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.

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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 
#include <bits/stdc++.h>
using namespace std;
const int Inf = 1e9;
const int A = 24;
const int N = 6e5 + 1;
vector<int> g[N];
int la[N], xxx[N], sz[N], h[N], ans[N];
int arr[1LL << A];
void dfs0(int v) {
  sz[v] = 1;
  for (auto x : g[v]) {
    h[x] = h[v] + 1;
    xxx[x] = xxx[v] ^ (1LL << la[x]);
    dfs0(x);
    sz[v] += sz[x];
  }
}
int get(int v) {
  int maxi = arr[xxx[v]];
  for (int i = 0; i < A - 1; i++) maxi = max(maxi, arr[xxx[v] ^ (1LL << i)]);
  return maxi;
}
void clean(int v) {
  arr[xxx[v]] = -Inf;
  for (auto x : g[v]) clean(x);
}
int fin(int v, int base) {
  int maxi = get(v) - h[base] + h[v] - h[base];
  for (auto x : g[v]) maxi = max(maxi, fin(x, base));
  return maxi;
}
void add(int v) {
  arr[xxx[v]] = max(arr[xxx[v]], h[v]);
  for (auto x : g[v]) add(x);
}
void print(int v) {
  cout << "printing " << v + 1 << endl;
  for (int i = 0; i < (1LL << A); i++)
    if (arr[i] != -1)
      cout << i << ' ' << arr[i] + 1 << ' ' << h[arr[i]] << endl;
  cout << endl;
}
void dfs(int v) {
  int ind = -1;
  for (auto x : g[v])
    if (ind == -1 || sz[x] > sz[ind]) ind = x;
  if (ind == -1) {
    arr[xxx[v]] = max(arr[xxx[v]], h[v]);
    return;
  }
  for (auto x : g[v])
    if (x - ind) {
      dfs(x);
      ans[v] = max(ans[v], ans[x]);
      clean(x);
    }
  dfs(ind);
  ans[v] = max(ans[v], get(v) - h[v]);
  ans[v] = max(ans[v], ans[ind]);
  arr[xxx[v]] = max(arr[xxx[v]], h[v]);
  for (auto x : g[v])
    if (x - ind) {
      ans[v] = max(ans[v], fin(x, v));
      add(x);
    }
}
int main() {
  fill(arr, arr + (1LL << A), -Inf);
  int n;
  scanf("%d", &n);
  for (int i = 1; i < n; i++) {
    int p;
    char c;
    scanf("%d %c", &p, &c);
    g[--p].push_back(i);
    la[i] = c - 'a';
  }
  dfs0(0);
  dfs(0);
  for (int i = 0; i < n; i++) printf("%d ", ans[i]);
}
