###### Description

You are running a multi-level marketing where you and the people in your network are pyramid selling toothbrushes. If someone in the network sells a toothbrush, the profit gets distributed to the people in this network. After some sales, you want to figure out which people in your network earned how much profit. Suppose that your multi-level marketing network is as follows:

`center`

is you, and other blue rectangles indicate eight other workers in your network. This pyramid structure is a chain of referrals. The compensation rule is simple: Every salesperson distributes 10% of the sales profit to her recruiter and takes the rest of the sales profit. This is to say that every salesperson not only gets compensated for selling toothbrushes but also takes 10% of the profit that each person that she has recruited makes. If someone else has recruited that salesperson, then 10% of the profit that that salesperson makes goes to that recruiter. When calculating 10% of the profit, round down to the nearest dollar. If it is smaller than 1 dollar, you take all of it instead of distributing it.

Suppose that the sales history is as follows, where the profit for selling one toothbrush is 100 dollars:

Salesperson | Sales amount | Profit |
---|---|---|

young | 12 | 1,200 dollars |

john | 4 | 400 dollars |

tod | 2 | 200 dollars |

emily | 5 | 500 dollars |

mary | 10 | 1,000 dollars |

Salesperson `young`

has made a profit of 1,200 dollars. `young`

gives the 120 dollars—the 10% commission—to her recruiter, `edward`

, and keeps 1,080 dollars for herself. `edward`

gives `mary`

, his recruiter, 12 dollars—the 10% commission of the 120 dollars he had received from `young`

—and keeps 108 dollars for himself. `mary`

gives 1 dollar—the 10% of 12 dollars that she had received from `edward`

—to you, `center`

, and keeps 11 dollars for herself. All of this can be illustrated as follows:

`john`

also made 400 dollars of profit. `john`

gives 40 dollars—the 10% commission—to `center`

and keeps the rest—360 dollars. This can be illustrated as follows:

Another salesperson, `tod`

, has also made 200 dollars of profit. `tod`

keeps 180 dollars for himself and pays his recruiter `jaimie`

the 10% commission. `jaime`

receives 20 dollars from `tod`

, from which she keeps 18 dollars for herself and pays `mary`

two dollars for the 10% commission. Since the 10% of two dollars rounded down to the nearest dollar is 0, mary can keep the two dollars to herself. This can be illustrated as follows:

`emily`

has made 500 dollars of profit. According to the compensation rule, she gets to keep 450 dollars, `mary`

45 dollars, and `center`

5 dollars from it. This can be illustrated as follows:

Lastly, `mary`

has made 1,000 dollars of profit. She gets to keep 900 dollars from it and pays `center`

100 dollars. This can be illustrated as follows:

And here is the final result:

This is the result that you wanted to find out.

Suppose parameters `enroll`

, `referral`

, `seller`

, and `amount`

are given, where `enroll`

is an array containing names of the salespersons, `referral`

an array containing names of recruiters that have recruited other salespersons, `seller`

an array containing names of salespersons in the sales history, and `amount`

an array containing the sales history. Please write a function `solution`

that returns an array containing the total amount of compensation that each salesperson has received. Sort them (in integers) by the order in which the names are listed in `enroll`

.

##### Constraints

- The length of
`enroll`

is between 1 and 10,000.- Your name won't be in found
`enroll`

. Therefore, the length of`enroll`

is equal to the total number of people in your marketing network except you.

- Your name won't be in found
- The length of
`referral`

is equal to that of`enroll`

.- The
`i`

th name in`referral`

is the name of the person who recruited the`i`

th salesperson in`enroll`

. - For those who have been recruited by you, their recruiter name will be displayed as
`“-“`

in`referral`

. In the example above, such is the case for`john`

and`mary`

. - The names contained in
`enroll`

are sorted by the order they joined the network. - For example, if someone's name is the
`i`

th element of`enroll`

, then her recruiter—the`i`

th element of`referral`

—will be the`j`

th element of`enroll`

.

- The
- The length of
`seller`

is between 1 and 100,000.- The
`i`

th name in`seller`

indicates that this person has made the`i`

th entry in the sale history. - There can be overlapping names in
`seller`

.

- The
- The length of
`amount`

is equal to that of`seller`

.- The ith number in
`amount`

means the sales amount of the`i`

th entry in the sale history. - The elements of
`amount`

—the range of sales amount—are natural numbers between 1 and 100.

- The ith number in
- Each salesperson will make 100 dollars of profit for selling one toothbrush.
- Everyone's name is made up of less than 10 lowercase letters.

##### Examples

enroll | referral | seller | amount | result |
---|---|---|---|---|

`["john", "mary", "edward", "sam", "emily", "jaimie", "tod", "young"]` |
`["-", "-", "mary", "edward", "mary", "mary", "jaimie", "edward"]` |
`["young", "john", "tod", "emily", "mary"]` |
[12, 4, 2, 5, 10] | [360, 958, 108, 0, 450, 18, 180, 1080] |

`["john", "mary", "edward", "sam", "emily", "jaimie", "tod", "young"]` |
`["-", "-", "mary", "edward", "mary", "mary", "jaimie", "edward"]` |
`["sam", "emily", "jaimie", "edward"]` |
[2, 3, 5, 4] | [0, 110, 378, 180, 270, 450, 0, 0] |

Example #1

Demonstrated in the prompt above.

Example #2

Things have been slightly altered from Example 1. Since the compensation rules are the same, you can do a simple calculation to come up with the result shown in the table.

베타 기간 동안에는 한 문제당 1번만 물어볼 수 있어요.