Remove the dirt

Alice has $N$ jars each consisting of a specific amount of dirt $A$$i$. Now she starts playing with those jars. She wants to repeat the following operations exactly $N-1$ times until she is left with only one jar.Initial dirt value is 0 - Selects two random jars . let's denote them as $i$ and $j$. - Adds $A$$i$+$A$$j$ dirt value in a book where $A$$i$ and $A$$j$ are their respective dirt amounts