B"There is one apple tree in Arkady's garden. It can be represented as a set of junctions connected with branches so that there is only one way to reach any junctions from any other one using branches. The junctions are enumerated from 1 to n , the junction 1 is called the root. A subtree of a junction v is a set of junctions u such that the path from u to the root must pass through v . Note that v itself is included in a subtree of v . A leaf is such a junction that its subtree contains exactly one junction. The New Year is coming, so Arkady wants to decorate the tree. He will put a light bulb of some color on each leaf junction and then count the number happy junctions. A happy junction is such a junction t that all light bulbs in the subtree of t have different colors. Arkady is interested in the following question: for each k from 1 to n , what is the minimum number of different colors needed to make the number of happy junctions be greater than or equal to k ? The first line contains a single integer n ( 1 <= n <= 10^5 ) -- the number of junctions in the tree. The second line contains n - 1 integers p_2 , p_3 , ..., p_n ( 1 <= p_i < i ), where p_i means there is a branch between junctions i and p_i . It is guaranteed that this set of branches forms a tree. Output n integers. The i -th of them should be the minimum number of colors needed to make the number of happy junctions be at least i . In the first example for k = 1 and k = 2 we can use only one color: the junctions 2 and 3 will be happy. For k = 3 you have to put the bulbs of different colors to make all the junctions happy. In the second example for k = 4 you can, for example, put the bulbs of color 1 in junctions 2 and 4 , and a bulb of color 2 into junction 5 . The happy junc"...