Given an array of $n$ integers, your task is to find the number of different subset xors.

Input

The first line has an integer $n$: the size of the array.

The next line has $n$ integers $x_1,x_2,\dots,x_n$: the contents of the array.

Output

Print one integer: the number of different subset xors.

Constraints

• $1 \le n \le 2 \cdot 10^5$
• $0 \le x_i \le 10^9$

Example

Input:

3
3 6 5

Output:

4

Explanation: The following values can be the xor of a subset:

• $0 = \text{xor of the empty set}$
• $3 = 3$
• $5 = 3 \oplus 6$
• $6 = 3 \oplus 5$

In this case, no other values can be the xor of a subset.