Master Zhu and Instability

Consider an array $A$ of length $N$. The instability of $A$ is defined as $\sum\limits\_{i = 1}^{N - 1} (|A\[i + 1] - A\[i]|)\text{.}$

Master Zhu wants to stabilize an array. In order to do that, he wants to select an integer $X$ and change every element $A\[i]$ to $(A\[i] \oplus X)$. Here, $u \oplus v$ is the bitwise XOR of $u$ and $v$.

Find the smallest non-negative integer $X$ Master Zhu must choose to minimize the instability of a given array, and calculate the resulting instability.

The first line of input contains an integer $N$ ($1 \le N \le 10^5$). Next line contains $N$ integers $A\[i]$, indicating the elements of the array ($0 \le A\[i] < 2^{20}$).

Print a single line containing two integers: the smallest non-negative integer $X$ which must be used in order to reach the minimum possible instability and the resulting instability itself.