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You are given an array a_1, a_2, ..., 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 ≤ n ≤ 2 ⋅ 10^5) — the size of the array.

The second line contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 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 ⊕ 7 ⊕ 2 = 0. {[5, 5], [7, 2]} has the value of the subset of only the first segment being 5 ⊕ 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 ⊕ 5 ⊕ 7 ⊕ 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.

inputFormat

Input

The first line contains a single integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the size of the array.

The second line contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 10^9).

outputFormat

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 ⊕ 7 ⊕ 2 = 0. {[5, 5], [7, 2]} has the value of the subset of only the first segment being 5 ⊕ 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 ⊕ 5 ⊕ 7 ⊕ 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.

样例

3
1 2 3

-1