---{"category_name":"easy","problem_code":"CHEFRRUN","problem_name":"Chef and Round Run","languages_supported":{"0":"ADA","1":"ASM","2":"BASH","3":"BF","4":"C","5":"C99 strict","6":"CAML","7":"CLOJ","8":"CLPS","9":"CPP 4.3.2","10":"CPP 4.9.2","11":"CPP14","12":"CS2","13":"D","14":"ERL","15":"FORT","16":"FS","17":"GO","18":"HASK","19":"ICK","20":"ICON","21":"JAVA","22":"JS","23":"LISP clisp","24":"LISP sbcl","25":"LUA","26":"NEM","27":"NICE","28":"NODEJS","29":"PAS fpc","30":"PAS gpc","31":"PERL","32":"PERL6","33":"PHP","34":"PIKE","35":"PRLG","36":"PYPY","37":"PYTH","38":"PYTH 3.4","39":"RUBY","40":"SCALA","41":"SCM chicken","42":"SCM guile","43":"SCM qobi","44":"ST","45":"TCL","46":"TEXT","47":"WSPC"},"max_timelimit":1,"source_sizelimit":50000,"problem_author":"berezin","problem_tester":"xcwgf666","date_added":"8-04-2016","tags":{"0":"aug16","1":"berezin","2":"graph","3":"simple"},"editorial_url":"http://discuss.codechef.com/problems/CHEFRRUN","time":{"view_start_date":1471253400,"submit_start_date":1471253400,"visible_start_date":1471253400,"end_date":1735669800},"layout":"problem"}---<span class="solution-visible-txt">All submissions for this problem are available.</span><h3> Read problems statements in <a target="_blank" href="http://www.codechef.com/download/translated/AUG16/mandarin/CHEFRRUN.pdf">Mandarin Chinese</a>, <a target="_blank" href="http://www.codechef.com/download/translated/AUG16/russian/CHEFRRUN.pdf">Russian</a> and <a target="_blank" href="http://www.codechef.com/download/translated/AUG16/vietnamese/CHEFRRUN.pdf">Vietnamese</a> as well.</h3><p>Chef cooks nice receipes in the cafeteria of his company. The cafe contains <b>N</b> boxes with food enumerated from <b>1</b> to <b>N</b> and are placed in a circle in clocwise order (boxes <b>1</b> and <b>N</b> are adjacent). Each box has unlimited amount of food with a tastyness level of <b>A<sub>i</sub></b>. Chef invented a definition of a magic box!<ul><li>Chef picks a box <b>i</b> and stays in front of it. </li><li>Now Chef eats food from box <b>i</b> and <b>skips</b> next <b>A<sub>i</sub></b> boxes.</li><li>Now Chef is staying at some other (probably even the same!) box and repeats. </li><li>Box <b>i</b> is a magic box if at some point of such game started from box <b>i</b>, Chef will find himself staying in front of it again. </li></ul></p><p>When Chef came home, Chef's dog Tommy asked him about how many magic boxes were in the cafe? Help Chef to in finding that!</p><h3>Input</h3><p>The first line of the input contains an integer <b>T</b> denoting the number of test cases. The description of <b>T</b> test cases follows.</p><p>The first line of each test case contains a single integer <b>N</b> denoting the number of boxes.</p><p>The second line contains <b>N</b> space-separated integers <b>A<sub>1</sub></b>, <b>A<sub>2</sub></b>, ..., <b>A<sub>N</sub></b> denoting the tastyness levels of each box.</p><h3>Output</h3><p>For each test case, output a single line containing number of magical boxes.</p><h3>Constraints</h3><ul><li><b>1</b> ≤ sum of all <b>N</b> over all the test cases in a single test file ≤ <b>10<sup>6</sup></b></li><li><b>0</b> ≤ <b>A<sub>i</sub></b> ≤ <b>10<sup>9</sup></b></li></ul><h3>Subtasks</h3><ul><li><b>Subtask #1 (30 points):</b> <b>1</b> ≤ sum of all <b>N</b> over all the test cases ≤ <b>10<sup>4</sup></b>; <b>1</b> ≤ <b>N</b> ≤ <b>1000</b></li><li><b>Subtask #2 (70 points):</b> <b>1</b> ≤ sum of all <b>N</b> over all the test cases ≤ <b>10<sup>6</sup></b>; <b>1</b> ≤ <b>N</b> ≤ <b>10<sup>5</sup></b></li></ul><h3>Example</h3><pre><b>Input:</b><tt>341 1 1 143 0 0 040 0 0 2</tt><b>Output:</b><tt>412</tt></pre><h3>Explanation</h3><p><b>Example case 1.</b></p>Here are Chef's paths if he starting from each the box:<pre><b>1</b>-><b>3</b>-><b>1</b><b>2</b>-><b>4</b>-><b>2</b><b>3</b>-><b>1</b>-><b>3</b><b>4</b>-><b>2</b>-><b>4</b></pre>As you see, all <b>4</b> boxes are magical.<p><b>Example case 2.</b></p>Here are Chef's paths if he starts from each box appropriately:<pre><b>1</b>-><b>1</b><b>2</b>-><b>3</b>-><b>4</b>-><b>1</b>-><b>1</b><b>3</b>-><b>4</b>-><b>1</b>-><b>1</b><b>4</b>-><b>1</b>-><b>1</b></pre>AS you see, only box <b>1</b> is magical.