F. Choosing Two Pathstime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given an undirected unweighted tree consisting of n vertices.An undirected tree is a connected undirected graph with n - 1 edges.Your task is to choose two pairs of vertices of this tree (all the chosen vertices should be distinct) (x_1, y_1) and (x_2, y_2) in such a way that neither x_1 nor y_1 belong to the simple path from x_2 to y_2 and vice versa (neither x_2 nor y_2 should not belong to the simple path from x_1 to y_1).It is guaranteed that it is possible to choose such pairs for the given tree.Among all possible ways to choose such pairs you have to choose one with the maximum number of common vertices between paths from x_1 to y_1 and from x_2 to y_2. And among all such pairs you have to choose one with the maximum total length of these two paths.It is guaranteed that the answer with at least two common vertices exists for the given tree.The length of the path is the number of edges in it.The simple path is the path that visits each vertex at most once.InputThe first line contains an integer n — the number of vertices in the tree (6 \le n \le 2 \cdot 10^5).Each of the next n - 1 lines describes the edges of the tree.Edge i is denoted by two integers u_i and v_i, the labels of vertices it connects (1 \le u_i, v_i \le n, u_i \ne v_i).It is guaranteed that the given edges form a tree.It is guaranteed that the answer with at least two common vertices exists for the given tree.OutputPrint any two pairs of vertices satisfying the conditions described in the problem statement.It is guaranteed that it is possible to choose such pairs for the given tree.ExamplesInput71 41 51 62 32 44 7Output3 67 5Input99 33 51 24 34 71 74 63 8Output2 96 8Input106 810 33 75 81 77 22 92 81 4Output10 64 5Input111 22 33 41 51 66 75 85 94 104 11Output9 118 10NoteThe picture corresponding to the first example: The intersection of two paths is 2 (vertices 1 and 4) and the total length is 4 + 3 = 7.The picture corresponding to the second example: The intersection of two paths is 2 (vertices 3 and 4) and the total length is 5 + 3 = 8.The picture corresponding to the third example: The intersection of two paths is 3 (vertices 2, 7 and 8) and the total length is 5 + 5 = 10.The picture corresponding to the fourth example: The intersection of two paths is 5 (vertices 1, 2, 3, 4 and 5) and the total length is 6 + 6 = 12.
Input71 41 51 62 32 44 7
Output3 67 5
['dfs and similar', 'dp', 'greedy', 'trees', '*2500']