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: Initially, the collection contains n sets: {1}, {2}, {3}, ..., {n}. Input 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). Output For each type-3 command, output 2 integers: the number of elements and the sum of elements. Explanation 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} Sample Input 57 112 234 135 34 241 34 33 Sample Output 3 12 37 28 1pq Union the sets containing p and q. If p and q are already in the same set, ignore this command. 2pq Move p to the set containing q. If p and q are already in the same set, ignore this command. 3p Return the number of elements and the sum of elements in the set containing p.