DSU with Component Size

Extend your DSU with a size(int x) query that returns how many elements are in the component currently containing x. Each node starts in a singleton component of size 1. unite(a, b) merges the components containing a and b (a no-op if they're already connected); afterward, size must report the merged count for every member of that component, not just its root.

Operations arrive as U a b (unite) or S x (print size(x) on its own line).

Example: DSU dsu(5); dsu.unite(0, 1); dsu.unite(1, 2): nodes 0, 1, 2 are now one component of size 3, so dsu.size(0) == 3. Node 3 was never touched, so dsu.size(3) == 1; merging elsewhere doesn't inflate untouched singletons.

Input format: each test in tests/*.in is laid out as:

• Line 1: n q, the element count and the number of operations; elements are numbered 0 to n - 1.
• Next q lines: one operation each, either U a b (union) or S x (print the size of x's component).

Test 03.in reads:

3 2
S 0
S 2

This is 3 elements with no unions at all, just two size queries; every component is still a singleton, so both print 1.

Where you'll use it:

• 803. Bricks Falling When Hit
• Road Construction (CSES)