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

using ll=long long;
#define int ll

#define rng(i,a,b) for(int i=int(a);i<int(b);i++)
#define rep(i,b) rng(i,0,b)
#define gnr(i,a,b) for(int i=int(b)-1;i>=int(a);i--)
#define per(i,b) gnr(i,0,b)
#define pb push_back
#define eb emplace_back
#define a first
#define b second
#define bg begin()
#define ed end()
#define all(x) x.bg,x.ed
#ifdef LOCAL
#define dmp(x) cerr<<__LINE__<<" "<<#x<<" "<<x<<endl
#else
#define dmp(x) void(0)
#endif

template<class t,class u> void chmax(t&a,u b){if(a<b)a=b;}
template<class t,class u> void chmin(t&a,u b){if(b<a)a=b;}

template<class t> using vc=vector<t>;
template<class t> using vvc=vc<vc<t>>;

using pi=pair<int,int>;
using vi=vc<int>;

template<class t,class u>
ostream& operator<<(ostream& os,const pair<t,u>& p){
	return os<<"{"<<p.a<<","<<p.b<<"}";
}

template<class t> ostream& operator<<(ostream& os,const vc<t>& v){
	os<<"{";
	for(auto e:v)os<<e<<",";
	return os<<"}";
}

#define mp make_pair
#define mt make_tuple
#define one(x) memset(x,-1,sizeof(x))
#define zero(x) memset(x,0,sizeof(x))
#ifdef LOCAL
void dmpr(ostream&os){os<<endl;}
template<class T,class... Args>
void dmpr(ostream&os,const T&t,const Args&... args){
	os<<t<<" ";
	dmpr(os,args...);
}
#define dmp2(...) dmpr(cerr,"Line:",__LINE__,##__VA_ARGS__)
#else
#define dmp2(...) void(0)
#endif

using uint=unsigned;
using ull=unsigned long long;

template<int i,class T>
void print_tuple(ostream&,const T&){
}

template<int i,class T,class H,class ...Args>
void print_tuple(ostream&os,const T&t){
	if(i)os<<",";
	os<<get<i>(t);
	print_tuple<i+1,T,Args...>(os,t);
}

template<class ...Args>
ostream& operator<<(ostream&os,const tuple<Args...>&t){
	os<<"{";
	print_tuple<0,tuple<Args...>,Args...>(os,t);
	return os<<"}";
}

void print(ll x,int suc=1){
	cout<<x;
	if(suc==1)
		cout<<"\n";
	if(suc==2)
		cout<<" ";
}

ll read(){
	ll i;
	cin>>i;
	return i;
}

vi readvi(int n,int off=0){
	vi v(n);
	rep(i,n)v[i]=read()+off;
	return v;
}

template<class T>
void print(const vector<T>&v,int suc=1){
	rep(i,v.size())
		print(v[i],i==int(v.size())-1?suc:2);
}

string readString(){
	string s;
	cin>>s;
	return s;
}

template<class T>
T sq(const T& t){
	return t*t;
}

//#define CAPITAL
void yes(bool ex=true){
	#ifdef CAPITAL
	cout<<"YES"<<endl;
	#else
	cout<<"Yes"<<endl;
	#endif
	if(ex)exit(0);
}
void no(bool ex=true){
	#ifdef CAPITAL
	cout<<"NO"<<endl;
	#else
	cout<<"No"<<endl;
	#endif
	if(ex)exit(0);
}

constexpr ll ten(int n){
	return n==0?1:ten(n-1)*10;
}

const ll infLL=LLONG_MAX/3;

#ifdef int
const int inf=infLL;
#else
const int inf=INT_MAX/2-100;
#endif

int topbit(signed t){
	return t==0?-1:31-__builtin_clz(t);
}
int topbit(ll t){
	return t==0?-1:63-__builtin_clzll(t);
}
int botbit(signed a){
	return a==0?32:__builtin_ctz(a);
}
int botbit(ll a){
	return a==0?64:__builtin_ctzll(a);
}
int popcount(signed t){
	return __builtin_popcount(t);
}
int popcount(ll t){
	return __builtin_popcountll(t);
}
bool ispow2(int i){
	return i&&(i&-i)==i;
}
int mask(int i){
	return (int(1)<<i)-1;
}

bool inc(int a,int b,int c){
	return a<=b&&b<=c;
}

template<class t> void mkuni(vc<t>&v){
	sort(all(v));
	v.erase(unique(all(v)),v.ed);
}

ll rand_int(ll l, ll r) { //[l, r]
	#ifdef LOCAL
	static mt19937_64 gen;
	#else
    static random_device rd;
    static mt19937_64 gen(rd());
    #endif
    return uniform_int_distribution<ll>(l, r)(gen);
}

const int nmax=2010;

vi t[nmax];
int dep[nmax];

void dfs(int v,int d){
	dep[v]=d;
	for(auto c:t[v])
		dfs(c,d+1);
}

signed main(){
	cin.tie(0);
	ios::sync_with_stdio(0);
	cout<<fixed<<setprecision(20);
	
	int n;cin>>n;
	bool dbg=n<0;
	if(dbg){
		n=-n;
	}
	vi par(n,-1);
	rng(i,1,n){
		if(!dbg)cin>>par[i];
		else par[i]=rand_int(0,i-1);
		t[par[i]].pb(i);
	}
	dmp(par);
	
	dfs(0,0);
	
	vi a(n);
	if(!dbg)rep(i,n)cin>>a[i];
	else{
		iota(all(a),0);
		rep(i,n)swap(a[rand_int(0,i)],a[i]);
	}
	dmp(a);
	
	vi b(n);
	
	vi ans;
	auto rotate=[&](int i){
		ans.pb(i);
		vi vs;
		while(i>=0){
			vs.pb(i);
			i=par[i];
		}
		reverse(all(vs));
		rep(j,(int)vs.size()-1){
			swap(a[vs[j]],a[vs[j+1]]);
			swap(b[vs[j]],b[vs[j+1]]);
		}
		b[vs.back()]=1;
	};
	
	vi did(n);
	vi deg(n);
	rep(i,n)deg[i]=t[i].size();
	
	while(!did[0]){
		b=did;
		
		vi id(n,-1);
		vvc<int> vss;
		rep(i,n)if(!b[i]&&deg[i]==0){
			vi x;
			int w=i;
			while(w>=0&&deg[w]<=1){
				x.pb(w);
				w=par[w];
			}
			for(auto v:x)
				id[v]=vss.size();
			vss.pb(x);
		}
		vvc<int> cur(vss.size());
		
		while(b!=vi(n,1)){
			int v=a[0];
			if(id[v]==-1){
				int to=0;
				rep(i,n)if(!b[i]&&dep[i]>dep[to])
					to=i;
				rotate(to);
			}else{
				auto&w=cur[id[v]];
				int pos=0;
				while(pos<(int)w.size()){
					if(dep[v]>dep[w[pos]])break;
					pos++;
				}
				rotate(vss[id[v]][pos]);
				w.insert(w.bg+pos,v);
			}
		}
		dmp(b);
		
		dmp(vss);
		dmp(cur);
		
		rep(i,vss.size())
			assert(cur[i]==vss[i]);
		
		for(auto vs:vss){
			for(auto v:vs){
				did[v]=1;
				int p=par[v];
				if(p!=-1)
					deg[p]--;
			}
		}
	}
	
	rep(i,n){
		assert(a[i]==i);
	}
	
	print(ans.size());
	for(auto v:ans)
		print(v);
}

### Prompt

Construct a Cpp code solution to the problem outlined:

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

using ll=long long;
#define int ll

#define rng(i,a,b) for(int i=int(a);i<int(b);i++)
#define rep(i,b) rng(i,0,b)
#define gnr(i,a,b) for(int i=int(b)-1;i>=int(a);i--)
#define per(i,b) gnr(i,0,b)
#define pb push_back
#define eb emplace_back
#define a first
#define b second
#define bg begin()
#define ed end()
#define all(x) x.bg,x.ed
#ifdef LOCAL
#define dmp(x) cerr<<__LINE__<<" "<<#x<<" "<<x<<endl
#else
#define dmp(x) void(0)
#endif

template<class t,class u> void chmax(t&a,u b){if(a<b)a=b;}
template<class t,class u> void chmin(t&a,u b){if(b<a)a=b;}

template<class t> using vc=vector<t>;
template<class t> using vvc=vc<vc<t>>;

using pi=pair<int,int>;
using vi=vc<int>;

template<class t,class u>
ostream& operator<<(ostream& os,const pair<t,u>& p){
	return os<<"{"<<p.a<<","<<p.b<<"}";
}

template<class t> ostream& operator<<(ostream& os,const vc<t>& v){
	os<<"{";
	for(auto e:v)os<<e<<",";
	return os<<"}";
}

#define mp make_pair
#define mt make_tuple
#define one(x) memset(x,-1,sizeof(x))
#define zero(x) memset(x,0,sizeof(x))
#ifdef LOCAL
void dmpr(ostream&os){os<<endl;}
template<class T,class... Args>
void dmpr(ostream&os,const T&t,const Args&... args){
	os<<t<<" ";
	dmpr(os,args...);
}
#define dmp2(...) dmpr(cerr,"Line:",__LINE__,##__VA_ARGS__)
#else
#define dmp2(...) void(0)
#endif

using uint=unsigned;
using ull=unsigned long long;

template<int i,class T>
void print_tuple(ostream&,const T&){
}

template<int i,class T,class H,class ...Args>
void print_tuple(ostream&os,const T&t){
	if(i)os<<",";
	os<<get<i>(t);
	print_tuple<i+1,T,Args...>(os,t);
}

template<class ...Args>
ostream& operator<<(ostream&os,const tuple<Args...>&t){
	os<<"{";
	print_tuple<0,tuple<Args...>,Args...>(os,t);
	return os<<"}";
}

void print(ll x,int suc=1){
	cout<<x;
	if(suc==1)
		cout<<"\n";
	if(suc==2)
		cout<<" ";
}

ll read(){
	ll i;
	cin>>i;
	return i;
}

vi readvi(int n,int off=0){
	vi v(n);
	rep(i,n)v[i]=read()+off;
	return v;
}

template<class T>
void print(const vector<T>&v,int suc=1){
	rep(i,v.size())
		print(v[i],i==int(v.size())-1?suc:2);
}

string readString(){
	string s;
	cin>>s;
	return s;
}

template<class T>
T sq(const T& t){
	return t*t;
}

//#define CAPITAL
void yes(bool ex=true){
	#ifdef CAPITAL
	cout<<"YES"<<endl;
	#else
	cout<<"Yes"<<endl;
	#endif
	if(ex)exit(0);
}
void no(bool ex=true){
	#ifdef CAPITAL
	cout<<"NO"<<endl;
	#else
	cout<<"No"<<endl;
	#endif
	if(ex)exit(0);
}

constexpr ll ten(int n){
	return n==0?1:ten(n-1)*10;
}

const ll infLL=LLONG_MAX/3;

#ifdef int
const int inf=infLL;
#else
const int inf=INT_MAX/2-100;
#endif

int topbit(signed t){
	return t==0?-1:31-__builtin_clz(t);
}
int topbit(ll t){
	return t==0?-1:63-__builtin_clzll(t);
}
int botbit(signed a){
	return a==0?32:__builtin_ctz(a);
}
int botbit(ll a){
	return a==0?64:__builtin_ctzll(a);
}
int popcount(signed t){
	return __builtin_popcount(t);
}
int popcount(ll t){
	return __builtin_popcountll(t);
}
bool ispow2(int i){
	return i&&(i&-i)==i;
}
int mask(int i){
	return (int(1)<<i)-1;
}

bool inc(int a,int b,int c){
	return a<=b&&b<=c;
}

template<class t> void mkuni(vc<t>&v){
	sort(all(v));
	v.erase(unique(all(v)),v.ed);
}

ll rand_int(ll l, ll r) { //[l, r]
	#ifdef LOCAL
	static mt19937_64 gen;
	#else
    static random_device rd;
    static mt19937_64 gen(rd());
    #endif
    return uniform_int_distribution<ll>(l, r)(gen);
}

const int nmax=2010;

vi t[nmax];
int dep[nmax];

void dfs(int v,int d){
	dep[v]=d;
	for(auto c:t[v])
		dfs(c,d+1);
}

signed main(){
	cin.tie(0);
	ios::sync_with_stdio(0);
	cout<<fixed<<setprecision(20);
	
	int n;cin>>n;
	bool dbg=n<0;
	if(dbg){
		n=-n;
	}
	vi par(n,-1);
	rng(i,1,n){
		if(!dbg)cin>>par[i];
		else par[i]=rand_int(0,i-1);
		t[par[i]].pb(i);
	}
	dmp(par);
	
	dfs(0,0);
	
	vi a(n);
	if(!dbg)rep(i,n)cin>>a[i];
	else{
		iota(all(a),0);
		rep(i,n)swap(a[rand_int(0,i)],a[i]);
	}
	dmp(a);
	
	vi b(n);
	
	vi ans;
	auto rotate=[&](int i){
		ans.pb(i);
		vi vs;
		while(i>=0){
			vs.pb(i);
			i=par[i];
		}
		reverse(all(vs));
		rep(j,(int)vs.size()-1){
			swap(a[vs[j]],a[vs[j+1]]);
			swap(b[vs[j]],b[vs[j+1]]);
		}
		b[vs.back()]=1;
	};
	
	vi did(n);
	vi deg(n);
	rep(i,n)deg[i]=t[i].size();
	
	while(!did[0]){
		b=did;
		
		vi id(n,-1);
		vvc<int> vss;
		rep(i,n)if(!b[i]&&deg[i]==0){
			vi x;
			int w=i;
			while(w>=0&&deg[w]<=1){
				x.pb(w);
				w=par[w];
			}
			for(auto v:x)
				id[v]=vss.size();
			vss.pb(x);
		}
		vvc<int> cur(vss.size());
		
		while(b!=vi(n,1)){
			int v=a[0];
			if(id[v]==-1){
				int to=0;
				rep(i,n)if(!b[i]&&dep[i]>dep[to])
					to=i;
				rotate(to);
			}else{
				auto&w=cur[id[v]];
				int pos=0;
				while(pos<(int)w.size()){
					if(dep[v]>dep[w[pos]])break;
					pos++;
				}
				rotate(vss[id[v]][pos]);
				w.insert(w.bg+pos,v);
			}
		}
		dmp(b);
		
		dmp(vss);
		dmp(cur);
		
		rep(i,vss.size())
			assert(cur[i]==vss[i]);
		
		for(auto vs:vss){
			for(auto v:vs){
				did[v]=1;
				int p=par[v];
				if(p!=-1)
					deg[p]--;
			}
		}
	}
	
	rep(i,n){
		assert(a[i]==i);
	}
	
	print(ans.size());
	for(auto v:ans)
		print(v);
}

```