B'Nikita plays a new computer game. There are m levels in this game. In the beginning of each level a new class appears in the game; this class is a child-class of the class yi (and yi is called parent-class for this new class). Thus, the classes form a tree. Initially there is only one class with index 1. Changing the class to its neighbour (child-class or parent-class) in the tree costs 1 coin. You can not change the class back. The cost of changing the class a to the class b is equal to the total cost of class changes on the path from a to b in the class tree. Suppose that at i -th level the maximum cost of changing one class to another is x. For each level output the number of classes such that for each of these classes there exists some other class y, and the distance from this class to y is exactly x. First line contains one integer number m -- number of queries (1 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89m xe2 x80 x89 xe2 x89 xa4 xe2 x80 x893 xc2 xb7105). Next m lines contain description of queries. i -th line (1 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89i xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89m) describes the i -th level and contains an integer yi -- the index of the parent-class of class with index i xe2 x80 x89+ xe2 x80 x891 (1 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89yi xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89i). Suppose that at i -th level the maximum cost of changing one class to another is x. For each level output the number of classes such that for each of these classes there exists some other class y, and the distance from this class to y is exactly x. '...