All Tracks Algorithms Problem

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Tag(s):

Advanced Algorithms, Algorithms, Convolution, FFT, Fast Fourier Transformations, Medium-Hard

Problem
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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

\(1 \le n \le 100000\)

SAMPLE INPUT
4
abaa 
aaba
aaba
SAMPLE OUTPUT
4 0
Explanation

The minimum difference is obtained when the first string is rotated cyclically once while the difference is maximum without any rotation.

Time Limit: 3.0 sec(s) for each input file.
Memory Limit: 256 MB
Source Limit: 1024 KB
Marking Scheme: Marks are awarded when all the testcases pass.
Allowed Languages: Bash, C, C++, C++14, Clojure, C#, D, Erlang, F#, Go, Groovy, Haskell, Java, Java 8, JavaScript(Rhino), JavaScript(Node.js), TypeScript, Julia, Kotlin, Lisp, Lisp (SBCL), Lua, Objective-C, OCaml, Octave, Pascal, Perl, PHP, Python, Python 3, R(RScript), Racket, Ruby, Rust, Scala, Swift, Swift-4.1, Visual Basic

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This Problem was Asked in

HackerEarth

Challenge Name

November Easy' 18

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