal to the bitwise 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 $$$f(l, r)$$$.

Input

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 $$$n$$$.

Output

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.

Examples
Input
7
0010011
1111010
Output
1111111
Input
4
1010
1101
Output
1101
Note

In sample test case $$$l=19$$$, $$$r=122$$$. $$$f(x,y)$$$ is maximal and is equal to $$$127$$$, with $$$x=27$$$, $$$y=100$$$, for example.