Arpa’s letter-marked tree and Mehrdad’s Dokhtar-kosh paths

Time Limit: 3 seconds

Memory Limit: 256 megabytes

Description

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.

Input

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.

Output

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.

Sample Input

Input41 s2 a3 sOutput3 1 1 0 Input51 a2 h1 a4 hOutput4 1 0 1 0

Sample Output

None

None

None