Multiply 2 to Minimize

Given an array $A$, we can do the following operation as many times as needed : - Choose $(i, j)$ such that $1 \le i < j \le |A|$ and $A_i = A_j$, then delete both the values from the array, and append $2 \cdot A_i$ at the end of the array. For example, suppose $A = [3, 1, 3, 4, 4]$, and we choose $(i, j) = (1, 3)$, then the new array formed is $[1, 4, 4, 6]$. Let $f(A)$ denote the minimum pos