#include <bits/stdc++.h>   using namespace std;   const int N = 5e4 + 10, max_node = N * 200;   int n, m, q, C, c[N], a[N], size[N], heavy[N], dfn[N], dfn_t, top[N], father[N],       tt, lo[max_node], ro[max_node], addv[max_node];   long long sum[max_node], sum2[max_node];   vector<int> graph[N], nodes[N];   void dfs1(int u) {     size[u] = 1;     for (auto v : graph[u]) {       dfs1(v);       size[u] += size[v];       if (size[v] > size[heavy[u]]) {         heavy[u] = v;       }     }   }   void dfs2(int u, int t) {     top[u] = t;     dfn[u] = ++dfn_t;     if (heavy[u]) {       dfs2(heavy[u], t);       for (auto v : graph[u]) {         if (v != heavy[u]) {           dfs2(v, v);         }       }     }   }   void add(int l, int r, int o, int v) {     addv[o] += v;     sum2[o] += ((sum[o] << 1) + (r - l + 1) * v) * v;     sum[o] += (r - l + 1) * v;   }   void push_down(int l, int r, int o) {     if (addv[o]) {       int mid = l + r >> 1;       if (!lo[o]) {         lo[o] = ++tt;       }       if (!ro[o]) {         ro[o] = ++tt;       }       add(l, mid, lo[o], addv[o]);       add(mid + 1, r, ro[o], addv[o]);       addv[o] = 0;     }   }   void push_up(int o) {     sum[o] = sum[lo[o]] + sum[ro[o]];     sum2[o] = sum2[lo[o]] + sum2[ro[o]];   }   void modify(int l, int r, int& o, int ql, int qr, int v) {     if (!o) {       o = ++tt;     }     if (ql <= l && r <= qr) {       return add(l, r, o, v);     } else {       int mid = l + r >> 1;       push_down(l, r, o);       if (ql <= mid) {         modify(l, mid, lo[o], ql, qr, v);       }       if (qr > mid) {         modify(mid + 1, r, ro[o], ql, qr, v);       }       push_up(o);     }   }   struct info_t {     int root;     void init(vector<int>& nodes) {       for (auto v : nodes) {         for (int x = v; x; x = father[top[x]]) {           modify(1, n, root, dfn[top[x]], dfn[x], 1);         }       }     }     void update(int u, int type) {       for (int x = u; x; x = father[top[x]]) {         modify(1, n, root, dfn[top[x]], dfn[x], type);       }     }     double get_answer(int c) {       double result = (double)C * C;       result -= 2.0 * C * c * sum[root] / n;       result += 1.0 * c * c * sum2[root] / n;       return result;     }   } info[N];   int main() {     scanf( %d%d%d%d , &n, &m, &q, &C);     for (int i = 1; i <= n; ++i) {       scanf( %d , &a[i]);       nodes[a[i]].push_back(i);     }     for (int i = 2; i <= n; ++i) {       scanf( %d , &father[i]);       graph[father[i]].push_back(i);     }     for (int i = 1; i <= m; ++i) {       scanf( %d , &c[i]);     }     dfs1(1);     dfs2(1, 1);     for (int i = 1; i <= m; ++i) {       info[i].init(nodes[i]);     }     while (q--) {       int type, x, w;       scanf( %d , &type);       if (type == 1) {         scanf( %d%d , &x, &w);         info[a[x]].update(x, -1);         a[x] = w;         info[a[x]].update(x, 1);       } else {         scanf( %d , &x);         printf( %.12lf n , info[x].get_answer(c[x]));       }     }     return 0;   }   