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 $$$\{[5], [5, 7, 2]\}$$$, 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, $$$\{[5, 5, 7], [2]\}$$$ will lead to subsets $$$\{[5, 5, 7]\}$$$ of XOR $$$7$$$, $$$\{[2]\}$$$ of XOR $$$2$$$ and $$$\{[5, 5, 7], [2]\}$$$ of XOR $$$5 \oplus 5 \oplus 7 \oplus 2 = 5$$$.

Let's take a look at some division on $$$3$$$ segments — $$$\{[5], [5, 7], [2]\}$$$. It will produce subsets:

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

As you can see, subset $$$\{[5, 7], [2]\}$$$ 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 $$$\{[3], [1], [10]\}$$$. No subset of these segments has its XOR equal to $$$0$$$.