Sum Reduction

You are given an array $A$ of $N$ elements. In one operation, you may choose two distinct indices $i$ and $j$ such that the bitwise AND of $A_i$ and $A_j$ is $0$, i.e. $A_i \& A_j = 0$. Then, remove both $A_i$ and $A_j$ from the array, and insert their sum $A_i + A_j$ back into the array. Determine whether it is possible to reduce the array to exactly one element after performing a finite numbe