title: How to express integer using symbols + * () and 1 with minimal cost?
body: <p>The task is to build integers from the symbols <code>+ * ( )</code> (addition, multiplication and brackets) and the digit <code>1</code>. You are given an integer and must output an expression using the minimal number of characters. For example:</p>
  
  <pre><code>4    = 1+1+1+1  
  23   = 11+11+1  
  242  = (11+11)*11  
  1000 = 1+(1+1+1)*(1+1+1)*111 
  1997 = (1+1)*(1+1+1)*111+11*11*11 
  </code></pre>