github.com/captn3m0/codechef.git

---
category_name: school
problem_code: XENTASK
problem_name: 'Xenny and Alternating Tasks'
languages_supported:
    - ADA
    - ASM
    - BASH
    - BF
    - C
    - 'C99 strict'
    - CAML
    - CLOJ
    - CLPS
    - 'CPP 4.3.2'
    - 'CPP 4.9.2'
    - CPP14
    - CS2
    - D
    - ERL
    - FORT
    - FS
    - GO
    - HASK
    - ICK
    - ICON
    - JAVA
    - JS
    - 'LISP clisp'
    - 'LISP sbcl'
    - LUA
    - NEM
    - NICE
    - NODEJS
    - 'PAS fpc'
    - 'PAS gpc'
    - PERL
    - PERL6
    - PHP
    - PIKE
    - PRLG
    - PYPY
    - PYTH
    - 'PYTH 3.4'
    - RUBY
    - SCALA
    - 'SCM chicken'
    - 'SCM guile'
    - 'SCM qobi'
    - ST
    - TCL
    - TEXT
    - WSPC
max_timelimit: '1'
source_sizelimit: '50000'
problem_author: wittyceaser
problem_tester: xcwgf666
date_added: 15-02-2017
tags:
    - basic
    - cakewalk
    - march17
    - wittyceaser
editorial_url: 'https://discuss.codechef.com/problems/XENTASK'
time:
    view_start_date: 1489397400
    submit_start_date: 1489397400
    visible_start_date: 1489397400
    end_date: 1735669800
    current: 1492506700
layout: problem
---
All submissions for this problem are available.###  Read problems statements in [Mandarin Chinese](http://www.codechef.com/download/translated/MARCH17/mandarin/XENTASK.pdf?v=1), [Russian](http://www.codechef.com/download/translated/MARCH17/russian/XENTASK.pdf?v=1) and [Vietnamese](http://www.codechef.com/download/translated/MARCH17/vietnamese/XENTASK.pdf?v=1) as well.

Xenny and Yana were very keen to celebrate Valentine's Day at their home. To make preparations for the celebration, they listed down **N** tasks that they had to complete.

To complete the **ith** task, Xenny takes **Xi** seconds and Yana takes **Yi** seconds. In order to minimize the disparity in tasks performed, they decide to do the tasks **alternatingly**. If Xenny did the **1st** task, then Yana would just wait and watch him until he completes the task. After that, Yana would start the **2nd** task, and while she does her task, Xenny would just watch her. He would start the **3rd** task only after her completion, and they would keep doing tasks alternatingly uptil the **Nth** task. They could also do tasks in the other order - that is, Yana could do the **1st** task, after that Xenny could do the **2nd** task, and so on. Their eventual goal was to minimize the total time taken by them to complete all **N** tasks.

Please help them find the minimum total time they would take to complete all **N** tasks.

### Input

The first line of the input contains an integer **T** denoting the number of test cases. The description of **T** test cases follows.

The first line of each testcase contains a positive integer **N** - the number of tasks to be completed.

The second line contains **N** space-separated positive integers representing the time taken in seconds by Xenny to complete the **ith** task.

The third line contains **N** space-separated positive integers representing the time taken in seconds by Yana to complete the **ith** task.

### Output

For each testcase, print a single line containing the minimum total time in seconds Xenny and Yana would take to complete the tasks.

### Constraints

**Subtask 1: 40 points**

- **1** ≤ **T** ≤ **10**
- **1** ≤ **N** ≤ **3**
- **1** ≤ **Xi**, **Yi** ≤ **105**

**Subtask 2: 60 points**

- **1** ≤ **T** ≤ **10**
- **1** ≤ **N** ≤ **2\*104**
- **1** ≤ **Xi**, **Yi** ≤ **105**

### Sample Testcase

<pre><b>Input:</b>
<tt>1
3
2 1 2
3 2 1</tt>

<b>Output:</b>
<tt>5</tt>
</pre>### Explanation

Let's say Xenny does the 1st task. Then Yana would do the 2nd task and Xenny would do the 3rd task. Hence, the total time taken would be: 2 + 2 + 2 = 6 seconds.

Another possibility is that Yana does the 1st task, Xenny does the 2nd task and then Yana does the 3rd task. The total time taken in this case would be 5 seconds.

Hence, the **minimum** total time taken would be **5 seconds**.