I hope you know the beautiful Union-Find structure. In this problem, you're to implement something similar, but not identical.
The data structure you need to write is also a collection of disjoint sets, supporting 3 operations:
1 p q
Union the sets containing p and q. If p and q are already in the same set, ignore this command.
2 p q
Move p to the set containing q. If p and q are already in the same set, ignore this command
3 p
Return the number of elements and the sum of elements in the set containing p.
Initially, the collection contains n sets: {1}, {2}, {3}, ..., {n}.
There are several test cases. Each test case begins with a line containing two integers n and m (1<=n,m<=100,000), the number of integers, and the number of commands. Each of the next m lines contains a command. For every operation, 1<=p,q<=n. The input is terminated by end-of-file (EOF). The size of input file does not exceed 5MB.
For each type-3 command, output 2 integers: the number of elements and the sum of elements.
5 7 1 1 2 2 3 4 1 3 5 3 4 2 4 1 3 4 3 3
3 12 3 7 2 8
Initially: {1}, {2}, {3}, {4}, {5}
Collection after operation 1 1 2: {1,2}, {3}, {4}, {5}
Collection after operation 2 3 4: {1,2}, {3,4}, {5} (we omit the empty set that is produced when taking out 3 from {3})
Collection after operation 1 3 5: {1,2}, {3,4,5}
Collection after operation 2 4 1: {1,2,4}, {3,5}