E-Commerce Catalog Management

You are given a system to manage an e-commerce catalog organized as a hierarchical tree of categories. Each category can have products and subcategories. Your task is to implement the catalog system with three operations:

• add <category_id> <product_id>: Add a product with id product_id to the category category_id.
• query <category_id>: Query the total number of unique products in the category category_id and all of its descendant subcategories.
• <parent_id> <child_id>: Add a subcategory relationship by making child_id a direct child of parent_id.

Input consists of a series of operations, one per line. The sequence terminates with a single line containing a "0". For every query operation, print the answer on a new line.

Note: If a product is added to multiple categories within the same hierarchy, it should only be counted once in the query result.

inputFormat

The input is given from standard input (stdin) as multiple lines. Each line (except the last) represents an operation in one of the following formats:

• add <category_id> <product_id>
• query <category_id>
• <parent_id> <child_id> — to add a subcategory.

The last line of input is a single 0 which indicates the end of operations.

outputFormat

For each query operation encountered in the input, output one line containing a single integer representing the count of unique products in the queried category (including all its subcategories).

## sample

add 1 101
add 2 102
add 2 103
add 3 104
1 2
1 3
query 1
query 2
query 3
0

4
2
1

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