B'Pak Chanek has n blank heart-shaped cards. Card 1 is attached directly to the wall while each of the other cards is hanging onto exactly one other card by a piece of string. Specifically, card i ( i > 1 ) is hanging onto card p_i ( p_i < i ). In the very beginning, Pak Chanek must write one integer number on each card. He does this by choosing any permutation a of [1, 2, ... , n] . Then, the number written on card i is a_i . After that, Pak Chanek must do the following operation n times while maintaining a sequence s (which is initially empty): After that, Pak Chanek will have a sequence s with n elements. What is the maximum length of the longest non-decreasing subsequence ^ dagger of s at the end if Pak Chanek does all the steps optimally? ^ dagger A sequence b is a subsequence of a sequence c if b can be obtained from c by deletion of several (possibly, zero or all) elements. For example, [3,1] is a subsequence of [3,2,1] , [4,3,1] and [3,1] , but not [1,3,3,7] and [3,10,4] . The first line contains a single integer n ( 2 <= n <= 10^5 ) -- the number of heart-shaped cards. The second line contains n - 1 integers p_2, p_3, ... , p_n ( 1 <= p_i < i ) describing which card that each card hangs onto. Print a single integer -- the maximum length of the longest non-decreasing subsequence of s at the end if Pak Chanek does all the steps optimally. The following is the structure of the cards in the first example. Pak Chanek can choose the permutation a = [1, 5, 4, 3, 2, 6] . Let w_i be the number written on card i . Initially, w_i = a_i . Pak Chanek can do the following operations in order: One of the longest non-decreasing subsequences of s = [2, 6, 2, 4, 4, 1] is [2, 2, 4, 4] . Thus, the length of the longest non-decreasing subsequence of'...