##### 2009 Bulgarian Olympiad in Informatics

The frog-mutants in the metropolitan region have lost their mind. After years in the garbage, they are looking for a better life.

The boulevard they are living on is now fully covered with garbage bales. In particular, there are bales, labeled from left to right with the numbers from to , with positive heights .

On each of the bales there is a frog that is very tired and can only make up to jumps. Every jump is to the nearest bale on the right that is strictly higher than the current bale. A frog that can jump over all the bales succeeds in leaving the city - indicated with a height of . Find the maximal height that each frog can reach.

#### Input Specification

On the first line is the number of bales .

On the second line the natural numbers
are given, separated by spaces. The third line contains the natural
numbers , also separated by spaces.

#### Output Specification

Output integers - the maximal height each frog can reach.

#### Sample Input 1

```
8
3 1 4 5 6 2 3 8
1 2 1 3 4 2 1 2
```

#### Sample Output 1

`4 5 5 -1 -1 8 8 -1`

#### Sample Input 2

```
6
7 8 9 1 2 3
2 2 2 2 2 2
```

#### Sample Output 2

`9 -1 -1 3 -1 -1`

## Comments

https://dmoj.ca/problem/btoi07p3#comment-13823

This applies here as well.