title: how is this solution achieved? longest increasing sub-sequence
body: <p>so i was doing some algorithm solving problems and the first questions input/output test case i am not able to understand. I am not asking here any algorithm or code, i just want to understand how <code>Bob</code> is winning ?</p>
  
  <blockquote>
    <p>Alice and Bob play the following game:</p>
    
    <p>1) They choose a permutation of the first N numbers to begin with.</p>
    
    <p>2) They play alternately and Alice plays first.</p>
    
    <p>3) In a turn, they can remove any one remaining number from the
    permutation.</p>
    
    <p>4) The game ends when the remaining numbers form an increasing
    sequence. The person who played the last turn (after which the
    sequence becomes increasing) wins the game.</p>
    
    <p>Assuming both play optimally, who wins the game?</p>
  </blockquote>
  
  <hr>
  
  <p>Test case
  <code>5 3 2 1 4</code></p>
  
  <p>Now they say Bob will win the game.
  How ?</p>
  
  <pre><code>alice -&gt; remove 5
  bob -&gt; remove 3
  alice -&gt; remove 1/2 -&gt; Wins
  </code></pre>
  
  <p>OR</p>
  
  <pre><code>alice -&gt; remove 3
  bob -&gt; remove 5
  alice -&gt; remove 1/2 -&gt; Wins
  </code></pre>