title: how to solve ALICESIE on spoj. How it has common pattern for its answer
body: <p>What is the logic behind pattern i.e.(ans=(n+1)/2) in question <strong>ALICESIE</strong> on spoj.<br><br>
  <strong>Algorithm_given:</strong><br>
  1.Create a list of consecutive integers from N to 2 (N, N-1, N-2, ..., 3, 2). All of those N-1numbers are initially unmarked.<br>
  2.Initially, let P equal N, and leave this number unmarked.<br>
  3.Mark all the proper divisors of P (i.e. P remains unmarked).<br>
  4.Find the largest unmarked number from 2 to P – 1, and now let P equal this number.<br>
  5.If there were no more unmarked numbers in the list, stop. Otherwise, repeat from step 3.<br><br>
  Find total number of unmarked numbers.
  <br><br></p>
  
  <p>i know its O(sqrt(n)) solution but answer is  expected in O(1),it can found by seeing the common pattern i.e.(N+1)/2<br>
  But how to prove it Mathematically<br><br>
  link: <a href="https://www.spoj.com/problems/ALICESIE/" rel="nofollow noreferrer">ALICESIE</a></p>