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G. (Zero XOR Subset)-less

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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 $$$0$$$.

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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