Problem: You have a root tree containing n vertexes. Let's number the tree vertexes with integers from 1 to n. The tree root is in the vertex 1.

Each vertex (except fot the tree root) v has a direct ancestor pv. Also each vertex v has its integer value sv. 

Your task is to perform following queries:

  * P v u (u ≠ v). If u isn't in subtree of v, you must perform the assignment pv = u. Otherwise you must perform assignment pu = v. Note that after this query the graph continues to be a tree consisting of n vertexes.
  * V v t. Perform assignment sv = t. 



Your task is following. Before starting performing queries and after each query you have to calculate expected value written on the lowest common ancestor of two equiprobably selected vertices i and j. Here lowest common ancestor of i and j is the deepest vertex that lies on the both of the path from the root to vertex i and the path from the root to vertex j. Please note that the vertices i and j can be the same (in this case their lowest common ancestor coincides with them).

Input

The first line of the input contains integer n (2 ≤ n ≤ 5·104) — the number of the tree vertexes. 

The second line contains n - 1 integer p2, p3, ..., pn (1 ≤ pi ≤ n) — the description of the tree edges. It is guaranteed that those numbers form a tree.

The third line contains n integers — s1, s2, ... sn (0 ≤ si ≤ 106) — the values written on each vertex of the tree.

The next line contains integer q (1 ≤ q ≤ 5·104) — the number of queries. Each of the following q lines contains the description of the query in the format described in the statement. It is guaranteed that query arguments u and v lie between 1 and n. It is guaranteed that argument t in the queries of type V meets limits 0 ≤ t ≤ 106.

Output

Print q + 1 number — the corresponding expected values. Your answer will be considered correct if its absolute or relative error doesn't exceed 10 - 9.

Examples

Input

5
1 2 2 1
1 2 3 4 5
5
P 3 4
P 4 5
V 2 3
P 5 2
P 1 4


Output

1.640000000
1.800000000
2.280000000
2.320000000
2.800000000
1.840000000

Note

Note that in the query P v u if u lies in subtree of v you must perform assignment pu = v. An example of such case is the last query in the sample.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int n, m, tp, x, y, pa[55555], a[55555], sub[55555], q;
vector<int> g[55555];
long long ans;
char opt[11];
struct LCT {
  int ch[333333][2], f[333333], st[333333];
  int a[333333], p[333333], sub[333333], tag1[333333];
  long long sum[333333], sb[333333];
  bool isrt(int x) {
    if (!f[x]) return 1;
    return (ch[f[x]][0] != x && ch[f[x]][1] != x);
  }
  int get(int x) { return (ch[f[x]][1] == x); }
  void pushup(int x) {
    sum[x] = sum[ch[x][0]] + sum[ch[x][1]] + 1ll * a[x] * p[x];
    sub[x] = sub[ch[x][0]] + sub[ch[x][1]] + a[x];
  }
  void push1(int x, int y) {
    tag1[x] += y;
    sb[x] += (1ll * a[x] * y);
  }
  void pushdown(int x) {
    if (tag1[x]) {
      push1(ch[x][0], tag1[x]);
      push1(ch[x][1], tag1[x]);
      tag1[x] = 0;
    }
  }
  void rotate(int x) {
    int fa = f[x], gfa = f[fa];
    int wh = get(x);
    ch[fa][wh] = ch[x][wh ^ 1];
    f[ch[x][wh ^ 1]] = fa;
    ch[x][wh ^ 1] = fa;
    if (!isrt(fa)) ch[gfa][ch[gfa][1] == fa] = x;
    f[fa] = x;
    f[x] = gfa;
    pushup(fa);
  }
  void splay(int x) {
    int y = x, z = 0;
    st[++z] = y;
    while (!isrt(y)) {
      y = f[y];
      st[++z] = y;
    }
    while (z) pushdown(st[z--]);
    for (int fa; (fa = f[x]) && !isrt(x); rotate(x)) {
      if (!isrt(fa)) {
        if (get(fa) == get(x))
          rotate(fa);
        else
          rotate(x);
      }
    }
    pushup(x);
  }
  void access(int x) {
    for (int y = 0; x; y = x, x = f[x]) {
      splay(x);
      a[x] += sub[ch[x][1]];
      a[x] -= sub[y];
      ch[x][1] = y;
      pushup(x);
    }
  }
  int findroot(int x) {
    access(x);
    splay(x);
    int pos = x;
    while (ch[pos][0]) {
      pushdown(pos);
      pos = ch[pos][0];
    }
    splay(pos);
    return pos;
  }
  void fuckit(int x, int y) {
    access(x);
    access(pa[x]);
    int ss = sub[x];
    splay(pa[x]);
    a[pa[x]] -= ss;
    pushup(pa[x]);
    ans -= (2ll * sum[pa[x]] * ss);
    push1(pa[x], -2 * ss);
    access(y);
    f[x] = pa[x] = y;
    splay(y);
    ans += (2ll * sum[y] * ss);
    push1(y, 2 * ss);
    a[y] += ss;
    pushup(y);
  }
  void perform(int x, int y) {
    if (x == 1)
      fuckit(y, x);
    else {
      access(x);
      access(pa[x]);
      f[x] = 0;
      int ss = sub[x];
      splay(pa[x]);
      a[pa[x]] -= ss;
      pushup(pa[x]);
      if (findroot(y) == x) {
        access(pa[x]);
        f[x] = pa[x];
        splay(pa[x]);
        a[pa[x]] += ss;
        pushup(pa[x]);
        fuckit(y, x);
      } else {
        access(pa[x]);
        f[x] = pa[x];
        splay(pa[x]);
        a[pa[x]] += ss;
        pushup(pa[x]);
        fuckit(x, y);
      }
    }
  }
  void upd(int x, int y) {
    splay(x);
    p[x] += y;
    pushup(x);
    ans += (1ll * y * sb[x]);
  }
} lct;
void dfs(int i) {
  sub[i] = 1;
  for (int j = 0; j < g[i].size(); j++) {
    int to = g[i][j];
    dfs(to);
    sub[i] += sub[to];
  }
}
void Out() {
  double x = (double)ans / (double)n / (double)n;
  printf("%.9lf\n", x);
}
int main() {
  scanf("%d", &n);
  for (int i = 2; i <= n; i++) scanf("%d", &pa[i]);
  for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
  for (int i = 2; i <= n; i++) {
    g[pa[i]].push_back(i);
  }
  dfs(1);
  for (int i = 1; i <= n; i++) {
    ans += (1ll * sub[i] * sub[i] * a[i]);
    lct.sb[i] += (1ll * sub[i] * sub[i]);
    for (int j = 0; j < g[i].size(); j++) {
      int to = g[i][j];
      ans -= (1ll * sub[to] * sub[to] * a[i]);
      lct.sb[i] -= (1ll * sub[to] * sub[to]);
    }
  }
  for (int i = 1; i <= n; i++) {
    lct.a[i] = lct.sub[i] = sub[i];
    lct.p[i] = a[i];
    lct.sum[i] = 1ll * lct.a[i] * lct.p[i];
  }
  for (int i = 2; i <= n; i++) lct.f[i] = pa[i];
  Out();
  scanf("%d", &q);
  for (int i = 1; i <= q; i++) {
    scanf("%s", opt);
    if (opt[0] == 'P') {
      scanf("%d%d", &x, &y);
      lct.perform(x, y);
    } else {
      scanf("%d%d", &x, &y);
      lct.upd(x, y - a[x]);
      a[x] = y;
    }
    Out();
  }
  return 0;
}