After his leave from DMOJ, Wesley is very angry and demands you to construct an array of length consisting of **positive** integers such that each element satisfies the following requirements:

- There are elements before index that are strictly smaller than
- There are elements after index that are strictly smaller than
- There are elements before index that are strictly greater than
- There are elements after index that are strictly greater than

Luckily, Wesley is a kind person and will allow for your array to violate **at most** of the requirements above. In particular, you can pick an index and modify exactly one of , , and . In exchange however, he requests that your array is the lexicographically least one (it must be the lexicographically least array that violates at most requirement).

Note: We say that array is lexicographically less than array if and at the smallest index where and differ, .

#### Constraints

##### Subtask 1 [12%]

##### Subtask 2 [23%]

##### Subtask 3 [43%]

##### Subtask 4 [22%]

No additional constraints.

#### Input Specification

The first line contains a single integer .

The next line contains integers .

The next line contains integers .

The next line contains integers .

The next line contains integers .

#### Output Specification

If no such array exists, output `-1`

.

Otherwise, output the elements of the lexicographically least array on a single line.

#### Sample Input

```
5
0 0 2 2 1
1 0 2 1 0
0 1 0 1 2
2 1 0 0 0
```

#### Sample Output

`2 1 4 3 2`

#### Explanation for Sample

The array above satisfies all the requirements except for . It can be shown that this is the lexicographically least array that violates at most one requirement.

## Comments

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