Implementation of d-ary Heap Operations

Implement a d-ary heap with d = 3 that supports a set of operations. The heap should maintain a collection of integers and must support the following commands:

• insert x: Insert the integer x into the heap.
• extract_min: Remove and output the smallest element in the heap. Output NULL if the heap is empty.
• delete x: Delete the element x from the heap if it exists. If there are multiple occurrences, remove any one.
• show: Display the current elements in the heap in increasing order separated by spaces. If the heap is empty, output EMPTY.

Your program should read from standard input and write to standard output. The first line of input contains an integer Q specifying the number of operations, followed by Q lines each containing one command.

Note: All formulas or specific conditions should be written in LaTeX format if needed. For example, the d-ary heap is defined with $d=3$ in this problem.

inputFormat

The input begins with an integer Q, the number of operations. Each of the following Q lines contains one command. Commands are of the following form:

• insert x
• extract_min
• delete x
• show

There is a single space between the command and the integer (when applicable).

outputFormat

For each operation that produces an output (extract_min and show), print the result on a new line. The output should be exactly as follows:

• If the heap is empty and a show command is issued, print EMPTY.
• If the heap is empty and an extract_min command is issued, print NULL.
• Otherwise, print the smallest element or the sorted list of elements as required.

## sample

12
insert 5
insert 3
insert 4
show
extract_min
show
delete 4
show
extract_min
show
extract_min
show

3 4 5
3
4 5
5
5
EMPTY
NULL
EMPTY

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