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"title": "First Day Where You Have Been in All the Rooms",
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"content": "<p>There are <code>n</code> rooms you need to visit, labeled from <code>0</code> to <code>n - 1</code>. Each day is labeled, starting from <code>0</code>. You will go in and visit one room a day.</p>\n\n<p>Initially on day <code>0</code>, you visit room <code>0</code>. The <strong>order</strong> you visit the rooms for the coming days is determined by the following <strong>rules</strong> and a given <strong>0-indexed</strong> array <code>nextVisit</code> of length <code>n</code>:</p>\n\n<ul>\n\t<li>Assuming that on a day, you visit room <code>i</code>,</li>\n\t<li>if you have been in room <code>i</code> an <strong>odd</strong> number of times (<strong>including</strong> the current visit), on the <strong>next</strong> day you will visit a room with a <strong>lower or equal room number</strong> specified by <code>nextVisit[i]</code> where <code>0 <= nextVisit[i] <= i</code>;</li>\n\t<li>if you have been in room <code>i</code> an <strong>even</strong> number of times (<strong>including</strong> the current visit), on the <strong>next</strong> day you will visit room <code>(i + 1) mod n</code>.</li>\n</ul>\n\n<p>Return <em>the label of the <strong>first</strong> day where you have been in <strong>all</strong> the rooms</em>. It can be shown that such a day exists. Since the answer may be very large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>\n\n<p> </p>\n<p><strong>Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nextVisit = [0,0]\n<strong>Output:</strong> 2\n<strong>Explanation:</strong>\n- On day 0, you visit room 0. The total times you have been in room 0 is 1, which is odd.\n On the next day you will visit room nextVisit[0] = 0\n- On day 1, you visit room 0, The total times you have been in room 0 is 2, which is even.\n On the next day you will visit room (0 + 1) mod 2 = 1\n- On day 2, you visit room 1. This is the first day where you have been in all the rooms.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nextVisit = [0,0,2]\n<strong>Output:</strong> 6\n<strong>Explanation:</strong>\nYour room visiting order for each day is: [0,0,1,0,0,1,2,...].\nDay 6 is the first day where you have been in all the rooms.\n</pre>\n\n<p><strong>Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> nextVisit = [0,1,2,0]\n<strong>Output:</strong> 6\n<strong>Explanation:</strong>\nYour room visiting order for each day is: [0,0,1,1,2,2,3,...].\nDay 6 is the first day where you have been in all the rooms.\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>n == nextVisit.length</code></li>\n\t<li><code>2 <= n <= 10<sup>5</sup></code></li>\n\t<li><code>0 <= nextVisit[i] <= i</code></li>\n</ul>\n",
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"The only way to get to room i+1 is when you are visiting room i and room i has been visited an even number of times.",
"After visiting room i an odd number of times, you are required to visit room nextVisit[i] where nextVisit[i] <= i. It takes a fixed amount of days for you to come back from room nextVisit[i] to room i. Then, you have visited room i even number of times.nextVisit[i]",
"Can you use Dynamic Programming to avoid recomputing the number of days it takes to visit room i from room nextVisit[i]?"
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