#include <bits/stdc++.h>
using namespace std;

const int N=1e5+10;
const int BIT_SIZE=1e5+5;

int a[N];
pair<int, int> p[N];
vector<int> g[N];
int sol[N], t;
int bit[BIT_SIZE];
int lson[N], rson[N];
int n;

struct Query
{
    int pos, type, val, idx;
    bool operator<(const Query &qv) const
    {
        if (pos==qv.pos) return type<qv.type;
        return pos<qv.pos;
    }
};

vector<Query> q;

void update (int x, int val)
{
    while (x<=BIT_SIZE)
    {
        bit[x]+=val;
        x+=x&-x;
    }
}

int get (int x)
{
    int ret=0;
    while (x>0)
    {
        ret+=bit[x];
        x-=x&-x;
    }
    return ret;
}

void compress ()
{
    sort (p+1, p+n+1);
    int last=0, k=0;
    for (int i=1;i<=n;i++)
    {
        if (p[i].first==last) a[p[i].second]=k;
        else a[p[i].second]=++k;
        last=p[i].first;
    }
}

int dfs (int v, int prev)
{
    lson[v]=rson[v]=++t;
    q.push_back({lson[v], 1, a[v], 0});
    for (auto xt: g[v])
    {
        if (xt==prev) continue;
        rson[v]=dfs(xt, v);
    }
    return rson[v];
}

int main()
{
    freopen("promote.in", "r", stdin);
    freopen("promote.out", "w", stdout);

    scanf ("%d", &n);
    for (int i=1;i<=n;i++)
    {
        scanf ("%d", &a[i]);
        p[i]=make_pair(a[i], i);
    }

    compress();

    for (int i=2;i<=n;i++)
    {
        int x;
        scanf ("%d", &x);
        g[i].push_back(x);
        g[x].push_back(i);
    }

    dfs (1, 0);

    for (int i=1;i<=n;i++)
    {
        q.push_back({lson[i], 0, a[i], i});
        q.push_back({rson[i], 2, a[i], i});
    }

    sort (q.begin(), q.end());
    for (int i=0;i<q.size();i++)
    {
        Query xt=q[i];
        if (xt.type==1) update (xt.val, 1);
        if (xt.type==0) sol[xt.idx]-=get(xt.val);
        if (xt.type==2) sol[xt.idx]+=get(xt.val);
    }

    for (int i=1;i<=n;i++) printf ("%d\n", rson[i]-lson[i]+1-sol[i]);

    return 0;
}