Counting and filtering based on it, inside an xsl:for-each

I have a source XML generated automatically by a clumsy program, which contains repeated and empty entries.

I want to be able to select and show ONLY the entry the most represented, filtering the empty entries. For example, suppose my source XML is

<catalog>
    <letter>
      <char>A</char>
    </letter>
    <letter>
        <char>B</char>
    </letter>
    <letter>
        <char></char>
    </letter>
    <letter>
        <char>A</char>
    </letter>
    <letter>
        <char></char>
    </letter>
    <letter>
        <char></char>
    </letter>
</catalog>

Then, I want to get only A.

I can do:

<table><tr>
  <xsl:for-each select="letter[char='']">
    <td><xsl:value-of select="char" /></td>
  </xsl:for-each>
</tr></table>

which will show me a table containing only A, B, A (not the empty columns).

Now I want to get only A, because it is the one that appears most often. How do I do it?