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You ye Jiu yuan is the daughter of the Great GOD Emancipator. And when she becomes an adult, she will be queen of Tusikur, so she wanted to travel the world while she was still young. In a country, she found a small pub called Whitehouse. Just as she was about to go in for a drink, the boss Carola appeared. And ask her to solve this problem or she will not be allowed to enter the pub. The problem description is as follows:

There is a tree with $n$ nodes, each node $i$ contains weight $a[i]$, the initial value of $a[i]$ is $0$. The root number of the tree is $1$. Now you need to do the following operations:

$1)$ Multiply all weight on the path from $u$ to $v$ by $x$

$2)$ For all weight on the path from $u$ to $v$, increasing $x$ to them

$3)$ For all weight on the path from $u$ to $v$, change them to the **bitwise NOT** of them

$4)$ Ask the sum of the weight on the path from $u$ to $v$

The answer modulo $2^{64}$.

Jiu Yuan is a clever girl, but she was not good at algorithm, so she hopes that you can help her solve this problem. Ding$\backsim\backsim\backsim$

The **bitwise NOT** is a unary operation that performs logical negation on each bit, forming the ones' complement of the given binary value. Bits that are $0$ become $1$, and those that are $1$ become $0$. For example:

NOT 0111 (decimal 7) = 1000 (decimal 8)

NOT 10101011 = 01010100

The input contains multiple groups of data.

For each group of data, the first line contains a number of $n$, and the number of nodes.

The second line contains $(n - 1)$ integers $b_i$, which means that the father node of node $(i +1)$ is $b_i$.

The third line contains one integer $m$, which means the number of operations，

The next $m$ lines contain the following four operations:

At first, we input one integer opt

$1)$ If opt is $1$, then input $3$ integers, $u, v, x$, which means multiply all weight on the path from $u$ to $v$ by $x$

$2)$ If opt is $2$, then input $3$ integers, $u, v, x$, which means for all weight on the path from $u$ to $v$, increasing $x$ to them

$3)$ If opt is $3$, then input $2$ integers, $u, v$, which means for all weight on the path from $u$ to $v$, change them to the **bitwise NOT** of them

$4)$ If opt is $4$, then input $2$ integers, $u, v$, and ask the sum of the weights on the path from $u$ to $v$

$1 \le n,m,u,v \le 10^5$

$1 \le x < 2^{64}$

For each operation $4$, output the answer.

7 1 1 1 2 2 4 5 2 5 6 1 1 1 6 2 4 5 6 3 5 2 4 2 2 2 1 4 3 1 2 4 1 2 3 1 1 4 1 1

5 18446744073709551613 18446744073709551614 0