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 $$$-1$$$.

Input

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

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.

Note

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 $$$[0]$$$.

Vika and Wiki

Examples