On a board there are the following \(+\) and \(-\) signs drawn:
\[+\; + \; + \; - \; - \; + \; + \; - \; + \; - \; +\]
You can choose any two signs, erase them, and then draw a \(+\) sign if the signs you erased were both equal, and a \(-\) sign if the signs you erased were different. Show that regardless of the order you perform these erasures, the sign that is left at the end is always the same.