CF1044D.Deduction Queries

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.

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.

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

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.