XOR-AND Coupling

The key observation is if there is at least one dissimilar number in a group their AND will be zero. Let $A_{fmax}$ be the maximum frequent element and $A_{fc}$ be the maximum frequent element count and $S$ be the summation of all the array elements.

1. If

2. If $$\lfloor N/2 \rfloor < A_{fc} < N$,answer is $$\lfloor N/2 \rfloor < A_{fc}$)*A_{fmax}