Interesting XOR!

You are given an integer $C$. Let $d$ be the smallest integer such that $2^d$ is strictly greater than $C$. Consider all pairs of non-negative integers $(A,B)$ such that $A,B \lt 2^d$ and $A \oplus B = C$ ($\oplus$ denotes the bitwise XOR operation). Find the maximum value of $A \cdot B$ over all these pairs. ### Input - The first line of the input contains a single integer $T$ denoting the