F2. Korney Korneevich and XOR (hard version)time limit per test1.5 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputThis is a harder version of the problem with bigger constraints.Korney Korneevich dag up an array a of length n. Korney Korneevich has recently read about the operation bitwise XOR, so he wished to experiment with it. For this purpose, he decided to find all integers x \ge 0 such that there exists an increasing subsequence of the array a, in which the bitwise XOR of numbers is equal to x.It didn't take a long time for Korney Korneevich to find all such x, and he wants to check his result. That's why he asked you to solve this problem!A sequence s is a subsequence of a sequence b if s can be obtained from b by deletion of several (possibly, zero or all) elements.A sequence s_1, s_2, \ldots , s_m is called increasing if s_1 < s_2 < \ldots < s_m.InputThe first line contains a single integer n (1 \le n \le 10^6).The second line contains n integers a_1, a_2, \ldots, a_n (0 \le a_i \le 5000) — the elements of the array a.OutputIn the first line print a single integer k — the number of found x values.In the second line print k integers in increasing order x_1, x_2, \ldots x_k (0 \le x_1 < \ldots < x_k) — found x values.ExamplesInput
4
4 2 2 4
Output
4
0 2 4 6 
Input
8
1 0 1 7 12 5 3 2
Output
12
0 1 2 3 4 5 6 7 10 11 12 13 
NoteIn the first test case:  To get value x = 0 it is possible to choose and empty subsequence  To get value x = 2 it is possible to choose a subsequence [2]  To get value x = 4 it is possible to choose a subsequence [4]  To get value x = 6 it is possible to choose a subsequence [2, 4] 
4
4 2 2 4

4 0 2 4 6  
['binary search', 'brute force', 'dp', 'greedy', 'two pointers', '*2400']