#include<iostream>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<utility>
#include<cassert>
#include<complex>
#include<numeric>
using namespace std;

//#define int long long
typedef long long ll;

typedef unsigned long long ul;
typedef unsigned int ui;
constexpr ll mod = 1000000007;
const ll INF = mod * mod;
typedef pair<int, int>P;
#define stop char nyaa;cin>>nyaa;
#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
#define all(v) (v).begin(),(v).end()
typedef pair<ll, ll> LP;
typedef long double ld;
typedef pair<ld, ld> LDP;
const ld eps = 1e-12;
const ld pi = acos(-1.0);

ll mod_pow(ll x, ll n) {
	ll res = 1;
	while (n) {
		if (n & 1)res = res * x % mod;
		x = x * x % mod; n >>= 1;
	}
	return res;
}
struct modint {
	ll n;
	modint() :n(0) { ; }
	modint(ll m) :n(m) {
		if (n >= mod)n %= mod;
		else if (n < 0)n = (n % mod + mod) % mod;
	}
	operator int() { return n; }
};
bool operator==(modint a, modint b) { return a.n == b.n; }
modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= mod; return a; }
modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += mod; return a; }
modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; }
modint operator+(modint a, modint b) { return a += b; }
modint operator-(modint a, modint b) { return a -= b; }
modint operator*(modint a, modint b) { return a *= b; }
modint operator^(modint a, int n) {
	if (n == 0)return modint(1);
	modint res = (a * a) ^ (n / 2);
	if (n % 2)res = res * a;
	return res;
}

ll inv(ll a, ll p) {
	return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p);
}
modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); }

const int max_n = 1 << 20;
modint fact[max_n], factinv[max_n];
void init_f() {
	fact[0] = modint(1);
	for (int i = 0; i < max_n - 1; i++) {
		fact[i + 1] = fact[i] * modint(i + 1);
	}
	factinv[max_n - 1] = modint(1) / fact[max_n - 1];
	for (int i = max_n - 2; i >= 0; i--) {
		factinv[i] = factinv[i + 1] * modint(i + 1);
	}
}
modint comb(int a, int b) {
	if (a < 0 || b < 0 || a < b)return 0;
	return fact[a] * factinv[b] * factinv[a - b];
}


void solve() {
	int n; cin >> n;
	vector<int> par(n);
	par[0] = -1;
	vector<vector<int>> G(n);
	rep1(i, n - 1) {
		cin >> par[i];
		G[par[i]].push_back(i);
	}
	vector<int> a(n);
	rep(i, n)cin >> a[i];
	vector<int> inv(n);
	rep(i, n) {
		inv[a[i]] = i;
	}
	vector<int> ans;
	auto query=[&](int v) {
		ans.push_back(v);
		int memo = a[0];
		vector<int> ids;
		int cur = v;
		while (cur != 0) {
			ids.push_back(cur);
			cur = par[cur];
		}
		reverse(all(ids));
		for (int id : ids) {
			a[par[id]] = a[id];
		}
		a[v] = memo;
		for (int id : ids) {
			inv[a[id]] = id;
		}
		inv[a[0]] = 0;
	};

	vector<bool> exi(n, true);
	while (true) {
		int tmp = 0;
		rep(i, n)if (exi[i])tmp++;
		if (tmp == 1)break;

		vector<vector<int>> vs;

		vector<int> trans(n);
		per(i, n) {
			if (!exi[i])continue;
			if (G[i].size())continue;
			int cur = i;
			vector<int>ids;
			ids.push_back(cur);
			while (true) {
				cur = par[cur];
				if (cur == 0)break;
				if (G[cur].size() > 1)break;
				ids.push_back(cur);
			}
			reverse(all(ids));
			for (int id : ids) {
				trans[id] = vs.size();
			}
			vs.push_back(ids);

		}

		vector<vector<int>> ald(vs.size());

		set<int> rest;
		for (vector<int> v : vs)for (int id : v)rest.insert(id);
		while (rest.size()) {
			int id = a[0];
			if (rest.find(id) != rest.end()) {
				rest.erase(id);
				int tid = trans[id];

				int tmp = 0;
				for (int aid : ald[tid]) {
					if (aid > id)tmp++;
				}
				query(vs[tid][vs[tid].size() - 1 - tmp]);
				ald[tid].push_back(id);
			}
			else {
				int ma = -1;
				int chk = -1;
				for (int id : rest) {
					int loc = inv[id];
					if (loc > ma) {
						ma=loc;
						chk = id;
					}
				}
				query(inv[chk]);
			}
		}

		for (vector<int> v : vs)for (int id : v) {
			exi[id] = false;
		}
		rep(i, n)if (exi[i]) {
			vector<int> nw;
			for (int to : G[i]) {
				if(exi[to])nw.push_back(to);
			}
			swap(G[i], nw);
		}
	}
	assert(ans.size() <= 30000);
	cout << ans.size() << "\n";
	rep(i, ans.size()) {
		cout << ans[i] << "\n";
	}
}




signed main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	//cout << fixed << setprecision(10);
	//init();
	//int t; cin >> t; rep(i, t)
	solve();
	return 0;
}

### Prompt

Please create a solution in CPP to the following problem:

You are given a rooted tree with N vertices. The vertices are numbered 0, 1, ..., N-1. The root is Vertex 0, and the parent of Vertex i (i = 1, 2, ..., N-1) is Vertex p_i.

Initially, an integer a_i is written in Vertex i. Here, (a_0, a_1, ..., a_{N-1}) is a permutation of (0, 1, ..., N-1).

You can execute the following operation at most 25 000 times. Do it so that the value written in Vertex i becomes i.

* Choose a vertex and call it v. Consider the path connecting Vertex 0 and v.
* Rotate the values written on the path. That is, For each edge (i, p_i) along the path, replace the value written in Vertex p_i with the value written in Vertex i (just before this operation), and replace the value of v with the value written in Vertex 0 (just before this operation).
* You may choose Vertex 0, in which case the operation does nothing.

Constraints

* 2 \leq N \leq 2000
* 0 \leq p_i \leq i-1
* (a_0, a_1, ..., a_{N-1}) is a permutation of (0, 1, ..., N-1).

Input

Input is given from Standard Input in the following format:


N
p_1 p_2 ... p_{N-1}
a_0 a_1 ... a_{N-1}


Output

In the first line, print the number of operations, Q. In the second through (Q+1)-th lines, print the chosen vertices in order.

Examples

Input

5
0 1 2 3
2 4 0 1 3


Output

2
3
4


Input

5
0 1 2 2
4 3 1 2 0


Output

3
4
3
1

### Response

```cpp
#include<iostream>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<utility>
#include<cassert>
#include<complex>
#include<numeric>
using namespace std;

//#define int long long
typedef long long ll;

typedef unsigned long long ul;
typedef unsigned int ui;
constexpr ll mod = 1000000007;
const ll INF = mod * mod;
typedef pair<int, int>P;
#define stop char nyaa;cin>>nyaa;
#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
#define all(v) (v).begin(),(v).end()
typedef pair<ll, ll> LP;
typedef long double ld;
typedef pair<ld, ld> LDP;
const ld eps = 1e-12;
const ld pi = acos(-1.0);

ll mod_pow(ll x, ll n) {
	ll res = 1;
	while (n) {
		if (n & 1)res = res * x % mod;
		x = x * x % mod; n >>= 1;
	}
	return res;
}
struct modint {
	ll n;
	modint() :n(0) { ; }
	modint(ll m) :n(m) {
		if (n >= mod)n %= mod;
		else if (n < 0)n = (n % mod + mod) % mod;
	}
	operator int() { return n; }
};
bool operator==(modint a, modint b) { return a.n == b.n; }
modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= mod; return a; }
modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += mod; return a; }
modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; }
modint operator+(modint a, modint b) { return a += b; }
modint operator-(modint a, modint b) { return a -= b; }
modint operator*(modint a, modint b) { return a *= b; }
modint operator^(modint a, int n) {
	if (n == 0)return modint(1);
	modint res = (a * a) ^ (n / 2);
	if (n % 2)res = res * a;
	return res;
}

ll inv(ll a, ll p) {
	return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p);
}
modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); }

const int max_n = 1 << 20;
modint fact[max_n], factinv[max_n];
void init_f() {
	fact[0] = modint(1);
	for (int i = 0; i < max_n - 1; i++) {
		fact[i + 1] = fact[i] * modint(i + 1);
	}
	factinv[max_n - 1] = modint(1) / fact[max_n - 1];
	for (int i = max_n - 2; i >= 0; i--) {
		factinv[i] = factinv[i + 1] * modint(i + 1);
	}
}
modint comb(int a, int b) {
	if (a < 0 || b < 0 || a < b)return 0;
	return fact[a] * factinv[b] * factinv[a - b];
}


void solve() {
	int n; cin >> n;
	vector<int> par(n);
	par[0] = -1;
	vector<vector<int>> G(n);
	rep1(i, n - 1) {
		cin >> par[i];
		G[par[i]].push_back(i);
	}
	vector<int> a(n);
	rep(i, n)cin >> a[i];
	vector<int> inv(n);
	rep(i, n) {
		inv[a[i]] = i;
	}
	vector<int> ans;
	auto query=[&](int v) {
		ans.push_back(v);
		int memo = a[0];
		vector<int> ids;
		int cur = v;
		while (cur != 0) {
			ids.push_back(cur);
			cur = par[cur];
		}
		reverse(all(ids));
		for (int id : ids) {
			a[par[id]] = a[id];
		}
		a[v] = memo;
		for (int id : ids) {
			inv[a[id]] = id;
		}
		inv[a[0]] = 0;
	};

	vector<bool> exi(n, true);
	while (true) {
		int tmp = 0;
		rep(i, n)if (exi[i])tmp++;
		if (tmp == 1)break;

		vector<vector<int>> vs;

		vector<int> trans(n);
		per(i, n) {
			if (!exi[i])continue;
			if (G[i].size())continue;
			int cur = i;
			vector<int>ids;
			ids.push_back(cur);
			while (true) {
				cur = par[cur];
				if (cur == 0)break;
				if (G[cur].size() > 1)break;
				ids.push_back(cur);
			}
			reverse(all(ids));
			for (int id : ids) {
				trans[id] = vs.size();
			}
			vs.push_back(ids);

		}

		vector<vector<int>> ald(vs.size());

		set<int> rest;
		for (vector<int> v : vs)for (int id : v)rest.insert(id);
		while (rest.size()) {
			int id = a[0];
			if (rest.find(id) != rest.end()) {
				rest.erase(id);
				int tid = trans[id];

				int tmp = 0;
				for (int aid : ald[tid]) {
					if (aid > id)tmp++;
				}
				query(vs[tid][vs[tid].size() - 1 - tmp]);
				ald[tid].push_back(id);
			}
			else {
				int ma = -1;
				int chk = -1;
				for (int id : rest) {
					int loc = inv[id];
					if (loc > ma) {
						ma=loc;
						chk = id;
					}
				}
				query(inv[chk]);
			}
		}

		for (vector<int> v : vs)for (int id : v) {
			exi[id] = false;
		}
		rep(i, n)if (exi[i]) {
			vector<int> nw;
			for (int to : G[i]) {
				if(exi[to])nw.push_back(to);
			}
			swap(G[i], nw);
		}
	}
	assert(ans.size() <= 30000);
	cout << ans.size() << "\n";
	rep(i, ans.size()) {
		cout << ans[i] << "\n";
	}
}




signed main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	//cout << fixed << setprecision(10);
	//init();
	//int t; cin >> t; rep(i, t)
	solve();
	return 0;
}

```