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

#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
#define ordered_set tree<int, null_type,less<int>, rb_tree_tag,tree_order_statistics_node_update>

const long long maxn = 1e5+10;
int n;
int val[maxn];
ordered_set num[maxn];
vector<int>g[maxn];
int ans[maxn];
void swap_ordered_set(ordered_set &a, ordered_set &b) {
    a.swap(b);
}
void solve(int node,int par)
{
    for(auto ax:g[node])
    {
        if(ax==par)continue;
        solve(ax,node);
        if(num[node].size()<num[ax].size())
        {
            swap_ordered_set(num[node],num[ax]);
        }
        for(auto i:num[ax])
        {
            num[node].insert(i);
        }
    }
    ///pomali od val[node]+1;
    int L=num[node].order_of_key(val[node]+1);
    ans[node]=num[node].size()-L;
    num[node].insert(val[node]);
}

int main() {
    ios_base::sync_with_stdio(false);
    freopen("promote.in", "r", stdin);
    freopen("promote.out", "w", stdout);
    ///ordered_set o_set;
    cin>>n;
    for(int i=0;i<n;i++)
    {
        cin>>val[i];
        
    }
    for(int i=1;i<n;i++)
    {
        int x;
        cin>>x;
        x--;
        g[x].push_back(i);
    }
    solve(0,-1);
    for(int i=0;i<n;i++)
    {
        cout<<ans[i]<<'\n';
    }
    return 0;
}