All Subarray Xors

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