Codeforces Round 750 (Div. 2) |
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Finished |
This 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 $$$s_1 < s_2 < \ldots < s_m$$$.
The 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 $$$a$$$.
In 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.
4 4 2 2 4
4 0 2 4 6
8 1 0 1 7 12 5 3 2
12 0 1 2 3 4 5 6 7 10 11 12 13
In the first test case:
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