In the beginning there was a node denoted as 1 and it represented the root of a tree. Your task is to
support \(Q\) queries of the form:
• Add x y – Adds a new node to the tree as a child of node \(x\). The newly added node and node \(x\) are
connected with an edge of weight \(y\). The newly added node is denoted by a number equal to the
number of nodes that the tree consists of after its addition.
• Query a b – Finds the longest path in a tree which starts in node \(a\) and ends in some node from
the subtree of node \(b\) (which itself is considered to be in its own subtree). The length of the path is
defined as exclusive or (xor) of weights of all edges that the path consists of.

Subtask
Score
Constraints
1
11
\(Q \le 200\)
2
22
\(Q \le 2\,000\)
3
33
In all queries of type Query it holds \(b = 1\)
4
44
No additional constraints.

The first line contains an integer \(Q\) (\(1 \le Q \le 200\,000\)) from the task description.
The \(i-th\) of the next \(Q\) lines contains the \(i-th\) query whose format corresponds to one of the queries from
the task description. Values \(x\), \(a\) and \(b\) will refer to an existing node at that moment and value \(y\) will not
be greater than \(2^{30}\).

You should output an answer to each query of type Query. Each answer should be printed in a separate
line in the order in which corresponding queries appear in the input.

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출처 COCI 2019/2020 Contest 4