Eurokod

This year, for the first time, the Eurokod is being held, an international competition in writing beautiful and readable code.

There are $n$ contestants, labeled from $1$ to $n$. Each of them has written one code.

An association of computer scientists evaluates the codes. The association consists of a president and members. The president and the members award points in different ways.

President's points: The president ranks the codes from the most beautiful to the least beautiful. The first code receives $n$ points, and each following code receives one point less than the previous one.

Members' points: Each member votes for the code he considers the most beautiful. After all votes are cast, the codes are ranked in descending order of votes. The first code receives $n$ points, and each following code receives one point less than the previous one.

Total points: The total for each code is the sum of the points from the president and the points from the members.

Print the codes in descending order of total points. If codes have the same total, the code that received more points from the members is ranked higher.

The first line contains an integer $n$ ($1 \le n \le 50$), the number of contestants.

The second line contains $n$ integers $a_i$ ($1 \le a_i \le n$). The $i$-th integer is the label of the code that the president ranked $i$-th, from the most beautiful to the least beautiful. Every label from $1$ to $n$ appears exactly once.

The third line contains $n$ integers $b_i$ ($0 \le b_i \le 200$). The $i$-th integer is the number of votes that code $i$ received from the members. No two codes receive the same number of votes.

Print $n$ lines with the ranking in descending order of total points. Each line has the form [rank]. Kod[label] ([number of points]). The label is written with two digits and a leading zero when needed. For example, if code 3 is first with 12 points, the first line is 1. Kod03 (12).

In the first example, Kod03 and Kod02 both have 3 points, but Kod03 received more votes from the members, so it is ranked higher.

In the second example, the president ranked Kod05 first, so it received $n = 5$ points.