G. (Zero XOR Subset)-less
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given an array $a_1, a_2, \dots, a_n$ of integer numbers.

Your task is to divide the array into the maximum number of segments in such a way that:

• each element is contained in exactly one segment;
• each segment contains at least one element;
• there doesn't exist a non-empty subset of segments such that bitwise XOR of the numbers from them is equal to $0$.

Print the maximum number of segments the array can be divided into. Print -1 if no suitable division exists.

Input

The first line contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the size of the array.

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ($0 \le a_i \le 10^9$).

Output

Print the maximum number of segments the array can be divided into while following the given constraints. Print -1 if no suitable division exists.

Examples
Input
4
5 5 7 2

Output
2

Input
3
1 2 3

Output
-1

Input
3
3 1 10

Output
3

Note

In the first example $2$ is the maximum number. If you divide the array into $\{, [5, 7, 2]\}$, the XOR value of the subset of only the second segment is $5 \oplus 7 \oplus 2 = 0$. $\{[5, 5], [7, 2]\}$ has the value of the subset of only the first segment being $5 \oplus 5 = 0$. However, $\{[5, 5, 7], \}$ will lead to subsets $\{[5, 5, 7]\}$ of XOR $7$, $\{\}$ of XOR $2$ and $\{[5, 5, 7], \}$ of XOR $5 \oplus 5 \oplus 7 \oplus 2 = 5$.

Let's take a look at some division on $3$ segments — $\{, [5, 7], \}$. It will produce subsets:

• $\{\}$, XOR $5$;
• $\{[5, 7]\}$, XOR $2$;
• $\{, [5, 7]\}$, XOR $7$;
• $\{\}$, XOR $2$;
• $\{, \}$, XOR $7$;
• $\{[5, 7], \}$, XOR $0$;
• $\{, [5, 7], \}$, XOR $5$;

As you can see, subset $\{[5, 7], \}$ has its XOR equal to $0$, which is unacceptable. You can check that for other divisions of size $3$ or $4$, non-empty subset with $0$ XOR always exists.

The second example has no suitable divisions.

The third example array can be divided into $\{, , \}$. No subset of these segments has its XOR equal to $0$.