#include <cstdio>

#include <cstring>

#include <iostream>

#include <algorithm>

#define N 100001

int n, m, cnt, size;

int head[N], to[N << 1], next[N << 1], root[N], sum[N * 20], ls[N * 20], rs[N * 20], ans[N], a[N], b[N];

inline int read()

{

	int x = 0, f = 1;

	char ch = getchar();

	for(; !isdigit(ch); ch = getchar()) if(ch == '-') f = -1;

	for(; isdigit(ch); ch = getchar()) x = (x << 1) + (x << 3) + ch - '0';

	return x * f;

}

inline void add(int x, int y)

{

	to[cnt] = y;

	next[cnt] = head[x];

	head[x] = cnt++;

}

inline void insert(int &now, int l, int r, int x)

{

	now = ++size;

	if(l == r)

	{

		sum[now] = 1;

		return;

	}

	int mid = (l + r) >> 1;

	if(x <= mid) insert(ls[now], l, mid, x);

	else insert(rs[now], mid + 1, r, x);

	sum[now] = sum[ls[now]] + sum[rs[now]];

}

inline void merge(int &x, int y)

{

	if(!x || !y)

	{

		x += y;

		return;

	}

	sum[x] += sum[y];

	merge(ls[x], ls[y]);

	merge(rs[x], rs[y]);

}

inline int query(int now, int l, int r, int x, int y)

{

	if(x <= l && r <= y) return sum[now];

	int mid = (l + r) >> 1, ret = 0;

	if(x <= mid) ret += query(ls[now], l, mid, x, y);

	if(mid < y) ret += query(rs[now], mid + 1, r, x, y);

	return ret;

}

inline void dfs(int u)

{

	int i, v;

	for(i = head[u]; i ^ -1; i = next[i])

	{

		v = to[i];

		dfs(v);

		merge(root[u], root[v]);

	}

	ans[u] = query(root[u], 1, m, a[u] + 1, m);

}

int main()

{

	int i, x;

	n = read();

	memset(head, -1, sizeof(head));

	for(i = 1; i <= n; i++) a[i] = b[i] = read();

	for(i = 2; i <= n; i++)

	{

		x = read();

		add(x, i);

	}

	std::sort(b + 1, b + n + 1);

	m = std::unique(b + 1, b + n + 1) - b - 1;

	for(i = 1; i <= n; i++)

		a[i] = std::lower_bound(b + 1, b + m + 1, a[i]) - b;

	for(i = 1; i <= n; i++)

		insert(root[i], 1, m, a[i]);

	dfs(1);

	for(i = 1; i <= n; i++)

		printf("%d\n", ans[i]);

	return 0;

}