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 v 1 , v 2 , ..., v k ( k ≥ 1 ) and meet the following conditions: Objects with numbers v 1 , v 2 , ..., v k - 1 are mountains and the object with number v k is the hotel. For any integer i (1 ≤ i < k ) , there is exactly one ski track leading from object v i . This track goes to object v i + 1 . The path contains as many objects as possible ( k is maximal). Help Valera. Find such path that meets all the criteria of our hero! The first line contains integer n ( 1 ≤ n ≤ 10 5 ) — the number of objects. The second line contains n space-separated integers type 1 , type 2 , ..., type n — the types of the objects. If type i equals zero, then the i -th object is the mountain. If type i 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 a 1 , a 2 , ..., a n ( 0 ≤ a i ≤ n ) — the description of the ski tracks. If number a i equals zero, then there is no such object v , that has a ski track built from v to i . If number a i doesn't equal zero, that means that there is a track built from object a i to object i . In the first line print k — the maximum possible path length for Val