Codeforces Round 705 (Div. 2) |
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Finished |

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bitmasks

constructive algorithms

greedy

math

strings

two pointers

*2600

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E. Enormous XOR

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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.

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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