human
A binary search tree can be unbalanced depending on features of data. For example, if we insert $n$ elements into a binary search tree in ascending order, the tree become a list, leading to long search times. One of strategies is to randomly shuffle the elements to be inserted. However, we should consider to maintain the balanced binary tree where different operations can be performed one by one depending on requirement.

We can maintain the balanced binary search tree by assigning a priority randomly selected to each node and by ordering nodes based on the following properties. Here, we assume that all priorities are distinct and also that all keys are distinct.

* binary-search-tree property. If $v$ is a left child of $u$, then $v.key < u.key$ and if $v$ is a right child of $u$, then $u.key < v.key$
* heap property. If $v$ is a child of $u$, then $v.priority < u.priority$


This combination of properties is why the tree is called Treap (tree + heap).

An example of Treap is shown in the following figure.


Insert
To insert a new element into a Treap, first of all, insert a node which a randomly selected priority value is assigned in the same way for ordinal binary search tree. For example, the following figure shows the Treap after a node with key = 6 and priority = 90 is inserted.


It is clear that this Treap violates the heap property, so we need to modify the structure of the tree by rotate operations. The rotate operation is to change parent-child relation while maintaing the binary-search-tree property.


The rotate operations can be implemented as follows.

rightRotate(Node t)
Node s = t.left
t.left = s.right
s.right = t
return s // the new root of subtree

|

leftRotate(Node t)
Node s = t.right
t.right = s.left
s.left = t
return s // the new root of subtree

---|---

The following figure shows processes of the rotate operations after the insert operation to maintain the properties.


The insert operation with rotate operations can be implemented as...
The above is tricky. Write me a correct solution in PYTHON3.
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#Here is the Python code you requested.

import sys
from collections import namedtuple

Node = namedtuple('Node', ['key', 'priority', 'left', 'right'])

class Treap:
    MAX_KEY = 2000000000
    MAX_PRIORITY = 2000000000

    def __init__(self):
        self.root = None

    def insert(self, key, priority):
        def _insert(node):
            if node is None:
                return Node(key, priority, None, None)
            k, p, left, right = node
            if key < k:
                node = Node(k, p, _insert(left), right)
                if p < node.left.priority:
                    node = self._rotate_right(node)
            elif key > k:
                node = Node(k, p, left, _insert(right))
                if p < node.right.priority:
                    node = self._rotate_left(node)
            else:  # node.key == key
                pass
            # assert(self._bst_invariant(node))
            # assert(self._heap_invariant(node))
            return node

        self.root = _insert(self.root)

    def delete(self, key):
        def _delete(node):
            if node is None:
                return None
            k, p, left, right = node
            if key < k:
                node = node._replace(left=_delete(left))
            elif key > k:
                node = node._replace(right=_delete(right))
            else:  # key == k
                if left is None:
                    node = right
                elif right is None:
                    node = left
                else:
                    if left.priority > right.priority:
                        node = _delete(self._rotate_right(node))
                    else:
                        node = _delete(self._rotate_left(node))
            # assert(self._bst_invariant(node))
            # assert(self._heap_invariant(node))
            return node

        self.root = _delete(self.root)

    def find(self, key):
        def _find(node):
            if node is None:
                return False
            if key < node.key:
                return _find(node.left)
   ...