/*{{{*/
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<cmath>
#include<algorithm>
#include<string>
#include<iostream>
#include<sstream>
#include<set>
#include<map>
#include<queue>
#include<bitset>
#include<vector>
#include<limits.h>
#include<assert.h>
#define SZ(X) ((int)(X).size())
#define ALL(X) (X).begin(), (X).end()
#define REP(I, N) for (int I = 0; I < (N); ++I)
#define REPP(I, A, B) for (int I = (A); I < (B); ++I)
#define FOR(I, A, B) for (int I = (A); I <= (B); ++I)
#define FORS(I, S) for (int I = 0; S[I]; ++I)
#define RS(X) scanf("%s", (X))
#define SORT_UNIQUE(c) (sort(c.begin(),c.end()), c.resize(distance(c.begin(),unique(c.begin(),c.end()))))
#define GET_POS(c,x) (lower_bound(c.begin(),c.end(),x)-c.begin())
#define CASET int ___T; scanf("%d", &___T); for(int cs=1;cs<=___T;cs++)
#define MP make_pair
#define PB push_back
#define MS0(X) memset((X), 0, sizeof((X)))
#define MS1(X) memset((X), -1, sizeof((X)))
#define LEN(X) strlen(X)
#define F first
#define S second
using namespace std;
typedef int64_t LL;
typedef uint64_t ULL;
typedef long double LD;
typedef pair<int,int> PII;
typedef vector<int> VI;
typedef vector<LL> VL;
typedef vector<PII> VPII;
typedef pair<LL,LL> PLL;
typedef vector<PLL> VPLL;
template<class T> void _R(T &x) { cin >> x; }
void _R(int &x) { scanf("%d", &x); }
void _R(int64_t &x) { scanf("%lld", &x); }
void _R(double &x) { scanf("%lf", &x); }
void _R(char &x) { scanf(" %c", &x); }
void _R(char *x) { scanf("%s", x); }
void R() {}
template<class T, class... U> void R(T &head, U &... tail) { _R(head); R(tail...); }
template<class T> void _W(const T &x) { cout << x; }
void _W(const int &x) { printf("%d", x); }
void _W(const int64_t &x) { printf("%lld", x); }
void _W(const double &x) { printf("%.16f", x); }
void _W(const char &x) { putchar(x); }
void _W(const char *x) { printf("%s", x); }
template<class T,class U> void _W(const pair<T,U> &x) {_W(x.F); putchar(' '); _W(x.S);}
template<class T> void _W(const vector<T> &x) { for (auto i = x.begin(); i != x.end(); _W(*i++)) if (i != x.cbegin()) putchar(' '); }
void W() {}
template<class T, class... U> void W(const T &head, const U &... tail) { _W(head); putchar(sizeof...(tail) ? ' ' : '\n'); W(tail...); }
template<class T, class... U> void DEBUG(const T &head, const U &... tail) { 
#ifdef HOME
    _W('#'); _W(head); putchar(sizeof...(tail) ? ' ' : '\n'); W(tail...);
#endif
}
int MOD = 1e9+7;
void ADD(LL& x,LL v){x=(x+v)%MOD;if(x<0)x+=MOD;}
/*}}}*/
const int SIZE = 2018;
int deg[SIZE];
int p[SIZE];
int h[SIZE];
VI e[SIZE];
int a[SIZE];
int N;
VI ans;
int good[SIZE];
bool game_over(){
    REP(i,N)
        if(a[i]!=i)return 0;
    return 1;
}
int bottom[SIZE],choose[SIZE],num;
void find_important_vertice(int top){
    int x=top;
    while(x!=-1&&deg[x]<=1){
        num++;
        bottom[x]=top;
        x=p[x];
    }
}
void push(int x){
    ans.PB(x);
    int now=a[0];
    while(x!=-1){
        swap(now,a[x]);
        x=p[x];
    }
}
int bfs[SIZE],cnt[SIZE];
int greedy_choose(){
    bfs[0]=0;
    int rr=1;
    int ma=0,id=-1;
    REP(i,rr){
        int x=bfs[i];
        REP(j,SZ(e[x])){
            int y=e[x][j];
            if(good[a[y]])continue;
            bfs[rr++]=y;
            cnt[y]=cnt[x]+(bottom[a[y]]!=-1);
            if(cnt[y]>ma){
                ma=cnt[y];
                id=y;
            }
        }
    }
    return id;
}
int main(){
    p[0]=-1;
    R(N);
    REPP(i,1,N){
        R(p[i]);
        deg[p[i]]++;
        h[i]=h[p[i]]+1;
        e[p[i]].PB(i);
    }
    REP(i,N)R(a[i]);
    while(!game_over()){
        num=0;
        MS1(bottom);
        REP(i,N){
            if(!good[i]&&deg[i]==0){
                find_important_vertice(i);
            }
        }
        while(num>0){
            int me=a[0];
            if(bottom[me]!=-1){
                num--;
                good[me]=1;
                deg[p[me]]--;
                int x=bottom[me];
                while(good[a[x]]&&h[a[x]]>h[me])x=p[x];
                push(x);
            }
            else{
                push(greedy_choose());
            }
        }
    }
    W(SZ(ans));
    for(int x:ans)W(x);
    return 0;
}

### Prompt

In CPP, your task is to solve 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<cstdio>
#include<cstdlib>
#include<cstring>
#include<cmath>
#include<algorithm>
#include<string>
#include<iostream>
#include<sstream>
#include<set>
#include<map>
#include<queue>
#include<bitset>
#include<vector>
#include<limits.h>
#include<assert.h>
#define SZ(X) ((int)(X).size())
#define ALL(X) (X).begin(), (X).end()
#define REP(I, N) for (int I = 0; I < (N); ++I)
#define REPP(I, A, B) for (int I = (A); I < (B); ++I)
#define FOR(I, A, B) for (int I = (A); I <= (B); ++I)
#define FORS(I, S) for (int I = 0; S[I]; ++I)
#define RS(X) scanf("%s", (X))
#define SORT_UNIQUE(c) (sort(c.begin(),c.end()), c.resize(distance(c.begin(),unique(c.begin(),c.end()))))
#define GET_POS(c,x) (lower_bound(c.begin(),c.end(),x)-c.begin())
#define CASET int ___T; scanf("%d", &___T); for(int cs=1;cs<=___T;cs++)
#define MP make_pair
#define PB push_back
#define MS0(X) memset((X), 0, sizeof((X)))
#define MS1(X) memset((X), -1, sizeof((X)))
#define LEN(X) strlen(X)
#define F first
#define S second
using namespace std;
typedef int64_t LL;
typedef uint64_t ULL;
typedef long double LD;
typedef pair<int,int> PII;
typedef vector<int> VI;
typedef vector<LL> VL;
typedef vector<PII> VPII;
typedef pair<LL,LL> PLL;
typedef vector<PLL> VPLL;
template<class T> void _R(T &x) { cin >> x; }
void _R(int &x) { scanf("%d", &x); }
void _R(int64_t &x) { scanf("%lld", &x); }
void _R(double &x) { scanf("%lf", &x); }
void _R(char &x) { scanf(" %c", &x); }
void _R(char *x) { scanf("%s", x); }
void R() {}
template<class T, class... U> void R(T &head, U &... tail) { _R(head); R(tail...); }
template<class T> void _W(const T &x) { cout << x; }
void _W(const int &x) { printf("%d", x); }
void _W(const int64_t &x) { printf("%lld", x); }
void _W(const double &x) { printf("%.16f", x); }
void _W(const char &x) { putchar(x); }
void _W(const char *x) { printf("%s", x); }
template<class T,class U> void _W(const pair<T,U> &x) {_W(x.F); putchar(' '); _W(x.S);}
template<class T> void _W(const vector<T> &x) { for (auto i = x.begin(); i != x.end(); _W(*i++)) if (i != x.cbegin()) putchar(' '); }
void W() {}
template<class T, class... U> void W(const T &head, const U &... tail) { _W(head); putchar(sizeof...(tail) ? ' ' : '\n'); W(tail...); }
template<class T, class... U> void DEBUG(const T &head, const U &... tail) { 
#ifdef HOME
    _W('#'); _W(head); putchar(sizeof...(tail) ? ' ' : '\n'); W(tail...);
#endif
}
int MOD = 1e9+7;
void ADD(LL& x,LL v){x=(x+v)%MOD;if(x<0)x+=MOD;}
/*}}}*/
const int SIZE = 2018;
int deg[SIZE];
int p[SIZE];
int h[SIZE];
VI e[SIZE];
int a[SIZE];
int N;
VI ans;
int good[SIZE];
bool game_over(){
    REP(i,N)
        if(a[i]!=i)return 0;
    return 1;
}
int bottom[SIZE],choose[SIZE],num;
void find_important_vertice(int top){
    int x=top;
    while(x!=-1&&deg[x]<=1){
        num++;
        bottom[x]=top;
        x=p[x];
    }
}
void push(int x){
    ans.PB(x);
    int now=a[0];
    while(x!=-1){
        swap(now,a[x]);
        x=p[x];
    }
}
int bfs[SIZE],cnt[SIZE];
int greedy_choose(){
    bfs[0]=0;
    int rr=1;
    int ma=0,id=-1;
    REP(i,rr){
        int x=bfs[i];
        REP(j,SZ(e[x])){
            int y=e[x][j];
            if(good[a[y]])continue;
            bfs[rr++]=y;
            cnt[y]=cnt[x]+(bottom[a[y]]!=-1);
            if(cnt[y]>ma){
                ma=cnt[y];
                id=y;
            }
        }
    }
    return id;
}
int main(){
    p[0]=-1;
    R(N);
    REPP(i,1,N){
        R(p[i]);
        deg[p[i]]++;
        h[i]=h[p[i]]+1;
        e[p[i]].PB(i);
    }
    REP(i,N)R(a[i]);
    while(!game_over()){
        num=0;
        MS1(bottom);
        REP(i,N){
            if(!good[i]&&deg[i]==0){
                find_important_vertice(i);
            }
        }
        while(num>0){
            int me=a[0];
            if(bottom[me]!=-1){
                num--;
                good[me]=1;
                deg[p[me]]--;
                int x=bottom[me];
                while(good[a[x]]&&h[a[x]]>h[me])x=p[x];
                push(x);
            }
            else{
                push(greedy_choose());
            }
        }
    }
    W(SZ(ans));
    for(int x:ans)W(x);
    return 0;
}

```