4474: Arpa’s letter-marked tree and Mehrdad’s Dokhtar-kosh paths
题目描述
Just 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.
The 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.
Print 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.
4
1 s
2 a
3 s
3 1 1 0
5
1 a
2 h
1 a
4 h
4 1 0 1 0