D. Arpa’s letter-marked tree and Mehrdad’s Dokhtar-kosh pathstime limit per test3 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputJust in case somebody missed it: we have wonderful girls in Arpa’s land.Arpa has a rooted tree (connected acyclic graph) consisting of n vertices. The vertices are numbered 1 through n, the vertex 1 is the root. There is a letter written on each edge of this tree. Mehrdad is a fan of Dokhtar-kosh things. He call a string Dokhtar-kosh, if we can shuffle the characters in string such that it becomes palindrome.  He asks Arpa, for each vertex v, what is the length of the longest simple path in subtree of v that form a Dokhtar-kosh string.InputThe first line contains integer n (1  ≤  n  ≤  5·105) — the number of vertices in the tree.(n  -  1) lines follow, the i-th of them contain an integer pi + 1 and a letter ci + 1 (1  ≤  pi + 1  ≤  i, ci + 1 is lowercase English letter, between a and v, inclusively), that mean that there is an edge between nodes pi + 1 and i + 1 and there is a letter ci + 1 written on this edge.OutputPrint n integers. The i-th of them should be the length of the longest simple path in subtree of the i-th vertex that form a Dokhtar-kosh string.ExamplesInput41 s2 a3 sOutput3 1 1 0 Input51 a2 h1 a4 hOutput4 1 0 1 0 
Input41 s2 a3 s
Output3 1 1 0 
['data structures', 'dfs and similar', 'trees', '*2900']