Deduction Queries

2000ms

262144K

Description:

There is an array $$$a$$$ of $$$2^{30}$$$ integers, indexed from $$$0$$$ to $$$2^{30}-1$$$. Initially, you know that $$$0 \leq a_i < 2^{30}$$$ ($$$0 \leq i < 2^{30}$$$), but you do not know any of the values. Your task is to process queries of two types:

1 l r x: You are informed that the bitwise xor of the subarray $$$[l, r]$$$ (ends inclusive) is equal to $$$x$$$. That is, $$$a_l \oplus a_{l+1} \oplus \ldots \oplus a_{r-1} \oplus a_r = x$$$, where $$$\oplus$$$ is the bitwise xor operator. In some cases, the received update contradicts past updates. In this case, you should ignore the contradicting update (the current update).
2 l r: You are asked to output the bitwise xor of the subarray $$$[l, r]$$$ (ends inclusive). If it is still impossible to know this value, considering all past updates, then output $$$-1$$$.

Note that the queries are encoded. That is, you need to write an online solution.

Input:

The first line contains a single integer $$$q$$$ ($$$1 \leq q \leq 2 \cdot 10^5$$$) — the number of queries.

Each of the next $$$q$$$ lines describes a query. It contains one integer $$$t$$$ ($$$1 \leq t \leq 2$$$) — the type of query.

The given queries will be encoded in the following way: let $$$last$$$ be the answer to the last query of the second type that you have answered (initially, $$$last = 0$$$). If the last answer was $$$-1$$$, set $$$last = 1$$$.

If $$$t = 1$$$, three integers follow, $$$l'$$$, $$$r'$$$, and $$$x'$$$ ($$$0 \leq l', r', x' < 2^{30}$$$), meaning that you got an update. First, do the following: $$$l = l' \oplus last$$$, $$$r = r' \oplus last$$$, $$$x = x' \oplus last$$$
and, if $$$l > r$$$, swap $$$l$$$ and $$$r$$$.
This means you got an update that the bitwise xor of the subarray $$$[l, r]$$$ is equal to $$$x$$$ (notice that you need to ignore updates that contradict previous updates).
If $$$t = 2$$$, two integers follow, $$$l'$$$ and $$$r'$$$ ($$$0 \leq l', r' < 2^{30}$$$), meaning that you got a query. First, do the following: $$$l = l' \oplus last$$$, $$$r = r' \oplus last$$$
and, if $$$l > r$$$, swap $$$l$$$ and $$$r$$$.
For the given query, you need to print the bitwise xor of the subarray $$$[l, r]$$$. If it is impossible to know, print $$$-1$$$. Don't forget to change the value of $$$last$$$.

It is guaranteed there will be at least one query of the second type.

Output:

After every query of the second type, output the bitwise xor of the given subarray or $$$-1$$$ if it is still impossible to know.

Sample Input:

12
2 1 2
2 1 1073741822
1 0 3 4
2 0 0
2 3 3
2 0 3
1 6 7 3
2 4 4
1 0 2 1
2 0 0
2 4 4
2 0 0

Sample Output:

-1
-1
-1
-1
5
-1
6
3
5

Sample Input:

Sample Output:

Note:

In the first example, the real queries (without being encoded) are:

12
2 1 2
2 0 1073741823
1 1 2 5
2 1 1
2 2 2
2 1 2
1 2 3 6
2 1 1
1 1 3 0
2 1 1
2 2 2
2 3 3

The answers for the first two queries are $$$-1$$$ because we don't have any such information on the array initially.
The first update tells us $$$a_1 \oplus a_2 = 5$$$. Note that we still can't be certain about the values $$$a_1$$$ or $$$a_2$$$ independently (for example, it could be that $$$a_1 = 1, a_2 = 4$$$, and also $$$a_1 = 3, a_2 = 6$$$).
After we receive all three updates, we have enough information to deduce $$$a_1, a_2, a_3$$$ independently.

In the second example, notice that after the first two updates we already know that $$$a_5 \oplus a_6 = 12$$$, so the third update is contradicting, and we ignore it.

Informação

Provedor Codeforces

Código CF1044D