A. Distinct Xor Subsequences
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given a sequence of $$$n$$$ integers $$$a_1, a_2, \dots , a_n$$$ .

Count the distinct numbers you can produce by choosing any subsequence from $$$a$$$ and calculate their bitwise XOR. The chosen subsequence can be empty.

Input

The first line of input contains a single integer $$$n \ (1 \le n \le 10^5)$$$.

Then, the second line contains $$$n$$$ integers $$$a_1, \dots , a_n \ (0 \le a_i \lt 2^{60})$$$.

Output

Print a line of a single integer denoting the answer.

Examples
Input
4
7 2 1 5
Output
8
Input
7
1 1 1 1 1 1 1
Output
2