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<p>You are given three integers <code>x</code>, <code>y</code>, and <code>z</code>.</p>
<p>You have <code>x</code> strings equal to <code>&quot;AA&quot;</code>, <code>y</code> strings equal to <code>&quot;BB&quot;</code>, and <code>z</code> strings equal to <code>&quot;AB&quot;</code>. You want to choose some (possibly all or none) of these strings and concactenate them in some order to form a new string. This new string must not contain <code>&quot;AAA&quot;</code> or <code>&quot;BBB&quot;</code> as a substring.</p>
<p>You have <code>x</code> strings equal to <code>&quot;AA&quot;</code>, <code>y</code> strings equal to <code>&quot;BB&quot;</code>, and <code>z</code> strings equal to <code>&quot;AB&quot;</code>. You want to choose some (possibly all or none) of these strings and concatenate them in some order to form a new string. This new string must not contain <code>&quot;AAA&quot;</code> or <code>&quot;BBB&quot;</code> as a substring.</p>
<p>Return <em>the maximum possible length of the new string</em>.</p>