#include<bits/stdc++.h>
using namespace std;
const int N = 100010;
vector<int> G[N];
int n, sum, cnt;
int t[N], id[N], size[N * 20], lc[N * 20], rc[N * 20], ans[N], root[N * 20];
bool cp(int i, int j) { return t[i] < t[j]; } 
void update(int l, int r, int &x, int pos)
{
    x = ++cnt; int mid = (l + r) >> 1;
    ++size[x]; if(l == r) return; 
    if(pos <= mid) update(l, mid, lc[x], pos);
    else update(mid + 1, r, rc[x], pos); 
}
int merge(int x, int y)
{
    if(!x || !y) return x + y;
    sum += size[lc[x]] * size[rc[y]];
    lc[x] = merge(lc[x], lc[y]);
    rc[x] = merge(rc[x], rc[y]);
    size[x] = size[lc[x]] + size[rc[x]];
    return x; 
}
void dfs(int u)
{
    int last = 0;
    for(int i = 0; i < G[u].size(); ++i)
    {
        int v = G[u][i];
        dfs(v); root[v] = merge(root[v], root[last]);
        last = v;
    }
    sum = 0; root[u] = merge(root[u], root[last]);
    ans[u] = sum;
}
int main()
{
    scanf("%d", &n);
    for(int i = 1; i <= n; ++i) 
    {
        scanf("%d", &t[i]); id[i] = i;
    }
    sort(id + 1, id + n + 1, cp);
    for(int i = 1; i <= n; ++i) t[id[i]] = t[id[i - 1]] + (t[id[i]] != t[id[i - 1]]);
    for(int i = 1; i <= n; ++i) update(1, n, root[i], t[i]);
    for(int i = 2; i <= n; ++i) 
    {
        int x; scanf("%d", &x);
        G[x].push_back(i);
    }
    dfs(1);
    for(int i = 1; i <= n; ++i) printf("%d\n", ans[i]);
    return 0;
}