#P741D. Arpa’s letter-marked tree and Mehrdad’s Dokhtar-kosh paths

    ID: 348 远端评测题 3000ms 256MiB 尝试: 0 已通过: 0 难度: (无) 上传者: 标签>data structuresdfs and similartrees*2900

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

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.

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.

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.

Samples

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