A11120. Nikita and game

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 $y_{i}$ (and $y_{i}$ 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 ( $1<=m<=3·10^{5}$ ).

Next $m$ lines contain description of queries. $i$ -th line ( $1<=i<=m$ ) describes the $i$ -th level and contains an integer $y_{i}$ — the index of the parent-class of class with index $i+1$ ( $1<=y_{i}<=i$ ).

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 $x$ .