Notebook

Ivan is writing down numbers in his notebook. In the beginning he has a set of integers $S$ written down. Afterwards, he may write down new numbers in his notebook, by using the following operations:

• If he has the number $x$ written, he may write down $2x$.
• If he has the number $x$ written, and $x$ is divisible by $2$, he may write down $\frac{x}{2}$.
• If he has the distinct numbers $x$ and $y$ written, he may write down $x \text{ xor } y$.

Denote by $f(S)$ the minimal number Ivan can write down in his notebook for the starting set $S$.

You are given an array of length $N$ and $Q$ queries where you have to perfortm one of the following operations:

• Change the value of the $a\[x]$ to $y$.
• Find the value of $f(\\{a\[L],a\[L+1],\cdots,a\[R]\\})$.

In the first line of input is the numbers $N$ ($N\leq 100000$): the length of the array.

In the second line of input is $N$ integers $a\[1],a\[2],\cdots,a\[N]$ ($0\<a\[i]<2^{62}$), the elements of $a$.

In the thirst line of input is the number $Q$ ($Q\leq 100000$): the number of queries.

The following $Q$ lines describe the queires. A query can either be of the format "$1$ $x$ $y$" meaning set $a\[x]$ ($1\leq x\leq N$) to $y$ ($0\<y<2^{62}$), or of the format "$2$ $l$ $r$" meaning find the value of  $f(\\{a\[L],a\[L+1],\cdots,a\[R]\\})$ ($1\leq L\leq R\leq N$).

For every query of type two print the value of $f(\\{a\[L],a\[L+1],\cdots,a\[R]\\})$ in a single line.