Problem1675--Arpa’s letter-marked tree and Mehrdad’s Dokhtar-kosh paths

1675: Arpa’s letter-marked tree and Mehrdad’s Dokhtar-kosh paths

Time Limit: 2 Sec  Memory Limit: 256 MB
Submit: 0  Solved: 0
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Description

time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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.

Examples
Input
4
1 s
2 a
3 s
Output
3 1 1 0
Input
5
1 a
2 h
1 a
4 h
Output
4 1 0 1 0

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