Problem F
Heap

Write your own implementation of a heap, specialized to store $32$-bit signed integers. Heaps only have a few operations.

The data structure should support the following operations:

• Default construction - initializes an empty heap. This is not tested explicitly here!

• Assignment and copy construction - must properly copy the contents of another instance of the data structure. Ensure the two instances do not share memory afterwards!

• Push - must insert an element to the heap.

• Pop - must remove the smallest element from the heap.

• Peek - must provide access to the smallest element in the heap.

• Size - must provide the size of the heap.

You must avoid any memory leaks or other memory errors in your implementation.

Input

The input starts with a line containing an integer $q$, representing the number of lines that follow. Each line will represent an operation that is run. The lines have the following format: <id> <operation> [arg]

The instance ID will be an integer from $1$ to $1,000$, representing an instance of the data structure. Each instance should be default initialized at the start as an empty heap.

The operations are the following:

• a - construct a copy of the heap, takes integer argument for the instance ID of the heap to copy

• + - push a value to the heap, takes integer argument for the value to push

• - - pop the heap, no additional arguments

• p - output the smallest element in the heap, see output section

• s - output size of heap, see output section

You may assume requested operations will not cause an error in a correctly implemented data structure. For example, a pop operation on an empty heap will not occur in the input.

Output

For each peek operation, output a line with the smallest element in the heap.

For each size operation, output a line with the size of the heap.

7
1 + 1
1 p
1 + 2
1 p
1 s
1 -
1 s

1
1
2
1

6
1 + -9
1 + 6
1 + 42
2 + -5
1 s
2 s

3
1