Given an array of $n$ integers, your task is to find all integers that are the xor sum in some subarray.

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

First print an integer $k$: the number of distinct integers that are the xor sum in some subarray.

After this print $k$ integers: the xor sums in increasing order.

Constraints

• $1 \le n \le 2 \cdot 10^5$
• $0 \le x_i \le 10^6$

Example

Input:

4
5 1 5 9

Output:

7
1 4 5 8 9 12 13