You are given three strings $a$, $b$ and $c$  each of length $n$ consisting of lower case English letters. The difference between the three strings is defined as $\sum\limits_{i=1}^n \ |a[i]-b[i]|+|a[i]-c[i]|$ where $|a[i]-b[i]|$ and $|a[i]-c[i]|$ are the absolute differences between ASCII values of the characters at the position $i$ in strings $a,b$ and $a,c$ respectively. However, the string $a$ can be rotated cyclically (for example the rotations of the string $xyz$ are $xyz,zxy,yzx$). There are a total of $n$ possible rotations of a string of length $n$.

Print the maximum and minimum difference of the three strings for all the possible rotations of the string $a$.

Input format

First line: Single integer $n$ (the length of the three strings)

Next three lines: Strings $a,b$ and $c$ respectively

Output Format:

Print two space-separated integers: the maximum and minimum difference of the three strings for all possible rotations of string $a$.

Constraints

$1 \le n \le 100000$