## Friend

We build a social network from n people numbered 0, …, n − 1. Some pairs of people in the network will be friends. If person x becomes a friend of person y, then person y also becomes a friend of person x.

The people are added to the network in n stages, which are also numbered from 0 to n − 1. Person i is added in stage i. In stage 0, person 0 is added as the only person of the network. In each of the next n − 1 stages, a person is added to the network by a host, who may be any person already in the network. At stage i (0 < i < n), the host for that stage can add the incoming person i into the network by one of the following three protocols:

• IAmYourFriend makes person i a friend of the host only.
• MyFriendsAreYourFriends makes person i a friend of each person, who is a friend of the host at this moment. Note that this protocol does not make person i a friend of the host.
• WeAreYourFriends makes person i a friend of the host, and also a friend of each person, who is a friend of the host at this moment.

After we build the network we would like to pick a sample for a survey, that is, choose a group of people from the network. Since friends usually have similar interests, the sample should not include any pair of people who are friends with each other. Each person has a survey confidence, expressed as a positive integer, and we would like to find a sample with the maximum total confidence.

### Example

10IAmYourFriend(1, 0)
20MyFriendsAreYourFriends(2, 1)
31WeAreYourFriend(3, 1), (3, 0), (3, 2)
42MyFriendsAreYourFriends(4, 1), (4, 3)
50IAmYourFriend(5, 0)

Initially the network contains only person 0. The host of stage 1 (person 0) invites the new person 1 through the IAmYourFriend protocol, hence they become friends. The host of stage 2 (person 0 again) invites person 2 by MyFriendsAreYourFriends, which makes person 1 (the only friend of the host) the only friend of person 2. The host of stage 3 (person 1) adds person 3 through WeAreYourFriends, which makes person 3 a friend of person 1 (the host) and people 0 and 2 (the friends of the host). Stages 4 and 5 are also shown in the table above. The final network is shown in the following figure, in which the numbers inside the circles show the labels of people, and the numbers next to the circles show the survey confidence. The sample consisting of people 3 and 5 has totalsurvey confidence equal to 20 + 15 = 35, which is the maximum possible total confidence.

Given the description of each stage and the confidence value of each person, find a sample with the maximum total confidence.

### Input Format

Line 1: n, the number of people
Line 2: `confidence[0]`, …, `confidence[n-1]`
Line 3: `host[1]`, `protocol[1]`, `host[2]`, `protocol[2]`, …, `host[n-1]`, `protocol[n-1]`.

• `confidence`: array of length n; `confidence[i]` gives the confidence value of person i.
• `host`: array of length n; `host[i]` gives the host of stage i.
• `protocol`: array of length n; `protocol[i]` gives the protocol code used in stage i (0 < i < n): 0 for IAmYourFriend, 1 for MyFriendsAreYourFriends, and 2 for WeAreYourFriends.
• Since there is no host in stage 0, `host[0]` and `protocol[0]` are undefined and will not be part of the input

### Output Format

The output should consist of one line containing one value, the maximum possible total confidence of a sample.

### Sample Input 1

```6
13 3 6 20 10 15
0 0 0 1 1 2 2 1 0 0
```

`35`

```2
10 20
0 1
```

`30`

```2
10 20
0 2
```

`20`

```2
10 20
0 0
```

`20`

```3
1 1 1
0 0 0 1
```

`2`

### Sample Input 6

```6
13 3 6 20 10 15
0 0 0 1 1 2 2 1 0 0
```

### Sample Output 6

`35`

subtask% of pointsn`confidence`protocols used
1112 ≤ n ≤ 101 ≤ `confidence` ≤ 1,000,000All three protocols
282 ≤ n ≤ 1,0001 ≤ `confidence` ≤ 1,000,000Only MyFriendsAreYourFriends
382 ≤ n ≤ 1,0001 ≤ `confidence` ≤ 1,000,000Only WeAreYourFriends
4192 ≤ n ≤ 1,0001 ≤ `confidence` ≤ 1,000,000Only IAmYourFriend
5232 ≤ n ≤ 1,000All `confidence` values are 1Both MyFriendsAreYourFriends and IAmYourFriend
6312 ≤ n ≤ 100,0001 ≤ `confidence` ≤ 10,000All three protocols

Point Value: 25 (partial)
Time Limit: 1.00s
Memory Limit: 16M