CF1848F.Vika and Wiki

Recently, Vika was studying her favorite internet resource - Wikipedia.

On the expanses of Wikipedia, she read about an interesting mathematical operation bitwise XOR, denoted by $\oplus$ .

Vika began to study the properties of this mysterious operation. To do this, she took an array $a$ consisting of $n$ non-negative integers and applied the following operation to all its elements at the same time: $a_i = a_i \oplus a_{(i+1) \bmod n}$ . Here $x \bmod y$ denotes the remainder of dividing $x$ by $y$ . The elements of the array are numbered starting from $0$ .

Since it is not enough to perform the above actions once for a complete study, Vika repeats them until the array $a$ becomes all zeros.

Determine how many of the above actions it will take to make all elements of the array $a$ zero. If this moment never comes, output $-1$ .

The first line contains a single integer $n$ ( $1 \le n \le 2^{20}$ ) - the length of the array $a$ .

It is guaranteed that $n$ can be represented as $2^k$ for some integer $k$ ( $0 \le k \le 20$ ).

The second line contains $n$ integers $a_0, a_1, a_2, \dots, a_{n-1}$ ( $0 \le a_i \le 10^9$ ) - the elements of the array $a$ .

Output a single number - the minimum number of actions required to make all elements of the array $a$ zero, or $-1$ if the array $a$ will never become zero.

In the first example, after one operation, the array $a$ will become equal to $[3, 3, 3, 3]$ . After one more operation, it will become equal to $[0, 0, 0, 0]$ .

In the second example, the array $a$ initially consists only of zeros.

In the third example, after one operation, the array $a$ will become equal to $[0]$ .