Goodwin has a sequence of numbers from which he wants to remove three elements so that the sequence is the prettiest.
The curvature of the sequence is set by the function 
 — the number of elements in the original sequence. The second line contains n space-separated integers — sequence members separated by spaces. All numbers in the sequence modulo do not exceed 10<sup>9</sup>.</p>
</div>
<p>
<strong>Output</strong></p>
<div>
<p>
Print a single number — the minimum curvature of a sequence that can be obtained from a given one by removing three elements.</p>
</div>
<p>
Test examples</p>
<div>
<p>
Input</p>
<div>
<div>
<pre>
4
1 2 3 4
</pre>
</div>
<div>
<div>
Output</div>
<pre>
1</pre>
</div>
<div>
<div>
Input data</div>
<pre>
5
1 2 3 4 5
</pre>
</div>
<div>
<div>
Output</div>
<pre>
-4</pre>
</div>
</div>
</div>
<p>
Note</p>
<div>
<p>
Tests are divided into groups, but scored separately</p>
<ul type=)
n ≤ 81 — 20 points
n ≤ 300 — 10 points
n ≤ 5000 — 20 points
Without additional restrictions — 50 points