C. Flipped DNA
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

An organism's DNA can be represented by a string consisting of the characters "A", "T", "C", and "G". Due to the structure of DNA, "A" pairs with "T" and "C" pairs with "G", and these are called complementary pairs.

Daniel has sequenced a specific gene from an organism and has determined its DNA corresponds to the string $$$X$$$ with length $$$n$$$. He wants to compare this string to the target DNA $$$Y$$$ which is also a string of length $$$n$$$.

Daniel knows that because of mutations, the strings $$$X$$$ and $$$Y$$$ may not be equal. However, he hypothesizes that the only type of mutation that $$$X$$$ has is swapping complementary pairs. For example, a character "G" in the $$$i$$$-th location in $$$Y$$$ may have mutated into a character "C" at that same location but not a character "A", since "A" and "G" are not complementary.

Given both strings $$$X$$$ and $$$Y$$$, help Daniel determine whether his hypothesis is correct.

Input

The first line will contain an integer $$$n$$$ ($$$1 \leq n \leq 10^5$$$) the length of the DNA sequence.

The second line will contain the string $$$X$$$ ($$$\lvert X \rvert = n$$$), the gene Daniel has sequenced.

The third line will contain the string $$$Y$$$ ($$$\lvert Y \rvert = n$$$), the target gene Daniel wants to compare to.

It is guaranteed that both $$$X$$$ and $$$Y$$$ only consist of the characters "A", "T", "C", and "G".

Output

Print "YES" (without quotes) if Daniel's hypothesis is correct and the only mutations are complementary pair swaps and "NO" otherwise.

Examples
Input
8
GCAAGCCT
CCATCCCT
Output
YES
Input
10
CGTATGGACA
ATACTCACCA
Output
NO