B"You are given a rooted undirected tree consisting of n vertices. Vertex 1 is the root. Let's denote a depth array of vertex x as an infinite sequence [d_{x, 0}, d_{x, 1}, d_{x, 2}, ... ] , where d_{x, i} is the number of vertices y such that both conditions hold: The dominant index of a depth array of vertex x (or, shortly, the dominant index of vertex x ) is an index j such that: For every vertex in the tree calculate its dominant index. The first line contains one integer n ( 1 <= n <= 10^6 ) -- the number of vertices in a tree. Then n - 1 lines follow, each containing two integers x and y ( 1 <= x, y <= n , x ne y ). This line denotes an edge of the tree. It is guaranteed that these edges form a tree. Output n numbers. i -th number should be equal to the dominant index of vertex i . "...