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;
const int MAXN = 50005;
struct node {
  int isroot;
  long long sum, sumtot, sumval, lazy, val, tot, all;
  node *ch[2], *p, *fa;
  node() {
    isroot = sum = sumtot = sumval = lazy = val = tot = all = 0;
    ch[0] = ch[1] = p = fa = this;
  }
  void setc(node *o, int d) {
    ch[d] = o;
    o->p = this;
  }
  int cd() { return this == p->ch[1] ? 1 : 0; }
  void add(long long x) {
    all += x * tot * 2;
    lazy += x;
  }
  void pd();
  void pushup() {
    sumval = ch[0]->sumval + ch[1]->sumval + val;
    sumtot = ch[0]->sumtot + ch[1]->sumtot + tot;
    sum = ch[0]->sum + ch[1]->sum + val * tot;
  }
} Tnull, *null = &Tnull;
node hehe[MAXN];
node *vex[MAXN];
node *C = hehe;
void node::pd() {
  if (lazy != 0) {
    for (int i = 0; i < 2; i++)
      if (ch[i] != null) ch[i]->add(lazy);
    lazy = 0;
  }
}
node *newnode() {
  C->isroot = C->sum = C->sumtot = C->sumval = C->lazy = C->val = C->tot =
      C->all = 0;
  C->fa = C->ch[1] = C->ch[0] = C->p = null;
  return C++;
}
void pushdown(node *o) {
  node *stk[MAXN];
  int top = 0;
  while (o != null) {
    stk[top++] = o;
    o = o->p;
  }
  for (int i = top - 1; i >= 0; i--) stk[i]->pd();
}
void rot(node *o) {
  int d = o->cd();
  node *k = o->p;
  k->setc(o->ch[d ^ 1], d);
  k->p->setc(o, k->cd());
  o->setc(k, d ^ 1);
  k->pushup();
  if (k->isroot) {
    k->isroot = 0;
    o->isroot = 1;
    o->fa = k->fa;
    k->fa = null;
  }
}
void splay(node *o) {
  pushdown(o);
  while (o->p != null) {
    if (o->p->p == null)
      rot(o);
    else
      o->cd() == o->p->cd() ? (rot(o->p), rot(o)) : (rot(o), rot(o));
  }
  o->pushup();
}
void access(node *o) {
  for (node *v = null; o != null; o = o->fa) {
    splay(o);
    o->ch[1]->isroot = 1;
    o->ch[1]->fa = o;
    o->ch[1]->p = null;
    o->tot += o->ch[1]->sumtot;
    o->setc(v, 1);
    o->tot -= v->sumtot;
    o->pushup();
    v->isroot = 0;
    v->fa = null;
    v = o;
  }
}
vector<int> head[MAXN];
int a[MAXN];
long long ans;
void dfs(int u, int p) {
  vex[u] = newnode();
  vex[u]->val = a[u];
  vex[u]->fa = vex[p];
  vex[u]->tot = 1;
  vex[u]->all = 1;
  int L = head[u].size();
  for (int i = 0; i < L; i++) {
    int v = head[u][i];
    if (v == p) continue;
    dfs(v, u);
    vex[u]->all += vex[u]->tot * vex[v]->tot * 2;
    vex[u]->tot += vex[v]->tot;
  }
  ans += vex[u]->all * vex[u]->val;
  vex[u]->pushup();
}
node *getfa(node *o) {
  splay(o);
  if (o->ch[0] == null) return o->fa;
  node *k = o->ch[0];
  while (k->ch[1] != null) {
    k = k->ch[1];
  }
  return k;
}
void fx(node *u, node *v) {
  access(u), splay(v);
  if (v->fa != null) swap(u, v);
  node *k = getfa(u);
  if (k == v) return;
  access(k), splay(k);
  k->tot -= u->sumtot, k->pushup();
  ans -= u->sumtot * k->sum * 2;
  k->add(-u->sumtot);
  access(v), splay(v);
  ans += u->sumtot * v->sum * 2;
  v->add(u->sumtot);
  v->tot += u->sumtot, v->pushup();
  u->fa = v;
}
void addw(node *u, long long w) {
  access(u), splay(u);
  ans += u->all * (w - u->val);
  u->val = w;
}
int main() {
  int n;
  scanf("%d", &n);
  for (int i = 2; i <= n; i++) {
    int p;
    scanf("%d", &p);
    head[p].push_back(i);
  }
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
  }
  ans = 0;
  vex[0] = null;
  dfs(1, 0);
  printf("%.10lf\n", ans * 1.0 / ((long long)n * (long long)n));
  int m;
  scanf("%d", &m);
  for (int i = 0; i < m; i++) {
    char s[2];
    int u, v;
    scanf("%s%d%d", s, &u, &v);
    if (s[0] == 'P') {
      fx(vex[v], vex[u]);
    } else {
      addw(vex[u], v);
    }
    printf("%.10lf\n", ans * 1.0 / ((long long)n * (long long)n));
  }
  return 0;
}