# Deduction Queries

## 题意翻译

q此操作$(1 \leq q \leq 2 \times 10^5)$，两种操作类型： 1,l,r,x：表示l到r的异或和为x； 2,l,r：表示询问l到r的异或和。 强制在线。$(0 \leq l,r,x \leq 2^{30})$

## 题目描述

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.

## 输入输出格式

### 输入格式

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.

### 输出格式

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

## 输入输出样例

### 输入样例 #1

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


### 输出样例 #1

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


### 输入样例 #2

4
1 5 5 9
1 6 6 5
1 6 5 10
2 6 5


### 输出样例 #2

12


## 说明

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.