350_B. Resort
Valera's finally decided to go on holiday! He packed up and headed for a ski resort.

Valera's fancied a ski trip but he soon realized that he could get lost in this new place. Somebody gave him a useful hint: the resort has n objects (we will consider the objects indexed in some way by integers from 1 to n), each object is either a hotel or a mountain.

Valera has also found out that the ski resort had multiple ski tracks. Specifically, for each object v, the resort has at most one object u, such that there is a ski track built from object u to object v. We also know that no hotel has got a ski track leading from the hotel to some object.

Valera is afraid of getting lost on the resort. So he wants you to come up with a path he would walk along. The path must consist of objects v1, v2, ..., vk (k ≥ 1) and meet the following conditions:

  1. Objects with numbers v1, v2, ..., vk - 1 are mountains and the object with number vk is the hotel. 
  2. For any integer i (1 ≤ i < k), there is exactly one ski track leading from object vi. This track goes to object vi + 1. 
  3. The path contains as many objects as possible (k is maximal). 



Help Valera. Find such path that meets all the criteria of our hero!

Input

The first line contains integer n (1 ≤ n ≤ 105) — the number of objects.

The second line contains n space-separated integers type1, type2, ..., typen — the types of the objects. If typei equals zero, then the i-th object is the mountain. If typei equals one, then the i-th object is the hotel. It is guaranteed that at least one object is a hotel.

The third line of the input contains n space-separated integers a1, a2, ..., an (0 ≤ ai ≤ n) — the description of the ski tracks. If number ai equals zero, then there is no such object v, that has a ski track built from v to i. If number ai doesn't equal zero, that means that there is a track built from object ai to object i.

Output

In the first line print k — the maximum possible path length for Valera. In the second line print k integers v1, v2, ..., vk — the path. If there are multiple solutions, you can print any of them.

Examples

Input

5
0 0 0 0 1
0 1 2 3 4


Output

5
1 2 3 4 5


Input

5
0 0 1 0 1
0 1 2 2 4


Output

2
4 5


Input

4
1 0 0 0
2 3 4 2


Output

1
1
```python
import sys
def Z(s):
    return int(s)-1

n=int(sys.stdin.readline())

Hotels=[False]*(n)

Rep=[0]*(n+1)
Chains=[]

Type=list(map(int,sys.stdin.readline().split()))
for i in range(n):
    if(Type[i]==1):
        Hotels[i]=True
A=list(map(Z,sys.stdin.readline().split()))

for item in A:
    Rep[item]+=1
for i in range(n):
    if(Hotels[i]):
        Chains.append([i])
        x=A[i]
        if(x==-1):
            continue
        while(A[x]!=-1 and Rep[x]<=1):
            Chains[-1].append(x)
            x=A[x]
        if(Rep[x]<=1):
            Chains[-1].append(x)


    
        
if(n==1):
    print(1)
    print(1)
else:
        
    X=max(Chains,key=len)



    sys.stdout.write(str(len(X))+"\n")
    sys.stdout.write(str(X[-1]+1))

    for i in range(len(X)-2,-1,-1):
        sys.stdout.write(" "+str(X[i]+1))       
        

```