P10650 [ROI 2017] Sorting Illusion (Day 1)

Given an integer sequence $a$ of length $n$, if an integer $b$ satisfies: $$ (a_1 \operatorname{xor} b) \le (a_2 \operatorname{xor} b) \le \dots \le (a_n \operatorname{xor} b) $$ then $b$ is called a **magic number** of the sequence $a$. Next, there are $q$ modifications. In each modification, one number $a_{u_i}$ is changed to an integer $k_i$. Each modification affects the queries that follow. You need to find the smallest magic number of the sequence before the first modification and after each modification. In particular, if no magic number exists, output $-1$.

The first line contains an integer $n$, indicating the length of the sequence. The second line contains $n$ integers, representing the integer sequence $a$. The third line contains an integer $q$, indicating the number of queries. The next $q$ lines each contain two integers $u_i$ and $k_i$, meaning that $a_{u_i}$ is modified to $k_i$.

Output a total of $(q + 1)$ lines. Each line contains one integer, representing the smallest magic number of the current sequence. If there is no magic number, output $-1$.

#### Constraints | Subtask ID | Score | $1 \le n \le$ | $1 \le q \le$ | $0 \le a_i, k_i \le$ | | :----------: | :----------: | :----------: | :----------: | :----------: | | $1$ | $30$ | $500$ | $500$ | $2^9$ | | $2$ | $29$ | $10^3$ | $10^3$ | $2^{30}$ | | $3$ | $21$ | $10^5$ | $10^5$ | $2^{30}$ | | $4$ | $30$ | $10^6$ | $10^6$ | $2^{30}$ | Translated by ChatGPT 5