Graph
Tag(s):

## Algorithms, Dynamic Programming, Medium, Tree

Problem
Editorial
Analytics

Given two sequences $s_1{\dots}s_n$ and $w_1{\dots}w_n$. A graph is built with n vertices and n directed edges $(i,s_i)$. Cost to change some $s_i$ is  $w_i$ . Your goal is to make the graph strongly connected with minimum cost.

Input

The first line contains an integer n.

The second line contains n intergers, $s_1{\dots}s_n$.

The third line contains n integers $w_1{\dots}w_n$.

Output

Constraints

$1 \le n \le 10^5$

$1 \le s_i \le n$

$1 \le w_i \le 10^9$

SAMPLE INPUT
4
2 1 1 1
3 1 1 3

SAMPLE OUTPUT
2

Explanation

Change $s_2$ to 3 and $s_3$ to 4.

Time Limit: 1.0 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), 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, TypeScript, Visual Basic

## CODE EDITOR

Initializing Code Editor...

## This Problem was Asked in Challenge Name

April Circuits '18

OTHER PROBLEMS OF THIS CHALLENGE
• Algorithms > Graphs
• Basic Programming > Implementation
• Math > Combinatorics
• Algorithms > Dynamic Programming
• Data Structures > Advanced Data Structures